# The Best Textbooks on Every Subject

For years, my self-education was stupid and wasteful. I learned by consuming blog posts, Wikipedia articles, classic texts, podcast episodes, popular books, video lectures, peer-reviewed papers, Teaching Company courses, and Cliff's Notes. How inefficient!

I've since discovered that *textbooks* are usually the quickest and best way to learn new material. That's what they are *designed* to be, after all. Less Wrong has often recommended the "read textbooks!" method. Make progress by accumulation, not random walks.

But textbooks vary widely in quality. I was forced to read some awful textbooks in college. The ones on American history and sociology were memorably bad, in my case. Other textbooks are exciting, accurate, fair, well-paced, and immediately useful.

What if we could compile a list of the best textbooks on every subject? That would be *extremely* useful.

Let's do it.

There have been other pages of recommended reading on Less Wrong before (and elsewhere), but this post is unique. Here are **the rules**:

- Post the title of your favorite textbook on a given subject.
- You must have read at least two other textbooks on that same subject.
- You must briefly name the other books you've read on the subject and explain why you think your chosen textbook is superior to them.

Rules #2 and #3 are to protect against recommending a bad book that only seems impressive because it's the only book you've read on the subject. Once, a popular author on Less Wrong recommended Bertrand Russell's *A History of Western Philosophy* to me, but when I noted that it was more polemical and inaccurate than the other major histories of philosophy, he admitted he hadn't really done much other reading in the field, and only liked the book because it was exciting.

I'll start the list with three of my own recommendations...

**Subject**: History of Western Philosophy

**Recommendation**: *The Great Conversation*, 6th edition, by Norman Melchert

**Reason**: The most popular history of western philosophy is Bertrand Russell's *A History of Western Philosophy*, which is exciting but also polemical and inaccurate. More accurate but dry and dull is Frederick Copelston's 11-volume *A History of Philosophy*. Anthony Kenny's recent 4-volume history, collected into one book as *A New History of Western Philosophy*, is both exciting and accurate, but perhaps too long (1000 pages) and technical for a first read on the history of philosophy. Melchert's textbook, *The Great Conversation*, is accurate but also the easiest to read, and has the clearest explanations of the important positions and debates, though of course it has its weaknesses (it spends too many pages on ancient Greek mythology but barely mentions Gottlob Frege, the father of analytic philosophy and of the philosophy of language). Melchert's history is also the only one to seriously cover the dominant mode of Anglophone philosophy done today: naturalism (what Melchert calls "physical realism"). Be sure to get the 6th edition, which has major improvements over the 5th edition.

**Recommendation**: *Cognitive Science*, by Jose Luis Bermudez

**Reason**: Jose Luis Bermudez's *Cognitive Science: An Introduction to the Science of Mind* does an excellent job setting the historical and conceptual context for cognitive science, and draws fairly from all the fields involved in this heavily interdisciplinary science. Bermudez does a good job of making himself invisible, and the explanations here are some of the clearest available. In contrast, Paul Thagard's *Mind: Introduction to Cognitive Science* skips the context and jumps right into a systematic comparison (by explanatory merit) of the leading theories of mental representation: logic, rules, concepts, analogies, images, and neural networks. The book is only 270 pages long, and is also more idiosyncratic than Bermudez's; for example, Thagard refers to the dominant paradigm in cognitive science as the "computational-representational understanding of mind," which as far as I can tell is used only by him and people drawing from his book. In truth, the term refers to a set of competing theories, for example the computational theory and the representational theory. While not the best place to start, Thagard's book is a decent follow-up to Bermudez's text. Better, though, is Kolak et. al.'s *Cognitive Science: An Introduction to Mind and Brain*. It contains more information than Bermudez's book, but I prefer Bermudez's flow, organization and content selection. Really, though, both Bermudez and Kolak offer excellent introductions to the field, and Thagard offers a more systematic and narrow investigation that is worth reading after Bermudez and Kolak.

**Subject**: Introductory Logic for Philosophy

**Recommendation**: *Meaning and Argument* by Ernest Lepore

**Reason**: For years, the standard textbook on logic was Copi's *Introduction to Logic*, a comprehensive textbook that has chapters on language, definitions, fallacies, deduction, induction, syllogistic logic, symbolic logic, inference, and probability. It spends too much time on methods that are rarely used today, for example Mill's methods of inductive inference. Amazingly, the chapter on probability does not mention Bayes (as of the 11th edition, anyway). Better is the current standard in classrooms: Patrick Hurley's *A Concise Introduction to Logic.* It has a table at the front of the book that tells you which sections to read depending on whether you want (1) a traditional logic course, (2) a critical reasoning course, or (3) a course on modern formal logic. The single chapter on induction and probability moves too quickly, but is excellent for its length. Peter Smith's An Introduction to Formal Logic instead focuses tightly on the usual methods used by today's philosophers: propositional logic and predicate logic. My favorite in this less comprehensive mode, however, is Ernest Lepore's *Meaning and Argument*, because it (a) is highly efficient, and (b) focuses not so much on the manipulation of symbols in a formal system but on the arguably trickier matter of translating English sentences into symbols in a formal system in the first place.

I would love to read recommendations from experienced readers on the following subjects: physics, chemistry, biology, psychology, sociology, probability theory, economics, statistics, calculus, decision theory, cognitive biases, artificial intelligence, neuroscience, molecular biochemistry, medicine, epistemology, philosophy of science, meta-ethics, and much more.

Please, post your own recommendations! And, follow the rules.

**Recommendations so far** (that follow the rules; this list updated 04-14-2015):

- On
**history of western philosophy**, lukeprog recommends Melchert's*The Great Conversation*over Russell's*A History of Western Philosophy*, Copelston's*History of Philosophy*, and Kenney's*A New History of Western Philosophy*. - On
**cognitive science**, lukeprog recommends Bermudez's*Cognitive Science*over Thagard's*Mind: Introduction to Cognitive Science*and Kolak's*Cognitive Science*. - On
**introductory logic for philosophy**, lukeprog recommends Lepore's*Meaning and Argument*over Copi's*Introduction to Logic*, Hurley's*A Concise Introduction to Logic*, and Smith's*An Introduction to Formal Logic*. - On
**economics**, michaba03m recommends Mankiw's*Macroeconomics*over Varian's*Intermediate Microeconomics*and Katz & Rosen's*Macroeconomics*. - On
**economics**, realitygrill recommends McAfee's*Introduction to Economic Analysis*over Mankiw's*Macroeconomics*and Case & Fair's*Principles of Macroeconomics*. - On
**representation theory**, SarahC recommends Sternberg's*Group Theory and Physics*over Lang's*Algebra*, Weyl's*The Theory of Groups and Quantum Mechanics*, and Fulton & Harris'*Representation Theory: A First Course*. - On
**statistics**, madhadron recommends Kiefer's*Introduction to Statistical Inference*over Hogg & Craig's*Introduction to Mathematical Statistics*, Casella & Berger's*Statistical Inference*, and others. - On
**advanced Bayesian statistics**, Cyan recommends Gelman's*Bayesian Data Analysis*over Jaynes'*Probability Theory: The Logic of Science*and Bernardo's*Bayesian Theory*. - On
**basic Bayesian statistics**, jsalvatier recommends Skilling & Sivia's*Data Analysis: A Bayesian Tutorial*over Gelman's*Bayesian Data Analysis*, Bolstad's*Bayesian Statistics*, and Robert's*The Bayesian Choice*. - On
**real analysis**, paper-machine recommends Bartle's A Modern Theory of Integration over Rudin's*Real and Complex Analysis*and Royden's*Real Analysis*. - On
**non-relativistic quantum mechanics**, wbcurry recommends Sakurai & Napolitano's*Modern Quantum Mechanics*over Messiah's*Quantum Mechanics*, Cohen-Tannoudji's*Quantum Mechanics*, and Greiner's*Quantum Mechanics: An Introduction*. - On
**music theory**, komponisto recommends Westergaard's*An Introduction to Tonal Theory*over Piston's*Harmony*, Aldwell and Schachter's*Harmony and Voice Leading*, and Kotska and Payne's*Tonal Harmony*. - On
**business**, joshkaufman recommends Kaufman's*The Personal MBA: Master the Art of Business*over Bevelin's*Seeking Wisdom*and Munger's*Poor Charlie's Alamanack*. - On
**machine learning**, alexflint recommends Bishop's*Pattern Recognition and Machine Learning*over Russell & Norvig's*Artificial Intelligence: A Modern Approach*and Thrun et. al.'s*Probabilistic Robotics*. - On
**algorithms**, gjm recommends Cormen et. al.'s*Introduction to Algorithms*over Knuth's*The Art of Computer Programming*and Sedgwick's*Algorithms*. - On
**electrodynamics**, Alex_Altair recommends Griffiths'*Introduction to Electrodynamics*over Jackson's*Electrodynamics*and Feynman's*Lectures on Physics*. - On
**electrodynamics**, madhadron recommends Purcell's*Electricity and Magnetism*over Griffith's*Introduction to Electrodynamics*, Feynman's*Lectures on Physics*, and others. - On
**systems theory**, Davidmanheim recommends Meadows'*Thinking in Systems: A Primer*over Senge's*The Fifth Discipline: The Art & Practice of The Learning Organization*and Kim's*Introduction to Systems Thinking*. - On
**self-help**, lukeprog recommends Weiten, Dunn, and Hammer's*Psychology Applied to Modern Life*over Santrock's*Human Adjustment*and Tucker-Ladd's*Psychological Self-Help*. - On
**probability theory**, SarahC recommends Feller's*An Introduction to Probability Theory*+*Vol. 2*over Ross'*A First Course in Probability*and Koralov & Sinai's*Theory of Probability and Random Processes*. - On
**probability theory**, madhadron recommends Grimmett & Stirzaker's*Probability and Random Processes*over Feller's*Introduction to Probability Theory and Its Applications*and Nelson's*Radically Elementary Probability Theory*. - On
**topology**, jsteinhardt recommends Munkres'*Topology*over Armstrong's*Topology*and Massey's*Algebraic Topology*. - On
**linguistics**, etymologik recommends O'Grady et al.'s*Contemporary Linguistics*over Hayes et al.'s*Linguistics: An Introduction to Linguistic Theory*and Carnie's*Syntax: A Generative Introduction*. - On
**meta-ethics**, lukeprog recommends Miller's*An Introduction to Contemporary Metaethics*over Jacobs'*The Dimensions of Moral Theory*and Smith's*Ethics and the A Priori*. - On
**decision-making & biases**, badger recommends Bazerman & Moore's*Judgment in Managerial Decision Making*over Hastie & Dawes'*Rational Choice in an Uncertain World*, Gilboa's*Making Better Decisions*, and others. - On
**neuroscience**, kjmiller recommends Bear et al's*Neuroscience: Exploring the Brain*over Purves et al's*Neuroscience*and Kandel et al's*Principles of Neural Science*. - On
**World War II**, Peacewise recommends Weinberg's*A World at Arms*over Churchill's*The Second World War*and Day's*The Politics of War*. - On
**elliptic curves**, magfrump recommends Koblitz'*Introduction to Elliptic Curves and Modular Forms*over Silverman's*Arithmetic of Elliptic Curves*and Cassel's*Lectures on Elliptic Curves*. - On
**improvisation**, Arepo recommends Salinsky & Frances-White's*The Improv Handbook*over Johnstone's*Impro*, Johnston's*The Improvisation Game*, and others. - On
**thermodynamics**, madhadron recommends Hatsopoulos & Keenan's*Principles of General Thermodynamics*over Fermi's*Thermodynamics*, Sommerfeld's*Thermodynamics and Statistical Mechanics*, and others. - On
**statistical mechanics**, madhadron recommends Landau & Lifshitz'*Statistical Physics, Volume 5*over Sethna's*Entropy, Order Parameters, and Complexity*and Reichl's*A Modern Course in Statistical Physics*. - On
**criminal justice**, strange recommends Fuller's*Criminal Justice: Mainstream and Crosscurrents*over Neubauer & Fradella's*America's Courts and the Criminal Justice System*and Albanese'*Criminal Justice*. - On
**organic chemistry**, rhodium recommends Clayden et al's*Organic Chemistry*over McMurry's*Organic Chemistry*and Smith's*Organic Chemistry*. - On
**special relativity**, iDante recommends Taylor & Wheeler's*Spacetime Physics*over Harris'*Modern Physics*, French's*Special Relativity*, and others. - On
**abstract algebra**, Bundle_Gerbe recommends Dummit & Foote's*Abstract Algebra*over Lang's*Algebra*and others. - On
**decision theory**, lukeprog recommends Peterson's*An Introduction to Decision Theory*over Resnik's*Choices*and Luce & Raiffa's*Games and Decisions*. - On
**calculus**, orthonormal recommends Spivak's*Calculus*over Thomas'*Calculus*and Stewart's*Calculus*. - On
**analysis in R**, orthonormal recommends Strichartz's^{n}*The Way of Analysis*over Rudin's*Principles of Mathematical Analysis*and Kolmogorov & Fomin's*Introduction to Real Analysis*. - On
**real analysis and measure theory**, orthonormal recommends Stein & Shakarchi's*Measure Theory, Integration, and Hilbert Spaces*over Royden's*Real Analysis*and Rudin's*Real and Complex Analysis*. - On
**partial differential equations**, orthonormal recommends Strauss'*Partial Differential Equations*over Evans'*Partial Differential Equations*and Hormander's*Analysis of Partial Differential Operators*. - On
**introductory real analysis**, SatvikBeri recommends Pugh's Real Mathematical Analysis over Lang's*Real and Functional Analysis*and Rudin's*Principles of Mathematical Analysis*. - On
**commutative algebra**, SatvikBeri recommends MacDonald's*Introduction to Commutative Algebra*over Lang's*Algebra*and Eisenbud's*Commutative Algebra With a View Towards Algebraic Geometry*. - On
**animal behavior**, Natha recommends Alcock's*Animal Behavior, 6th edition*over Dugatkin's*Principles of Animal Behavior*and newer editions of the Alcock textbook. - On
**calculus**, Epictetus recommends Courant's*Differential and Integral Calculus*over Stewart's*Calculus*and Kline's*Calculus*. - On
**linear algebra**, Epictetus recommends Shilov's*Linear Algebra*over Lay's*Linear Algebra and its Appications*and Axler's*Linear Algebra Done Right*. - On
**numerical methods**, Epictetus recommends Press et al.'s*Numerical Recipes*over Bulirsch & Stoer's*Introduction to Numerical Analysis*, Atkinson's*An Introduction to Numerical Analysis*, and Hamming's*Numerical Methods of Scientists and Engineers*. - On
**ordinary differential equations**, Epictetus recommends Arnold's*Ordinary Differential Equations*over Coddington's*An Introduction to Ordinary Differential Equations*and Enenbaum & Pollard's*Ordinary Differential Equations*. - On
**abstract algebra**, Epictetus recommends Jacobson's*Basic Algebra*over Bourbaki's*Algebra*, Lang's*Algebra*, and Hungerford's*Algebra*. - On
**elementary real analysis**, Epictetus recommends Rudin's*Principles of Mathematical Analysis*over Ross'*Elementary Analysis*, Lang's*Undergraduate Analysis*, and Hardy's*A Course of Pure Mathematics*.

## Comments (312)

Best*19 points [-]Subject: Representation Theory

Recommendation: Group Theory and Physics by Shlomo Sternberg.

This is a remarkable book pedagogically. It is the most extremely, ridiculously concrete introduction to representation theory I've ever seen. To understand representations of finite groups you literally start with crystal structures. To understand vector bundles you think about vibrating molecules. When it's time to work out the details, you literally work out the details, concretely, by making character tables and so on. It's unique, so far as I've read, among math textbooks on any subject whatsoever, in its shameless willingness to draw pictures, offer physical motivation, and give examples with (gasp)

literal numbers.Math for dummies? Well, actually, it

isrigorous, just not as general as it could potentially be. Also, many people's optimal learning style is quite concrete; I believe your first experience with a subject should be example-based, to fix ideas. After all, when you were a kid you played around with numbers long before you defined the integers. There's something to the old Dewey idea of "learning by doing." And I have only seen it triedoncein advanced mathematics.Fulton and Harris won't do this. The representation theory section in Lang's

Algebrawon't do this -- it starts about three levels of abstraction up and stays there. Weyl's classicThe Theory of Groups and Quantum Mechanicsisn't actually the best way to learn -- the group theory and the physics are in separate sections and both are a little compressed and archaic in terminology. Sternberg is really a different thing entirely: it's almost more like having a teacher than reading a textbook.The treatment is really most relevant for physicists, but

even if you're not a physicist(and I'm not), if you have general interest in math, and background up to a college abstract algebra course, you should check this out just to see what unusually clear, intuitive mathematical writing looks like. It willmake you happy.Won't do

what? Almost everything you say about Sternberg seems to me to apply to Fulton & Harris. I have not looked at Sternberg, and it may well be better in all these ways, but your binary dismissal of F&H seems odd to me.Have you ever read Group Theory and Its Applications in Physics by Inui, Tanabe, Onodera? I have never been able to find this book and it's been recommended to me several times as the pedagogically best math/physics book they've ever read.

I hasten to point out (well, actually I didn't hasten, I waited a day or two, but...) that while this is true for many people, it isn't true for all, and, in particular, it isn't true for me. (See here.)

I don't think the way I learned mathematics as a young child (or indeed in school at any time, up to and including graduate school) was anywhere near optimal for the way my mind works.

The best way for me would have been to work through Bourbaki, chapter by chapter, book by book, in order. I'm dead serious. (If I were making an edition for my young self I would include plenty of colorful but abstract pictures/diagrams.)

I assumed there were some folks like you but I'd never met one. Shame on me for making too many assumptions.

It's not as stark as that. For example, Alicorn, whom I believe you've met, shares with me a psychological need for concepts to be presented in logical order.

In my case, if you're curious, I think the reason I'm the way I am comes down to efficient memory. To remember something reliably I have to be able to mentally connect it to something I already know, and ultimately to something inherently simple. The reason I can't stand ad-hoc presentations of mathematics is that remembering their contents (let alone being able to apply those contents to solve problems) is extremely cognitively burdensome. It requires me to create a new mental directory when I would prefer to file new material as a subdirectory under an existing directory. (I don't mind having lots of nested layers, but strongly prefer to minimize the number of directories at any given level; I like to expand my tree vertically rather than horizontally.)

This explains why it took me forever to learn the meaning of "k-algebra". The reason was that (for a long time) every time I encountered the term, the definition was always being presented in passing, on the way to explaining something else (usually some problem in algebraic geometry, no doubt), instead of being included among The Pantheon Of Algebraic Structures: Groups, Rings, Fields etc. -- so my brain didn't know where to store it.

Well, I can see the need to have the concepts fit together. What I need on a first pass through a subject is something that can attach to the pre-abstract part of my brain. A picture, even a "real-world example." Something to keep in mind while I

laterfill in the structure.The way I see it (which I realize is more of a metaphor than an explanation) human brains evolved to help us operate in large social groups of other primates. We're very good at understanding stories, socialization, human faces, sex and politics. I think for a lot of people (myself included) the farther we get from that core, the more help we need understanding concepts. I need to make concessions to human frailty by adding pictures and applications, if I want to learn as well as possible. (This is something that people in abstract fields rarely admit but I think LessWrong is a good place to be frank.)

I find it takes much more effort to learn things when different sources don't coordinate well on definitions, notation, and the material's hierarchical structure. For example, if everyone agreed on how to present the Nine Great Laws of Information Theory, that would make them much easier for me to remember them. It's as if, instead of learning the overlap between different presentations, my brain shuts down and doesn't trust any of them. But it's hard to settle on such cognitive coordination equilibria.

*1 point [-]Interesting. That sounds like my habit of making sure everything I learn plugs into my model for everything else, and how I'm bothered if it doesn't (literature and history class, I'm looking in your general direction here). Likewise, how I don't regard myself as understanding a subject until my model is working

andplugged in (level 2 in my article).This is why I've usually found it easy to explain "difficult" topics to people, at least in person: per my comment here, I just find the inferentially-nearest thing we both understand, and build out stepwise from there. And, in turn, why I'm bothered by those who can't likewise explain -- after all, what insights are they missing by having such a comparmentalized (level 1) understanding of the topic?

Music theory:An Introduction to Tonal Theoryby Peter Westergaard.Comparing this book to others is almost unfair, because in a sense, this is the only book on its subject matter that has ever been written. Other books purporting to be on the same topic are really on another, wrong(er) topic that is properly regarded as superseded by this one.

However, it's definitely worth a few words about what the difference is. The approach of "traditional" texts such as Piston's

Harmonyis to come up with a historically-based taxonomy (and a rather awkward one, it must be said) of common musical tropes for the student to memorize. There is hardly so much as an attempt at non-fake explanation, and certainly no understanding of concepts like reductionism or explanatory parsimony. The best analogy I know would be trying to learn a language from a phrasebook instead of a grammar; it's a GLUT approach to musical structure.(Why is this approach so popular? Because it doesn't require much abstract thought, and is easy to give students tests on.)

Not all books that follow this traditional line are quite as bad as Piston, but some are even worse. An example of not-quite-so-bad would be Aldwell and Schachter's

Harmony and Voice Leading; an example of even-worse would be Kotska and Payne'sTonal Harmony, or pretty much anything you can find in a non-university bookstore (that isn't a reprint of some centuries-old classic like Fux).I've always found traditional music theory to be useless if not actively damaging (seems to train people in bad thought habits for writing/appreciating music). Can you summarize Westergaard's approach? I know why the typical methods are bad, but I'm interested in what exactly his alternative is.

*8 points [-]In ITT itself, Westergaard offers the following summary (p.375):

(This, of course, is very similar to the methodology of theoretical linguistics.)

Westergaard basically considers tonal music to be a complex version of species counterpoint --- layers upon layers of it. He inherits from Schenker the idea of systematically reversing the process of "elaboration" to reveal the basic structures underlying a piece (or passage) of music, but goes even further than Schenker in completely explaining away "harmony" as a component of musical structure.

Notes are considered to be elements of

lines, not "chords". They operations by which they are generated within lines are highly intuitive. They essentially reduce to two: step motion, and borrowing from other lines.A key innovation of Westergaard is to

unifypitch-operations and rhythmic operations. Every operation on pitch occurs in the context of an operation on rhythm: segmentation, delay, or anticipation of a timespan. This is arguably implicit in Schenker (and even in species counterpoint itself) but Westergaard makes it explicit and systematic. Hence he arrives at his "theory of tonal rhythm" which is the core of the book (chapters 7-9).The table of contents, at the level of chapters, should give you an idea of how different Westergaard's book is from other texts:

Part I. Problems and Assumptions

Part II. A First Approximation: Species Counterpoint

4. Species counterpoint

5. Simple species

6. Combined species

Part III A little closer to the real thing -- a theory of tonal rhythm

7. Notes, beats and measures

8. Phrases, sections, and movements

9. Performance

Appendix: Constructing a pitch system for tonal music

EDIT:1,2,3 under Part II and Part III should be 4,5,6 and 7,8,9 respectively, which is what I typed. I mostly like the comment formatting system here, but that is one hell of a bug.EDIT2:: fixed.*1 point [-]Thanks for the summary. I may get this book.

You can defeat automatic list formatting if your source code looks like this:

except with spaces instead of "

`#`

" (to prevent the list items from being wrapped into one paragraph).Edit:If the list items have blank lines between them, the trailing spaces are not necessary.(The creator of the Markdown format says "At some point in the future, Markdown may support starting ordered lists at an arbitrary number.")

I have been using

Harmony and Voice Leadingfor a little while. IsAn Introduction to Tonal Theoryreally that much better?I've always felt that the way they explain concepts is very hand wavy and doesn't really explain anything and I tend to prefer things to be more mathematical or abstract.

I'll probably pick this book up on your suggestion.

Yes.

Don't get me wrong, Aldwell and Schachter are about the best you can do while still remaining in the traditional "vocabulary of chords" paradigm. (You can even see how they tried to keep the number of "chords" down to a minimum.) Unfortunately, that paradigm is simply wrong.

Also, Aldwell and Schachter, brilliant musicians though they may be (especially Schachter), lack the deeper intellectual preoccupations that Westergaard possesses in abundance. One should perhaps think of their book as being written for students at Mannes or Julliard, and of Westergaard's as being written for students at Columbia or Princeton. (There is a certain literal truth to these statements.)

You'll love ITT.

"One should perhaps think of their book as being written for students at Mannes or Julliard and of Westergaard's as being written for students at Columbia or Princeton. (There is a certain literal truth to these statements.)"

As a graduate of Juilliard I am curious about this assertion. Care to elaborate? Not that I personally have ever had much use as a performer for abstract notions about music theory. My experience has been that it gets in the way of actually performing music. Which leads to the question 'why should this be so' ? Those of my colleagues who were great adepts at theory were uninspired performers of the music they seemed to understand so well. All head and no heart. But why? I can understand that they are different skill sets, but why should they not be complementary skill sets?

I imagine that on this site, alarm bells may go off as I make an observation from experience, but I do not think that it would be possible to use any sort of methodology or system analysis to determine who is and who is not an inspired performer. Just try figuring out how orchestral auditions are run! Now that is a sloppy business!

Regarding textbooks: have any of you read W.A. Mathieu's

W.A. Mathieu Harmonic Experience: Tonal Harmony from Its Natural Origins to Its Modern Expression (1997) Inner Traditions Intl Ltd. ISBN 0-89281-560-4.

*4 points [-]It's a complicated question, but the short answer is that what usually passes for "music theory" is the wrong theory. At least, it's certainly the wrong theory for the purposes of turning people into inspired performers, because as you point out, it doesn't.

But then, if you'll forgive my cynicism, that isn't the purpose of music theory class, any more than the purpose of high-school Spanish class is to teach people Spanish. The purpose of such classes is to provide a test for students that's easy to grade them on and makes the school look good to outside observers.

(Nor, by the way, do students typically show up at Juilliard for the purpose of turning themselves from uninspired into inspired performers; rather, in order to get there in the first place they already have to be "inspired enough" by the standards of current musical culture, and are there simply for the purposes of networking and career-building.)

But music theory isn't

inherentlycounterproductive to or useless for becoming a good performer or composer; it's just that you need adifferent theoryfor that. Ultimately, inspired performers are that way because they know certain information that their less-inspired counterparts don't; to see what this sort of information looks like when written down, see Chapter 9 of Westergaard. (And after reading that chapter, tell me if you still think that knowledge of music theory "gets in the way of actually performing music".)Is this text useful for actually learning to write harmony, or does it teach about music theory in a more abstract kind of way?

I'm preparing for an exam for a teaching diploma in a few months' time, and I need to relearn harmony and counterpoint. (I was okay enough at them a few years ago to get by, but never really mastered them.) Also, I want to learn them for their own sake, it's just a useful skill to have.

I was planning on getting Lovelock's textbooks on harmony - they come recommended with the warning that it's very much harmony-by-the-numbers, but that they teach it systematically. I reckon a healthy skepticism towards his advice would minimize the damage done.

It depends on what you mean by "write harmony". I will say that if "abstract" is a bad word for you, you probably won't like it. However, that isn't typically an issue for LW readers.

Here is what Westergaard says in the preface (in the "To the teacher" section):

The best way to know if you'll like the book would be to take a look at it and see. Failing that, my advice would be as follows: if you want to actually learn how music works, this is the book to read. If you merely want to pass some kind of exam without actually learning how music works in the process, you probably don't need it.

(Added: I see that you're interested in reading about music cognition. In that case, you will definitely be interested in Westergaard.)

By abstract, I meant like Schenker (I then saw that you compare Schenker and Westergaard's approaches elsewhere in the thread). Schenker was pretty adamant that his method was for analysis only, and not a compositional tool. So I was wondering if the book gave an overview of how Westergaard thinks music works, or if it does this and also teaches how to do harmony exercises, perform species counterpoint, and the like.

To break it down into my goals: I have a general goal of learning how music actually works (I've got a reasonably good grasp as it is; kinda important to me professionally), hence the interest in music cognition. However, as a specific goal I need to pass this exam!

It certainly looks interesting; it seems a little too expensive for me to get right now, but if I can get a cheap copy or a loan, I'll look into it.

Cheers for the advice!

Oh, the book certainly contains

exercises, and is definitely intended as a practical textbook as opposed to a theoretical treatise (in fact, I actually wish a more comprehensive treatise on Westergaardian theory existed; the book is pretty much the only source). It's true that Westergaard's theory itself is descended from Schenker's, but his expository style is quite different! Part II of the book is basically a species counterpoint course on its own.What the book

doesn'tcontain is "harmony" exercises in the traditional sense. (In fact, I think the passage I quoted above might be the only time the word "harmony" occurs in the book!) However, this is not anomission, any more than the failure of chemistry texts to discuss phlogiston is. "Harmony" does not exist in Westergaard's theory; instead, its explanatory role is filled by other, better concepts (mainly the "borrowing" operation introduced in Section 7.7 -- of which the species rule B3 of Chapter 4 is a "toy" version).So in place of harmony exercises, it has Westergaardian exercises, which are strictly superior.

If you have access to a university library, there's a good chance you can find a copy there; at the very least, you should be able to get one through interlibrary loan.

*17 points [-]Updatesee my comment for new thoughtsTopic: Introductory Bayesian Statistics (as distinct from more advanced Bayesian statistics)

Recommendation:

Data Analysis: A Bayesian Tutorialby Skilling and SiviaWhy: Sivia's book is well suited for smart people who have not had little or no statistical training. It starts from the basics and covers a lot of important ground. I think it takes the right approach, first doing some simple examples where analytical solutions are available or it is feasible to integrate naively and numerically. Then it teaches into maximum likelihood estimation (MLE), how to do it and why it makes sense from a Bayesian perspective. I think MLE is a very very useful technique, especially so for engineers. I would overall recommend just Part I: The Essentials, I don't think the second half is so useful, except perhaps the MLE extensions chapter. There are better places to learn about MCMC approximation.

Why not other books?

Bayesian Data Analysisby Gelman - Geared more for people who have done statistics before.Bayesian Statisticsby Bolstad - Doesn't cover as much as Sivia's book, most notably doesn't cover MLE. Goes kinda slowly and spends a lot of time on comparing Bayesian statistics to Frequentist statistics.The Bayesian Choice- more of a mathematical statistics book, not suited for beginners.*8 points [-]Brandon Reinhart used both Sivia's book and Bolstad's book and found (3rd message) Bolstad's book better for those with no stats experience:

Based on these comments, I think I was underestimating inferential distance, and I now change my recommendation. You should read Bolstad's book first (skipping the parts comparing bayesian and frequentist methods unless that's important to you) and then read Sivia's book. If you have experience with statistics you may start with Sivia's book.

Nice!

*12 points [-]I suppose I can think up a few tomes of eldritch lore that I have found useful (college math specifically):

Calculus:Recommendation: Differential and Integral Calculus

Author: Richard Courant

Contenders:

Stewart,

Calculus: Early Transcendentals: This is a fairly standard textbook for freshman calculus. Mediocre overall.Morris Kline,

Calculus: An Intuitive and Physical Approach: Great book. As advertised, focuses on building intuition. Provides a lot of examples that aren't the usual contrived "applications". This would work well as a companion piece to the recommended text.Courant,

Differential and Integral Calculus(two volumes): One of the few math textbooks that manages to properly explain and motivate thingsandbe rigorous at the same time. You'll find loads of actual applications. There are plenty of side topics for the curious as well as appendices that expand on certain theoretical points. It's quite rigorous, so a companion text might be useful for some readers. There's an updated version edited by Fritz John (Introduction to Calculus and Analysis), but I am unfamiliar with it.Linear Algebra:Recommended Text: Linear Algebra

Author: Georgi Shilov

Contenders:

David Lay,

Linear Algebra and its Applications: Used this in my undergraduate class. Okay introduction that covers the usual topics.Sheldon Axler,

Linear Algebra Done Right: Ambitious title. The book develops linear algebra in a clean, elegant, and determinant-free way (avoiding determinants is the "done right" bit, though they are introduced in the last chapter). It does prove to be a drawback, as determinants are a useful tool if not abused. This book is also a bit abstract and is intended for students who have already studied linear algebra.Georgi Shilov,

Linear Algebra: No-nonsense Russian textbook. Explanations are clear and everything is done with full rigor. This is the book I used when I wanted to understand linear algebra and it delivered.Horn and Johnson,

Matrix Analysis: I'm putting this in for completion purposes. It's a truly stellar book that will teach you almost everything you wanted to know about matrices. The only reason I don't have this as the recommendation is that it's rather advanced and ill-suited for someone new to the subject.Numerical MethodsRecommendation: Numerical Recipes: The Art of Scientific Computing

Author: Press, Teukolsky, Vetterling, Flannery

Contenders:

Bulirsch and Stoer,

Introduction to Numerical Analysis: German rigor. Thorough and thoroughly terse, this is one of those good textbooks that only a sadist would recommend to a beginner.Kendall Atkinson,

An Introduction to Numerical Analysis: Rigorous treatment of numerical analysis. It covers the main topics and is far more accessible than the text by Bulirsch and Stoer.Press, Teukolsky, Vetterling, Flannery,

Numerical Recipes: The Art of Scientific Computing: Covers just about every numerical method outside of PDE solvers (though this is touched on). Provides source code implementing just about all the methods covered and includes plenty of tips and guidelines for choosing the appropriate method and implementing it. THE book for people with a practical bent. I would recommend using the text by Atkinson or Bulirsch and Stoer to brush up on the theory, however.Richard Hamming,

Numerical Methods for Scientists and Engineers: How can I fail to mention a book written by a master of the craft? This book is probably the best at communicating the "feel" of numerical analysis. Hamming begins with an essay on the principles of numerical analysis and the presentations in the rest of the book go beyond the formulas. I docked points for its age and more limited scope.Ordinary Differential EquationsRecommended: Ordinary Differential Equations

Author: Vladimir Arnold

Contenders:

Coddington,

An Introduction to Ordinary Differential Equations: Solid intro from the author of one ofthetexts in the field. Definite theoretical bent that doesn't really touch on applications.Tenenbaum and Pollard,

Ordinary Differential Equations: This book manages to be both elementary and comprehensive. Extremely well-written and divides the material into a series of manageable "Lessons". Covers lots and lots of techniques that you might not find elsewhere and gives plenty of applications.Vladimir Arnold,

Ordinary Differential Equations: Great text with a strong geometric bent. The language of flows and phase spaces is introduced early on, which becomes relevant as the book ends with a treatment of differential equations on manifolds. Explanations are clear and Arnold avoids a lot of the pedantry that would otherwise preclude this kind of treatment (although it requires more out of the reader). It's probably the best book I've seen for intuition on the subject and that's why I recommend it. Use Tenenbaum and Pollard as a companion if you want to see more solution methods.Abstract Algebra:Note: I am mainly familiar with graduate texts, so be warned that these books are not beginner-friendly.

Recommended: Basic Algebra

Author: Nathan Jacobson

Contenders:

Bourbaki,

Algebra: The French Bourbaki tradition in all its glory. Shamelessly general and unmotivated, this is not for the faint of heart. The drawback is its age, as there is no treatment of category theory.Lang,

Algebra: Lang was once a member of the aforementioned Bourbaki. In usual Serge Lang style, this is a tough, rigorous book that has no qualms with doing things in full generality. The language of category theory is introduced early and heavily utilized. Great for the budding algebraist.Hungerford,

Algebra: Less comprehensive, but more accessible than Lang's book. It's a good choice for someone who wants to learn the subject without having to grapple with Lang.Jacobson,

Basic Algebra(2 volumes): Note that the "Basic" in the title means "so easy, a first-year grad student can understand it". Mathematicians are a strange folk, but I digress. It's comprehensive, well-organized, and explains things clearly. I'd recommend it as being easier than Bourbaki and Lang yet more comprehensive and a better reference than Hungerford.Elementary Real Analysis:"Elementary" here means that it doesn't emphasize Lebesgue integration or functional analysis

Recommended: Principles of Mathematical Analysis

Author: Walter Rudin

Contenders:

Rudin,

Principles of Mathematical Analysis: Infamously terse. Rudin likes to do things in the greatest generality and the proofs tend to be slick (i.e. rely on clever arguments that don't really clarify the thing being proved). It's thorough, it's rigorous, and the exercises tend to be difficult. You won't find any straightforward definition-pushing here. If you had a rigorous calculus course (like Courant's book), you should be fine.Kenneth Ross,

Elementary Analysis: The Theory of Calculus: I'd put this book as a gap-filler. It doesn't go into topology and is rather straightforward. If you learned the "cookbook" approach to calculus, you'll probably benefit from this book. If your calculus class was rigorous, I'd skip it.Serge Lang,

Undergraduate Analysis: It's a Serge Lang book. Contrary to the title, I don't think I'd recommend it for undergraduates.G.H. Hardy,

A Course of Pure Mathematics: Classic text. Hardy was a first-rate mathematician and it shows. The downside is that the book is over 100 years old and there are a few relevant topics that came out in the intervening years.Updated, thanks!

*1 point [-]How can baby rudin possibly be recommended in almost all use cases there is something better -_-, less wrong is supposed to give good advice not status-signaling type.

Rudin = Bourbaki and I thought we were anti-bourbaki here

Alternatives: Abbot & Bressoud combo(has mathematica code), Pugh, or Strichartz's book(the one patrick says is good)

I recommend Rudin because he dives right into the topology and metric space approach. It's a lot easier to pick it up when it's used to develop the familiar theory of calculus. It also helps put a lot of point-set topology into perspective. I appreciated it once I started studying functional analysis and all those texts basically assumed the reader was familiar with the approach. The problems are great to work through and the terseness is a sign of things to come for a reader who wants to go on to advanced texts.

There is a caveat. Rudin is not a good text for a student's first foray into the rigors of real analysis. IF one has already seen a rigorous development of calculus, Rudin bridges the gap with a minimum of fluff. If not, the reader is better served elsewhere.

I'm no expert in undergraduate math texts so maybe there's something else that works better. I read Rudin on my own in undergrad and with my background at the time I got a lot out of it, so I'm recommending it.

Bourbaki has its place. There comes a time when you need a good reference for the general theory and that's where the Bourbaki style shines. It makes for bad pedagogy and is cruel to foist upon beginners, but on the other hand good pedagogical books tend to limit their scope and seldom make good references.

I agree with this post much more. My concern was more ability to learn the subject & less wrong aesthetic in this direction which I think is correct.

What? Did I miss an anti-Bourbaki fatwa? The one mention of their name in the post does not come close to a general stance on Bourbaki, and in any case there must be someone on the site who likes them. In fact, here's one.

*12 points [-]I can't help but question this post.

Textbook recommendations are

all over. From the old SIAI reading shelf to books individually recommended in articles and threads to wiki pages to here (is this even the first article to try to compile a reading list? I don't think it is.)Maybe we would be better off adding pages to the LW wiki. So for

`[[Economics]]`

a brief description why economics is important to know, links to relevant LW posts, and then a section`== Recommended reading ==`

. And so on for all the other subjects here.Work smarter, not harder!

*21 points [-]The problem is that lots of textbook recommendations are not very good. I've been recommended lots of bad books in my life. That's what is unique about this post: it demands that recommendations be given only by people who are fairly well-read on the subject (at least 3 textbooks).

But yes, adding this data to the Wiki would be great.

agreed, but the idea to add this info to the wiki once the thread has matured is a good one.

However, a centralized repository-of-textbooks is also a good idea.

Since the parent omitted a link: singinst.org/reading/

Link dead; try here: http://www.librarything.com/catalog/siai

Everyone should pass this post along to their favorite professors.

Professors will have read numerous textbooks on several subjects,

andcan often say which books work best for their students.General programming:

Structure and Interpretation of Computer Programs. Focuses on the essence of the subject with such clarity that a novice can understand the first chapter, yet an expert will have learned something by the last chapter.Specific programming languages:

The C Programming Language,The C++ Programming Language,CLR via C#. Informative to a degree that rarely coexists with such clarity and readability.AI:

Artificial Intelligence: a Modern Approach. Perhaps the rarest virtue of this work is that not only does it give about as comprehensive a survey of the field as will fit in a single book, but casts a cool eye on the limitations as well as strengths of each technique discussed.Compiler design:

Compilers: Principles, Techniques and Tools. The standard textbook for good reason.I don't agree on the dragon book (Compilers: Principles, Techniques and Tools). It focuses too much on theory of parsing for front end stuff, and doesn't really have enough space to give a good treatment on the back end. It's a book I'd recommend if you were writing another compiler-compiler like yacc.

I'd rather suggest Modern Compiler Implementation in ML; even though there are C and Java versions too, a functional language with pattern matching makes writing a compiler a much more pleasant experience.

(I work on a commercial compiler for a living.)

Is "The C Programming Language" Kernighan & Ritchie? (titles are often very generic so it's nice to see authors as well.)

rwallace,

Thanks for your recommendations! Your comment made me realize I was not specific enough in my list of rules, so I modified the third rule to the following:

"You must briefly name the other books you've read on the subject and explain why you think your chosen textbook is superior to them."

Would you please do us the favor of naming the other books you've read on these subjects, and why your recommendations are superior to them? That would be much appreciated.

*1 point [-]Disagree with "C++ the programming language" as a C++ textbook. Anything by Lippman, Koenig or Moo would be better.

Subject: Problem SolvingRecommendation: Street-Fighting Mathematics The Art of Educated Guessing and Opportunistic Problem SolvingReason: So, it has come to my attention that there is a freely available .pdf for the textbook for the MIT course Street Fighting Mathematics. It can be found here. I have only been reading it for a short while, but I would classify this text as something along the lines of 'x-rationality for mathematics'. Considerations such as minimizing the number of steps to solution minimizes the chance for error are taken into account, which makes it very awesome.in any event, I feel that this should be added to the list, maybe under problem solving? I'm not totally clear about that, it seems to be in a class of its own.

If you come up with relevant comparison volumes, let me know!

Seemingly relevant comparison volumes:

Numbers Rule Your World: The Hidden Influence of Probabilities and Statistics on Everything You Do

Back-of-the-Envelope Physics

How Many Licks? Or, How to Estimate Damn Near Anything

Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin

Also, the books below are listed as related resources in another class on approximation in science & engineering by the author of the Street-Fighting textbook on OCW, so they may be relevant for comparison, too, or at least interesting.

Engel, Arthur. Problem-solving Strategies. New York, NY: Springer, 1999. ISBN: 9780387982199.

Schmid-Nielsen, Knut. Scaling: Why is Animal Size So Important? New York, NY: Cambridge University Press, 1984. ISBN: 9780521319874.

Vogel, Steven. Life in Moving Fluids. 2nd rev. ed. Princeton, NJ: Princeton University Press, 1996. ISBN: 9780691026169.

Vogel, Steven. Comparative Biomechanics: Life's Physical World. Princeton, NJ: Princeton University Press, 2003. ISBN: 9780691112978.

Pólya, George. Induction and Analogy in Mathematics. Vol. 1, Mathematics and Plausible Reasoning. 1954. Reprint, Princeton, NJ: Princeton University Press, 1990. ISBN: 9780691025094.

*1 point [-]Well, they aren't necessarily comparison volumes, but the author suggested that the book should be used as a compliment to the following:

How to Solve It, Mathematics and Plausible Reasoning, Vol. II, The Art and Craft of Problem Solving

He implies that his book is more rough and ready for applications, but those books are more geared towards solving clearly stated problems in, say, a competition setting.

I would add Putnam and Beyond to the list, classifying it as

advancedcompetition style problem solving (some of the stuff in that book isprettytough).*8 points [-]Subject:Introductory Decision Making/Heuristics and BiasesRecommendation:Judgment in Managerial Decision Making by Max Bazerman and Don Moore.This book wins points by being comprehensive, including numerous exercises to demonstrate biases to the reader, and really getting to the point. Insights pop out at every page without lots of fluffy prose. The recommendations are also more practical than other books.

Alternatives:Excellent. I also like Baron's

Thinking and Deciding.While the following isn't really a textbook, I highly recommend it for helping you to improve your skill as a reader. "How to Read a Book" by Mortimer Adler and Charles Van Doren. It covers a variety of different techniques from how to analytically take apart a book to inspectional techniques for getting a quick overview of a book.

I never knew how to read analytically, I had never been taught any techniques for actually learning from a book. I always just assumed you read through it passively.

http://www.amazon.com/How-Read-Book-Touchstone-book/dp/0671212095

It looks interesting, but I am surprised it's 400 pages long, is there really that much in the way of reading strategies?

It has a fairly large appendix (~70 pgs) of recommended reading and sample tests/examples at the end of the book. It also has several sections on reading subject specific matter i.e. How to read History, Philosophy, Science, Practical books, etc. It also covers agreeing or disagreeing with an author, fairly criticizing a book, aids to reading. I think reading strategies may have been too narrow a choice of words. It really covers the "Art of Reading". A good set of English classes would probably cover similar ground, although I didn't see anything like this in my high school or undergraduate education.

*8 points [-]Luke -- I wonder if either permalinks to comments answering the task, or direct quotes of them could be added to your main post (say, after two+ weeks have passed)? I know in other posts where a question is asked it can be very difficult to sift through the "meta" comments and the actual answers, especially as comments get into the 100-200+ range!

I was thinking this myself. For example for michaba03m's recommendation below, I could add a line which reads:

Macroeconomicsover Varian'sIntermediate Microeconomicsand Katz & Rosen'sMacroeconomics.Sorry Luke I rushed that a little bit and didn't check before hitting 'comment'. In economics I would say you should read macroeconomics and microeconomics separately, and most college-level textbooks are on either one rather than both anyway. So Mankiw is definitely the best on Macro, whilst Varian is the best for Micro, but his is quite dry and mathsy, whereas for a Micro alternative Katz and Rosen is more readable but less mathematical.

So for Macro, go for Mankiw, and for Micro go Katz and Rosen if you can't handle Varian.

Hope that clears that up!

Calculus:Spivak's Calculus over Thomas' Calculus and Stewart's Calculus. This is a bit of an unfair fight, because Spivak is an introduction to proof, rigor, and mathematical reasoning disguised as a calculus textbook; but unlike the other two, reading it is actually exciting and meaningful.Analysis in R^n (not to be confused with Real Analysis and Measure Theory):Strichartz's The Way of Analysis over Rudin's Principles of Mathematical Analysis, Kolmogorov and Fomin's Introduction to Real Analysis (yes, they used the wrong title; they wrote it decades ago). Rudin is a lot of fun if you already know analysis, but Strichartz is a much more intuitive way to learn it in the first place. And after more than a decade, I still have trouble reading Kolmogorov and Fomin.Real Analysis and Measure Theory (not to be confused with Analysis in R^n):Stein and Shakarchi's Measure Theory, Integration, and Hilbert Spaces over Royden's Real Analysis and Rudin's Real and Complex Analysis. Again, I prefer the one that engages with heuristics and intuitions rather than just proofs.Partial Differential Equations:Strauss' Partial Differential Equations over Evans' Partial Differential Equations and Hormander's Analysis of Partial Differential Operators. Donotread the Hormander book until you've had a full course in differential equations, and want to suffer; the proofs are of the form "Apply Theorem 3.5.1 to Equations (2.4.17) and (5.2.16)". Evans is better, but has a zealot's disdain of useful tools like the Fourier transform for reasons of intellectual purity, and eschews examples. By contrast, Strauss is all about learning tools, examining examples, and connecting to real-world intuitions.*3 points [-]In my opinion the "good stuff" in evans is in chapters 5-12. Evans is a pretty good into book on the modern "theory" of Linear and Non-linear PDEs. Strauss by comparison is a much less demanding book that is concerned with concrete examples and applications to physics. (less demanding is a good thing if the material covered is similar, but in this case its not).

Possibly Strass is overall the better book. And I really dislike Evan's chapter 1-4 (he does not use Fourier theory when it helps, his discussion of the underlying physics of some equations is very lacking, etc). But directly comparing Strauss and Evans seems odd to me. The books have very different goals and target audiences.

If the comparison is evans 1-4 vs strauss then I too would recommend Strauss. And this restricted comparison makes a ton of sense imo.

I'll agree with that. Evans would be better for a second course on PDEs than a first course.

Thanks! Added.

Spivak was a lot of fun - and very readable. Amusing footnotes, too. (I still remember the rant against Newtonian notation for derivatives).

I'd love to give recommendations on probability, but I learned it from a person, not a book, and I have yet to find a book that really fits the subject as I know it. The one I usually recommend is Grimmett and Stirzaker. It develops the algebra of probability well without depending on too much measure theory, has decent exercises, and provides a usable introduction to most of the techniques of random processes. I found Feller's exposition of basic probability less clear, though his book's a useful reference for the huge amount of material on specific distribution in it. Feller also naturally covers much less ground (probability and stochastic processes has developed a lot since he wrote that book). Kolmogorov's little book (mentioned elsewhere in the threads) is typical Kolmogorov: deliciously elegant if you know probability theory and like symbols. I would love to be able to recommend Radically Elementary Probability Theory by Nelson, and it's certainly worth a read as a supplement to Grimmett and Stirzaker, but I would hesitate to hand it to someone trying to understand the subject for the first time.

For statistics, I favor Kiefer's 'Introduction to Statistical Inference'. It begins with the decision theoretic foundations and builds from there, skipping or bypassing huge numbers of standard topics, and using a notation I can only describe as Baroque, but it is the best source of real understanding and intuiton I know of. Hogg and Craig's 'Introduction to Mathematical Statistics' is a pretty nice text as well, but less precisely pitched than Kiefer's (and it covers a lot more of the standard topics). Casella and Berger's 'Statistical Inference' and Lehmann's two books 'Point Estimation' and 'Hypothesis Testing' are the more typical graduate statistics texts, but are hard going compared to my other recommendations.

I'm going to disagree about Griffiths for electromagnetism, but admit that I don't have a really good alternative to offer. I found the second volume of Feynman clearer. Jackson is utterly opaque, a book length exercise in Green's functions methods in linear partial differential equations, and one without mathematical rigor. Schwinger's 'Classical Electrodynamics' is actually a remarkably useful text. I would probably recommend Purcell's 'Electricity and Magnetism', but it's out of print.

For thermodynamics, Hatsopoulos and Keenan's 'Principles of General Thermodynamics' is the best text I know. It's certainly better than any of the recommendations I received in my physics department. There are lots of beautiful texts -- Fermi's, Sommerfeld's, the opening couple chapters of volume 5 of Landau and Lifshitz, etc. -- but they all assume a developed conception in the student's mind of the nature of a thermodynamic system, while Hatsopoulos and Keenan spell it out in utter clarity. My only caveat about this book is that their exercises are given in Imperial units.

For statistical mechanics, I still think that Landau and Lifshitz volume 5 is the best text I know of. Sethna's 'Entropy, Order Parameters, and Complexity' is really neat, and touches on a lot more modern techniques, but has less real meat, less direct physics, than L&L. After that I think Reichl is probably my favorite, and he does set things up in a nice way, but not as nicely as Sethna.

Despite six years of wearing the big white suit in a tuberculosis laboratory, I am unaware of a microbiology textbook that should be read instead of burned.

A small point, but an important one I think: Reichl is a woman.

Thanks for all your recommendations! Purcell's

Electricity and Magnetismis not out of print.*7 points [-]Introduction to NeuroscienceRecommendation:Neuroscience:Exploring the Brain by Bear, Connors, ParadisoReasons:BC&P is simply much better written, more clear, and intelligible than it's competitorsNeuroscienceby Dale Purves andFundamentals of Neural Scienceby Eric Kandel. Purves covers almost the same ground, but is just not written well, often just listing facts without really attempting to synthesize them and build understanding of theory. Bear is better than Purves in every regard. Kandel is the Bible of the discipline, at 1400 pages it goes into way more depth than either of the others, and way more depth than you need or will be able to understand if you're just starting out. It is quite well-written, but it should be treated more like an encyclopedia than a textbook.I also can't help recommending

Theoretical Neuroscienceby Peter Dayan and Larry Abbot, a fantastic introduction to computational neuroscience,Bayesian Brain, a review of the state of the art of baysian modeling of neural systems, andNeuroeconomicsby Paul Glimcher, a survey of the state of the art inthatfield, which is perhaps the most relevant of all of this to LW-type interests. The second two are the only books of their kind, the first has competitors inComputational Explorations in Cognitive Neuroscienceby Randall O'Reilly andFundamentals of Computational Neuroscienceby Thomas Trappenberg, but I've not read either in enough depth to make a definitive recommendation.*7 points [-]Subject: Basic mathematical physicsRecommendation: Bamberg and Sternberg's A Course in Mathematics for Students of Physics. (two volumes)Reason: It is difficult to compare this book with other text books since it isextremelyaccessible, going all the way from 2D linear algebra to exterior calculus/differential geometry, covering electrodynamics, topology and thermodynamics. There is potential for insights into electrodynamics even compared to Feynman's lectures (which I've slurped) or Griffith's. For ex: treating circuit theory and Maxwell's equations as the same mathematical thing. The treatment of exterior calculus is more accessible than the only other treatment I've read which is in Misner Thorne Wheeler'sGravitation.Comment deleted17 January 2011 04:28:14PM*[-]*6 points [-]Hmm. Upvoted for contributing to a good topic but I'm not sure I agree.

I just looked up the gauge integral because I wasn't familiar with it. For those curious about the debate, here's the introduction to the gauge integral I found, which has a lot of relevant information. My beef with this is precisely that it doesn't use the general background of measure theory (sigma-algebras, measurable functions, etc.) and you're going to

needthat background to do useful things. The gauge integral approach doesn't give you the tools to generalize to scenarios like Brownian motion where you need to construct different measures; also, the gauge integral doesn't come with a lot of nice convergence theorems the way the Lebesgue measure does.I don't find the standard treatment of measure theory especially hard; it takes about a month to understand everything up to the Lebesgue integral, which isn't an obscene time commitment.

Also, there's some virtue to just being familiar with the definitions and concepts that everybody else is. (It's not just mathematicians "refusing to update." I know for sure that economists, and potentially people in other fields, speak the language of standard measure theory. But maybe it's not everyone. What are you using measure theory for?)

If you're looking for an easier, more straightforward treatment than Rudin, I'd recommend Cohn's

Measure Theory. I'm not sure why, but it feels friendlier and less digressive.Here is a very similar post on Ask Metafilter. (It is actually Ask Metafilter's most favorited post of all time.)

Ah, yes, that list is one of my favorites. But, it doesn't enforce anything like the rules I've given above, which I think are useful.

*7 points [-]Subjects: algorithms/computational complexity, physics, Bayesian probability, programming

Introduction to Algorithms (Cormen, Rivest) is good enough that I read it completely in college. The exercises are nice (they're reasonably challenging and build up to useful little results I've recalled over my programming career). I think it's fine for self-study; I prefer it to the undergrad intro level or language-specific books. Obviously the interesting part about an algorithm is not the Java/Python/whatever language rendering of it. I also prefer it to Knuth's tomes (which I gave up on finishing - not enough fun). Knuth invents problems so he can solve them. He explains too much minutia. But his exercises are varied and difficult. If you like very hard puzzles, it's a good place to look.

Introduction to Automata Theory, Languages, and Computation (Hopcroft+Ullman) was also good enough for me to read. I've referred to it many times since. However, it's apparently not well-liked by others; maybe because it's too dense for them? I haven't read any other textbooks in the area.

The Feynman Lectures on Physics are also fun to read. But I doubt someone could use them as an intro course on their own. Because they're filled with entertaining tidbits, I was tempted to read through them without actually following the math 100%. Obviously this somewhat defeats the purpose. That's always a danger with well written technical material consumed for pleasure. I had already taken a few physics courses before I read Feynman; his lectures were better than the course textbooks (which I already forgot).

I didn't care for Jaynes. I only read about 700 pages, though. I remember there was some group reading effort that stopped showing up on LW after just a few chapters :)

For plain old programming, I've read quite a few books, and really liked The Practice of Programming - it was too short. I read Dijkstra's a discipline of programming and loved it for its idea to define program semantics precisely and to prove your code correct (nobody really practices this; it's too slow and hard compared to "debugging"), but it's probably not worth the price - I checked it out from a library.

I also agree with rwallace's recommendations also, except that the AI text is not especially useful (not that I know of a better one). I would not give SICP to a novice, though. Although I had done everything described in the book before (and already knew lisp), it did increase my appreciation of using closures and higher order functions as an alternative for the usual imperative/OO stuff. It also covers interpretation and compilation quite well (skipping the character-sequence parsing part - this is lisp, after all).

Jonathan_Graehl,

Thanks for your recommendations, though I've set a rule that I won't add recommendations to the list in the original post unless those recommendations conform to the rules. Would you mind adding to what you've written above so as to conform to rule #3?

For example, you could list two other books on algorithms and explain why you prefer

Introduction to Algorithmsto those other books. And you could do the same for the subject of physics, and the subject of programming, and so on.Well, let me do Jonathan's job for him on one of those.

Introduction to Algorithmsby Cormen, Leiserson, Rivest, and (as of the second edition) Stein is a first-rate single-volume algorithms text, covering a good selection of topics and providing nice clean pseudocode for most of what they do. The explanations are clear and concise. (Readers whose tolerance for mathematics is low may want to look elsewhere, though.)Two obvious comparisons: Knuth's TAOCP is wonderful but: very, very long; now rather outdated in the range of algorithms it covers; describes algorithms with wordy descriptions, flowcharts, and assembly language for a computer of Knuth's own invention. When you need Knuth, you

reallyneed Knuth, but mostly you don't. Sedgwick'sAlgorithms(warning: it's many years since I read this, and recent editions may be different) is shallower, less clearly written, and frankly never gave me the same the-author-is-really-smart feeling that CLRS does.(If you're going to get two algorithms books rather than one, a good complement to CLRS might be Skiena's "The algorithm design manual", more comments on which you can find on my website.)

Thanks. I really didn't have the ability to easily recall names of what few alternatives I've read (although in the area of programming in general, there are dozens of highly recommended books I've actually read - Design Patterns (ok), Pragmatic Programmer (ok), Code Complete (ok), Large Scale C++ Software Design (ok), Analysis Patterns (horrible), Software Engineering with Java (textbook, useless), Writing Solid Code (ok), object-oriented software construction (ok, sells the idea of design-by-contract), and I could continue listing 20 books, but what's the point. These are hardly textbooks anyway.

On algorithms, other than Knuth (after my disrecommendation of his work, I just bought his latest, "Combinatorial Algorithms, part 1"), really the only other one I read is "Data Structures in C" or some similar lower level textbook, which was unobjectionable but did not have the same quality.

For an AI text, I think any (text)book on a subject of your interest by Judea Pearl would fit the bill.

"Symbolic Logic and Mechanical Theorem Proving" by Chang and Lee is still an exceptionally lucid introduction to non-probabilistic AI.

I also prefer Hopcroft+Ullman (original edition) to later alternatives like their own later edition, Papadimitriou, and even Sipser who is widely regarded as having written the definitive intro text.

"A Discipline of Programming" is rather hard to follow. Dromey gives an introductory treatment that's a bit too introductory, "Progamming Pearls" by Bently includes another even more informal treatment, and Gries's "Science of Programming" would be the textbook version that I might recommend covering this material. All three are somewhat dated. More modern treatment would be either Apt's "Verification of Sequential and Concurrent Programs" or Manna's "The Calculus of Computation." and depending on your focus one would be better than the other. However, the ultimate book I would recommend in this field is "Interactive Theorem Proving and Program development" by Yves Bertot. It doesn't teach Hoare's invariant method like the other books, but uses a more powerful technique in functional programming for creating provably correct software.

*7 points [-]In Bayesian statistics, Gelman's

Bayesian Data Analysis, 2nd ed(I hear a third edition is coming soon) instead of Jaynes'sProbability Theory: The Logic of Science(but do read the first two chapters of Jaynes) and Bernardo'sBayesian Theory.Cyan,

Could you give us some reasons?

Both Jaynes's and Bernardo's texts have a lot of material on why one ought to do Bayesian statistics; Gelman text excels in showing

howto do it.*1 point [-]Gelman's text is very specifically targeted at the kinds of problems he enjoys in sociology and politics, though. If you're interested in solving problems in that field or like it (highly complex unobservable mechanisms, large number of potential causes and covariates, sensible multiple groupings of observations, etc) then his book is great. If you're looking at problems more like in physics, then it won't help you at all and you're better off reading Jaynes'.

(Also recommended over Gelman's Applied Regression and Modeling if the above condition holds.)

*1 point [-]Ah, interesting. I used the material I learned from that book in my thesis on data analysis for proteomics, so you can expand the list of topics to include biological data too; biology problems tend to fit your list of problem characteristics.

*6 points [-]Subject: Warfare, History Of and Major Topics In

Recommendation: Makers of Modern Strategy from Machiavelli to the Nuclear Age, by Peter Paret, Gordon Craig, and Felix Gilbert.

I recommend this book specifically over 'The Art of War' by Sun Tzu or 'On War' by Clausewitz, which seem to come up as the 'war' books that people have read prior to (poorly) using war as a metaphor. The Art of War is unfortunately vague- most of the recommendations could be used for any course of action, which is sort of a common problem with translations from chinese due to the heavy context requirements of the language. Clausewitz is actually one of the articles

inMakers of Modern Strategy- the critical portions of On War are in the book, in historical context.The important part of Makers of Modern Strategy is that each piece (the book is a collection of the most important essays in the development of military thought through the ages, starting with the medieval period and through nuclear warfare. I have other recommendations for the post-nuclear age of cyberwarfare and insurgency and I'll post them separately.) is placed in context and paraphrased for critical details. Military strategy is an ongoing composition, but the inexperienced read a single strategic author and think they have everything figured out.

This book is great because it walks you through each major strategic innovation, one at a time, showing how each is a response to the last and how each previous generation being sure they've got everything figured out is how their successors defeat them. My overall takeaway was one of humility- even the last section on nuclear war has been supplanted by cyber and insurgent warfare, and it is a sure bet that someone will always find a way to deploy force to defeat an opponent. This book walks you through how to defeat naive and inexperienced combatants in a strategic sense. Tactics, as always, are contingent on circumstances.

Non-relativistic Quantum Mechanics: Sakurai's Modern Quantum Mechanics

This is a textbook for graduate-level Quantum Mechanics. It's advantages over other texts, such as Messiah's Quantum Mechanics, Cohen-Tannoudji's Quantum Mechanics, and Greiner's Quantum Mechanics: An introduction is in it's use of experimental results. Sakurai weaves in these important experiments when they can be used to motivate the theoretical development. The beginning, using the Stern-Gerlach experiment to introduce the subject, is the best I have ever encountered.

What are the prerequisites for reading this? What level of mathematics and background of classical physics?

You need some solid Linear Algebra: Vector Space, dual vector space, unitary and hermitian matrices, eigenvectors and eigenvalues, trace... Mind that you should learn these things with mathematical approach, for example, vectors are elements of vector space which has certain axioms, and not 3D arrows, like pupils learn in school. Since book has this approach (matrix mechanics, rather than wave mechanics), you don't need too strong analysis, you can just trust that some things are working that way, but if you want to understand it fully, i recommend taking some analysis course as well, to be able to understand decomposition in eigenfunctions. Integrals and derivatives are MUST, however.

*5 points [-]For abstract algebra I recommend Dummit and Foote's

Abstract Algebraover Lang'sAlgebra, Hungerford'sAlgebra, and Herstein'sTopics in Algebra. Dummit and Foote is clearly written and covers a great deal of material while being accessible to someone studying the subject for the first time. It does a good job focusing on the most important topics for modern math, giving a pretty broad overview without going too deep on any one topic. It has many good exercises at varying difficulties.Lang is not a bad book but is not introductory. It covers a huge amount but is hard to read and has difficult exercises. Someone new to algebra will learn faster and with less frustration from a less advanced book. Hungerford is awful; it is less clear, less modern, harder, and covers less material than Dummit and Foote. Herstein is ok but too old fashioned and narrow, and has too much focus on finite group theory. The part about Galois theory is good though, as are the exercises.

For Elliptic Curves:

I recommend Koblitz' "Elliptic Curves and Modular Forms"

It stays more grounded and focused than Silverman's "Arithmetic of Elliptic Curves," and provides much more detail and background, as well as more exercises, than Cassel's "Lectures on Elliptic Curves."

Is this thread still being maintained? There was a recommendation for it to be a wiki page which seems like a great idea; I'd be willing to put the initial page together in a couple weeks if it hasn't been done but I don't think I can commit to maintaining it.

*5 points [-]World War II.

"A World at Arms" by Gerhard L. Weinberg is my preferred single book textbook (as a reference) on World War II.

It is a suitably weighty volume on WW2, and does well in looking at the war from a global perspective, it's extensive bibliography and notes are outstanding. In comparison with Churchill's "The Second World War" - in it's single volume edition, Weinburg's writing isn't as readable but does tend to be less personal. Churchill on the other hand is quite personal, when reading his tome, it's almost as if he is sitting there having a chat with you. Churchill is quite frank in revealing his thought processes for making decisions, in fact LWer's might particularly enjoy reading Churchills' account for that reason. Weinberg's A World at Arms is better at looking at multiple view points of the war, whereas Churchill tends to present everything from his point of view. "The Politics of War" by David Day is an Australian centric view point of WW2, it stands as an excellent reference from that perspective, but isn't able to provide an overall picture equal to either Weinburg or Churchill.

Related: The Best Intro Book for Any Topic.

It's not exactly a textbook series, but I've found the videos at khan academy http://www.khanacademy.org/#browse to be really helpful with getting the basics of a lot of things. The most advanced math it covers is calculus, which will get you a long way, and the language of the videos is always simple and straightforward.

... Guess I need to recommend it against other video series, to keep to the rules here.

I

dorecommend watching the stanford lecture videos http://www.youtube.com/user/StanfordUniversity?blend=1&ob=5 , but I recommend Khan over them for simplicity's sake on getting the basics. (Then watch stanford for a more complex understanding)And though it just covers abiogenesis and evolution, cdk007 http://www.youtube.com/user/cdk007?blend=1&ob=5#p/a does have quite a bit of overlap with khan's biology section. But it's a lot more narrow than what khan covers, and pretty much is just there to counter creationists. While that's a pretty good goal, and the videos

aregood, it's not as good for learning in my opinion.For topology, I prefer Topology by Munkres to either Topology by Amstrong or Algebraic Topology by Massey (the latter already assumes knowledge of basic topology, but the second half of Munkres covers some algebraic topology in addition to introducing point-set topology in the first half).

Both Armstrong and Massey try to make the subject more "intuitive" by leaving out formal details. I personally just found this confusing. Munkres is very careful about doing everything rigorously at the beginning, but this lets him cover much more material more quickly later, because he can safely talk about something without wondering whether the reader will correctly guess an implication, because the reader (in theory) understands the background material completely and will be able to tell what is going on.

Munkres' treatment is also far more comprehensive.

Munkres also has a lot of really good exercises, although I didn't get far enough into the other two books to really evaluate how good their exercises are.

One caveat: in topology it is easy to push definitions around without understanding what's going on. It helps to be able to draw pictures of e.g. Haussdorf condition to be able to figure out what's going on.

Subject: Economics

Recommendation: Introduction to Economic Analysis (www.introecon.com)

This is a very readable (and free) microecon book, and I recommend it for clarity and concision, analyzing interesting issues, and generally taking a more sophisticated approach - you know, when someone further ahead of you treats you as an intelligent but uninformed equal. It could easily carry someone through 75% of a typical bachelor's in economics. I've also read Case & Fair and Mankiw, which were fine but stolid, uninspiring texts.

I'd also recommend Wilkinson's An Introduction to Behavioral Economics as being quite lucid. Unfortunately it is the only textbook out on behavioral econ as of last year, so I can't say it's better than others.

Since many people will be buying books here, this is a good place to recommend that people use a book-price search engine to find the best possible price on a book. I have found the best one to be BooksPrice. DealOz is also decent. I am not affiliated with either of these in any way.

There are also price alert services that will email you when a book reaches a certain price. I've found this really useful, because while the latest version of a textbook might be $100 new and $60 used, you can sometimes get the same version used in great condition for much lower than the normal used price, especially after the end of a semester.

This is really useful when you don't need the book soon but know that you'd like to buy it at some point.

*5 points [-]It really depends on your learning style, and whether you learn best through examples=>generalizations or generalizations=>examples.

Similarly, some people may learn faster from a non-rigorous approach (and fill in the gaps later), while others may learn faster from a more rigorous approach. Some people might stare at a text for hours, but might be able to motivate themselves to learn the material much faster if they had some concrete examples first (using the Internet as a supplementary resource can help in that). I actually find it easier to learn molecular cell biology through Wikipedia articles than through textbooks, because Wikipedia articles often contain more of the information that's more emotionally significant to many people (even if not epistemically significant).

For example, I really do feel that I would have learned physics and math

muchfaster if I learned them through computer simulations (proofs could be done later - I tend to just stare at proofs if they're presented first). I'm an inductive learner, not a deductive learner, and I tend to stare at texts that are overly deductive (part of it owes to my severe inattentive ADD, but maybe some non-ADDers are in the same boat as I am there)In general, I find lectures extremely inefficient, unless there is space for

significantamounts of one-to-one feedback, either through insanely small classes or a teacher who allows you to be their pet. Since these rarely happen in college, I generally find learning from textbooks more efficient. Podcasts/video lectures are often VERY inefficient ways to learn since you can read MUCH faster than you can listen, and it's much more of a hassle to repeat a part you don't quite understand.Here's a quote I really like:

"Similarly, no one has been able to confirm any certain limits to the speed with which man can learn. Schools and universities have usually been organized as if to suggest that all students learn at about the same rather plodding and regular speed. But, whenever the actual rates at which different people learn have been tested, nothing has been found to justify such an organization. Not only do individuals learn at vastly different speeds and in different ways, but man seems capable of astonishing feats of rapid learning when the attendant circumstances are favorable. It seems that, in customary educational settings, one habitually uses only a tiny fraction of one's learning capacities." Encyclopedia Britannica, Philosophy of Education

====

That being said, here's a list of books I wish I had studied from instead of the standard textbooks: http://www.amazon.com/gp/richpub/syltguides/fullview/R2BKS9X5I8D9Y/ref=cm_sylt_byauthor_title_full_1

Also, Razib Khan has collected some pretty amazing books (you can find them on http://www.gnxp.com).

Subject: Introductory Real (Mathematical) Analysis:

Recommendation: Real Mathematical Analysis by Charles Pugh

The three

introductoryAnalysis books I've read cover-to-cover are Lang's, Pugh's, and Rudin's.What makes Pugh's book stand out is simply that he focuses on building up repeatedly useful machinery and concepts-a broad set of theorems that are clearly motivated and widely applicable to a lot of problems. Pugh's book is also chock-full of examples, which make understanding the material much faster. And finally, Pugh's book has a very large number of exercises of varying difficulty-Pugh has more than 500 exercises total.

In contrast, Rudin's book tends to focus on "magic." Rudin uses the shortest possible proofs for a given theorem. The problem is that the shortest proofs aren't necessarily the most instructive-while Baby Rudin is a beautiful work of Math qua Math, it's not a particularly good book to learn from.

Finally, Lang's book is frankly subpar. Lang leaves out critical details of some proofs (dismissing one 6 page proof as trivial!), is poorly motivated by examples, and has a number of mistakes.

If you want to really understand Mathematical Analysis and get to the point where you can use the concepts to create proofs and solve problems, Pugh is the best book on the topic. If you want a concise summary of undergraduate analysis to review, pick Rudin's book.

Thanks! Added.

*2 points [-]"Baby Rudin" refers to "Principles of Mathematical Analysis", not "Real and Complex Analysis" (as was currently listed up top.) (Source)

Fixed, thanks!

Subject: Electromagnetism, Electrodynamics

Recommendation: Introduction to Electrodynamics by David J. Griffiths

I first received this textbook for a sophomore-level class in electrodynamics. It was reused for a few more classes. I admit that I don't have much to compare it with, though I have looked at Feynman's lectures, a couple giant silly freshman physics tomes, and J. D. Jackson's Electrodynamics, and I know what textbooks are like in general.

I was

repeated flooredby the quality of this book. I felt personally lead through the theory of electrodynamics. In general, he does go from the simple and specific to the complex and general, as any mind requires. But at every stage, he knows exactly where there is risk of conceptual confusion, and he knows exactly how to correct it. He brings every clarification and result back to the thefundamentalsof the subject, and he keeps you radiantly aware of the context. After this kind of developed enlightenment, you walk away with a rationalist's mastery, at least in this specific subject. He does all this, from vector calculus review to special relativity, in 2 centimeters thick.I found that Griffiths is an excellent undergraduate textbook. It does, as you say, provide an astoundingly good conceptual understanding of electrodynamics.

I was very disappointed, however, at the level of detail and rigour. Jackson, (in my limited experience), while it may not provide the same amount of explanation at an intuitive level, shows exactly what happens and why, mathematically, and in many more cases.

This speaks to an important distinction between undergraduate and graduate textbooks. Graduate textbooks provide more detail, more rigour, and more material, while undergraduate textbooks provide insight.

There is something of a similar situation in quantum mechanics: Townsend's /A Modern Approach to Quantum Mechanics/ is very much an undergrad textbook, and indeed something of a dumbed-down version of (the first half of) Sakurai's /Modern Quantum Mechanics/. At this point I strongly prefer Sakurai, but I don't think I would be able to understand it without all the time I spent studying Townsend's more elementary presentation of the same approach.

To give yet another example, I've been slowly trying to teach myself GR, and while I love the approach and the rigor of Wald's

General Relativity, it was too hard for me to follow on its own terms. I found that Schutz'sA First Course in General Relativityprovides both the insight and better grounding in some of the necessary math (tensor analysis, getting used to Einstein's summation convention, using the metric to flip indices around) through gentler approach and richer examples. Having studied Schutz for some time, I feel (almost) ready to come back to Wald now.*3 points [-]Subject: Commutative Algebra

Recommendation:

Introduction to Commutative Algebraby Atiyah & MacDonaldContenders: the introductory chapters of

Commutative Algebra With a View Towards Algebraic Geometryby Eisenbud and the commutative algebra chapters ofAlgebraby Lang.Atiyah & MacDonald is a short book that covers the essentials of Commutative Algebra, while most books cover significantly more material. So this review should be seen as comparing Atiyah & MacDonald to the corresponding chapters of other Commutative Algebra books. There are a few reasons why

Introduction to Commutative Algebrais better than most other books:Better abstractions. The abstractions Atiyah & MacDonald use (especially towards rings and ideals) are simply more broadly applicable and make several proofs simpler. Conversely other books tend to use an older set of abstractions which make the same proofs significantly more complex.

Exercise-driven approach. Atiyah & MacDonald's exercises are beautifully structured so that you build up important parts of the theory yourself. There's a very satisfying feeling of castle-buildng: each exercise draws upon your understanding of the previous problem, and they come together to form very nice results. Many books can give you the feeling of understanding Commutative Algebra, but this one helps you discover it, which is much more enjoyable and provides a much deeper understanding.

The right kind of conciseness. Atiyah & MacDonald's book is short because they cover a limited range of topics, but they do cover all the essential tools that are widely used. In contrast most books tend to bloat by trying to cover too many things, or tend to leave out critical parts of the theory.

Thanks! Added.

*1 point [-]Atiyah-MacDonald isn't comparable to Eisenbud, as the latter covers a vastly wider swath of commutative algebra and algebraic geometry.

Good point. I've edited the comment to explicitly compare to the introductory chapters of Eisenbud.

*3 points [-]Special relativity: Spacetime Physics by Taylor and Wheeler is excellent. It reminds me of the general style of the Feynman lectures, but is in depth and has good problem sets. Like the Feynman lectures it is based on developing intuition, which is important for relativity because, like QM, every single human is born with the wrong intuition. It takes time and practice to develop. Also like Feynman, the writing style isn't akin to a barren wasteland like most textbooks. It is written to teach, not as an accompaniment to a university course. Finally, the problem sets are the best I've ever run into in any physics book.

The Feynman lectures has a few chapters about special relativity but they're short and not nearly as good as the rest of the lectures.

The first time I learned this material was through the book Modern Physics by Harris. Dodge this book at all costs. The writing is as clear as a muddied lake, or maybe a blizzard sky of deepest winter. The problems are numerous and boring. Rote physics indeed.

The MIT intro to special relativity is decent, but very dry like all the other MIT intro books. Not recommended for self study, but great as a class companion.

These are all that I've read, but there are many many more out there. This site is a bit dated but contains lots of good books. It recommended spacetime physics which turned out to be amazing. One book I see overlooked often is Einstein's own explanation of the subject. Be careful what printing you buy, or download it off of Gutenberg. It is somewhat outdated and very short, but if you only have a few hours to spare it will give you a good outline of both theories. Since it's free and short I'd recommend giving it a go before buying a textbook. I personally find SR fascinating, but others might not and this will help you decide.

Subject:Meta-ethicsRecommendation:Miller,An Introduction to Contemporary MetaEthicsReason:Jacobs'The Dimensions of Moral Theoryis shorter and easier, for beginners, but it doesn't explaincontemporarydebates hardly at all. Miller's books is more comprehensive, precise, and contemporary, and even includes some original arguments (the section on Railton is particularly good). I'd like to see an updated third edition, but the 2nd edition from 2003 is still the best thing out there for an overview of meta-ethics. Smith'sEthics and the A Prioriis pretty good, but of course it's the opinion of just one philosopher's views, and not good for an overview.The new edition (second edition - Luke must have got it wrong, the 2003 edition is the first) has arrived.

Recommended for LINGUISTICS: "Contemporary Linguistics", by William O'Grady, John Archibald, Mark Aronoff, & Janie Rees-Miller. Truly comprehensive, addressing ALL the areas of interesting work in linguistics -- phonetics, phonology, morphology, syntax, semantics, historical linguistics, comparative linguistics & language universals, sign languages, language acquisition and development, second language acquisition, psycholinguistics, neurolinguistics, sociolinguistics & discourse analysis, written vs spoken language, animal communication, & computational/corpus linguistics. Each chapter is sharp & targetted; you will really know what you want to read next after studying this text.

NOT recommended: "Linguistics: An Introduction to Linguistic Theory", edited by Victoria A. Fromkin & authored by Bruce Hayes, Susan Curtiss, Anna Szabolcsi, Tim Stowell, Edward Stabler, Dominique Sportiche, Hilda Koopman, Patricia Keating, Pamela Munro, Nina Hyams, & Donca Steriade. This text provides a solid guide to generative phonology, generative syntax, and formal semantics -- but only in their mainstream (aka Chomskian) formulations, and with no reference to actual language use (which, for theoretical reasons, is anathema to the Chomskian crowd). Interestingly, at least 8 of the authors I recognize as faculty from UCLA, which makes the text a bit ingrown for my taste.

NOT recommended: "Syntax: A Generative Introduction", by Andrew Carnie. First problem: This book covers syntax and only syntax, and does so solely from a generative perspective. Second problem: Although Carnie is a reknowned expert in Irish Gaelic syntax and doubtless knows his stuff, he can't write a clear expository textbook to save his soul. This is the most confusing book on linguistics that I've ever read.

I would also like to recommend two superb encyclopedia-style works on linguistics:

(1) "The Cambridge Encyclopedia of Language", by David Crystal

(2) "The Cambridge Encyclopedia of the English Language," by David Crystal

Both are characterized by lot of short articles, sidebars, pictures, cartoons, and examples of texts to the point at hand. I read them both cover to cover, and have refered to them again and again when beginning to explore a new topic in the field.

In the wake of publishing Scientific Self-Help: The State of Our Knowledge, I realized there is another subject on which I have read at least three textbooks: self-help!

Subject: Self-HelpRecommendation:Psychology Applied to Modern Lifeby Weiten, Dunn, and HammerReason: Tucker-Ladd'sPsychological Self-Helpis a 2,000 page behemoth of references from a passionate, life-long researcher in self-help. It was a work-in-progress for 20 years, and never mass-published. It's an excellent research resource, though it's now out-of-date. John Santrock'sHuman Adjustmentis a genuine university textbook on self-help, but it is not as mature, well-organized, or well-written as Weiten, Dunn, and Hammer'sPsychology Applied to Modern Life.*6 points [-]I don’t know how relevant improv is to Less Wrongers, but I find it helpful for everyday social interactions, so:

Primary recommendation:Salinsky & Frances-White’s The Improv Handbook.ReasonIt’s one of the only improv books which actually suggests physical strategies for you to try out that might improve your ability rather than referring to concepts that the author has a pet phrase for that they use as a substitute for explaining what it means. Not all of the suggetions worked for me, and they’re based on primarily on anecdotal evidence (plus the selection effect of the authors having run a reasonably successful improv group in the hostile London climate and only then written a book), but I know of no other book that has as constructive an approach. It also has a number of interview sections and similar, which are eminently skippable – only half the book is really worth reading for performance advice, but fortunately the table of contents make it pretty clear which half that is.I’m recommending it over Keith Johnstone’s ‘Impro’ and ‘Impro for Storytellers’, whose ideas it incorporates, breaks down and structures far better, over Chris Johnston’s ‘The Improvisation Game’, which is an awful mishmash of interviews and turgid academic writing, over Charna Halpern’s ‘Truth in Comedy’, which has quite a different set of ideas but spends more time boasting about how good they are than explaining them, over Jimmy Carrane and Liz Allen’s Improvising Better, which has a few nice tips and is mercifully short, but doesn’t have anything close to a coherent set of principles, ‘The Improvisation Book’, which I haven’t read in depth but seems to be little more than a list of games, and Dan Patterson and Mark Leveson’s ‘Whose Line is It Anyway’, which unsurprisingly is very heavily focused on emulating the restrictive format of the show of the same name.

Secondary recommendation:Mick Napier’s Improvise, which comes from a different school of thought to TIH’s – the same one as ‘Truth in Comedy’.ReasonIt's the only one of any of those I’ve mentioned (TIH included) to explicitly suggest scientific reasoning in developing and assessing improv methods. After the author’s initial proclamation to that effect, he doesn’t really communicate how he’s tried to do so, and his advice seems to assume you’re already quite comfortable with being in an unspecified scene with no preset rules (one of the hardest things for an improviser to find himself in, IME), so I wouldn’t recommend it as a beginner’s guide.This will be a study project to me after the semester so thanks for the recommendations.

Business:The Personal MBA: Master the Art of Businessby Josh Kaufman.I'm the author, so feel free to discount appropriately. However, the entire reason I wrote this book is because I spent

yearssearching for a comprehensive introductory primer on business practice, and I couldn't find one - so I created it.Business is a critically important subject for rationalists to learn, but most business books are either overly-narrow, shallow in useful content, or overly self-promotional. I've read thousands of them over the past six years, including textbooks.

Business schools typically fragment the topic into several disciplines, with little attempt to integrate them, so textbooks are usually worse than mainstream business books. It's possible to read business books for years (or graduate from business school) without ever forming a clear understanding of what businesses fundamentally

are, or how they actually work.If you're familiar with Charlie Munger's "mental model" approach to learning, you'll recognize the approach of

The Personal MBA- identify and master the set of business-related mental models that will actually help you operate a real business successfully.Because making good decisions requires rationality, and businesses are created by people, the book spend just as much time on evolutionary psychology, decision-making in the face of uncertainty, and anti-akrasia as it does on traditional business topics like marketing, sales, finance, etc.

Peter Bevelin's

Seeking Wisdomis comparable, but extremely dry and overly focused on investment vs. actually running a business. The Munger biographyPoor Charlie's Almanackcontains some helpful details about Munger's philosophy and approach, but is not comprehensive.If anyone has read another solid, comprehensive primer on general business practice, I'd love to know.

My summary of chapter 9, for anyone who cares:

Fear kills work. Inspire coworkers by showing them appreciation, courtesy, and respect. Show them they're important. Get them to work in their comparative advantage, and where they are intrinsically motivated. Explain the reasons why you ask for things. Someone must be responsible and accountable for each task. Avoid clanning; get staff to work together on shared projects and enjoy relaxation time together. Measure things, to see what works. Avoid unrealistic expectations. Shield workers from non-essential bureaucracy.

I like the book so far, it seems to pretty much a solid implementation of Munger's approach.

Spends a bit too much energy dissuading me from business school, including some arguments I found rhetorical (e.g. biz. schools started from people measuring how many seconds a railway worker does something or other. by this logic we should outlaw chemistry), but it might be useful to someone (though there are quite a few people in line to take their places).

Rather phenomenal Amazon reviews you have, sir.

*2 points [-]I remember the interview Josh did with Ben Casnocha as being very interesting. (Site contains links to streaming video and MP3 download + written interview summary.)

*2 points [-]I've added it to my list. I'm currently reading

Poor Charlie's Almanackand liking it a lot so far.The best business book I've read is probably

The Essays of Warren Buffett(second ed.), but it's certainly not exhaustive in what it covers.Update: I've got my copy from Amazon.ca (really fast shipping - 2 days). Will probably have a chance to read it in February.

I'm reading it now. I fully endorse this recommendation, but I haven't read

anyother business books, so take that for what it's worth.This book, or, to be accurate, the 20 or so pages I read, are terrible. For someone who prefers dense and thorough examinations of topics, The Personal MBA is cotton candy. It is viscerally pleasing, but it offers little to no sustenance. My advice: don't get an MBA or read this book.

The mistake I made was considering the author's appearance in this thread as strong evidence that his book would offer value to a rationalist. In fact, the author is a really good marketer whose book has little value to offer. Congratulations to him, however, since he got me to buy a brand-new copy of a book, something I rarely do.

Wow, Duke - that's a bit harsh.

It's true that the book is not densely written or overly technical - it was created for readers who are relatively new to business, and want to understand what's important as quickly as possible.

Not everyone wants what you want, and not everyone values what you value. For most readers, this is the first book they've ever read about how businesses actually operate. The

worst thing I could possibly dois write in a way that sounds and feels like a textbook or academic journal.I don't know you personally, but from the tone of your comment, it sounds like you're trying to signal that you're too sophisticated for the material. That may be true. Even so, categorical and unqualified statements like "terrible" / "cotton candy" / and "little value to offer" do a disservice to people who are in a better position to learn from this material than you are.

That said, I'll repeat my earlier comment: if you've read another solid, comprehensive primer on general business practice, I'd love to hear about it.

For the sake of clarity, my criticism of Josh's book was developed within the context of Josh promoting his book in a LW thread titled "The Best Textbooks on Every Subject."

Useful clarification. In that case, you should know that the book is currently being used by several undergraduate and graduate business programs as an introductory business textbook.

The book is designed to be a business primer ("an elementary textbook that serves as an introduction to a subject of study"), and business is a very important area of study that rewards rationality. At the time of my original post, no one had recommended a general business text. That's why I mentioned the book in this thread.

I appreciate your distaste for perceived self-promotion: as a long-time LW lurker, my intent was to contribute a resource LW readers might find valuable, nothing more.

If you're interested in the general topic and want a more academic treatment, you may enjoy Bevelin's

Seeking Wisdom. I found it a bit disorganized and overly investment-focused, but you may find it's more to your liking.I upvote you solely for the chutzpah of your self-promotion.

Which, in hindsight, is mostly what you're selling.

I think the title--and especially the subtitle, " Mastering the Art of Business,"--signals that the book will be a thorough examination of business principles. As well, I think that hocking your book in a thread called "The Best Textbooks on Every Subject" signals that the book will be, at least, textbook-like in range, complexity and information containment. You now call your book "not densely written or overly technical." I call it cotton candy.

I'd like to request Best Textbook suggestions for: climate science and/or climate policy.

Chris

Machine learning:Pattern Recognition and Machine Learningby Chris BishopGood Bayesian basis, clear exposition (though sometimes quite terse), very good coverage of the most modern techniques. Also thorough and precise, while covering a huge amount of material. Compared to

AI: A modern approachit is much more clearly based in Bayesian statistics, and compared toProbabilistic roboticsit's much more modern.Bishop, vs Russell & Norvig, are not in the same category. There's only two chapters in R&N that overlap with Bishop.

Within the category of planning, symbolic AI, and agent-based AI, I recommend Russell & Norvig, "Artificial Ingelligence: A Modern Approach", or Luger & Stubblefield, "Artificial Intelligence". They are aware of non-symbolic approaches and some of the tradeoffs involved. I do not recommend Charniak & McDermott, "An intro to artificial intelligence", or Nilsson, "Principles of artificial intelligence", or Winston, "Artificial Intelligence", as they go into too much detail about symbolic techniques that you'll probably never use, like alpha-beta pruning, and say nothing about non-symbolic techniques. A more complete treatement of symbolic AI is Barr & Feigenbaum, "The Handbook of Artificial Intelligence", but that's a reference work, and I'm recommending textbooks. I do recommend a symbolic AI reference work, Shapiro, "Encyclopedia of Artificial Intelligence", because the essays are reasonably short and easy to read.

Within machine learning, data mining, and pattern recognition, I haven't read Bishop's work. Mannila & Smyth, "Principles of Data Mining", are often used; but maybe just because they're from MIT. Larose, "Data mining methods and models", is okay, as is its companion volumne whose name I forget. My favorite is Data Mining: Practical Machine Learning Tools and Techniques (Second Edition), by Ian H. Witten and Eibe Frank. It is brief, to the point, and gives coding examples using Weka.

The best advice I can give related to statistical modeling is to look up your technique in the SAGE series, and buy the SAGE books on it. They cost about $16 apiece, less used on amazon, and are short yet detailed. Now, I

don'tmean the books SAGE tries to sell you on their website. I mean the series of about 200 small light-green-cover paperbacks that they for some reason don't tell you about on their website.But if you're reading this level of detail, it means you're going to be a specialist trying to implement or improve algorithms, and you're going to need to read entire books on each subject.

*4 points [-]Subject: Microeconomics

Recommendation: My Textbook

Obviously I have some massive bias issues in evaluating my own book, but the kind of person who regularly reads and contributes to LessWrong is probably the kind of person who would write a textbook LessWrongers might want to read. Plus, a used copy costs only $3 at Amazon.

My book even briefly discusses the singularity.

Mankiw's Principles of Microeconomics and Heyne's The Economic Way of Thinking are also good.

I'm glad you mentioned that you've written a textbook, but I'd discount your recommendation for obvious reasons. Has anyone else read Miller's

Principles of Microeconomics?*2 points [-]Does anyone have a recommendation for a comprehensive history textbook, covering ancient as well as modern history, and several geographical regions? Just something to teach me about major events and dates, wars, rulers & dynasties, interactions between civilisations, etc., without neglecting the non-geopolitical aspects of history. College-level, please. (A dumbed-down alternative to what I'm asking would be to start looking for my old high school textbooks, but obviously that wouldn't be very satisfactory.) Comprehensive accounts of single civilisations in a single period could work as well, but I'm looking for a book that is mainly didactic in purpose and with a broad subject matter.

Also: should I supplant whatever I'm studying with Wikipedia, so that I have the option of going in as much depth as I like? Or is it too unreliable even for basic learning purposes?

*1 point [-]Can't recommend a book I've read, but I've had J.M. Roberts'

The New Penguin History of the Worldon my reading list for a while now. It's more big picture than facts.If you're after rulers, dates and the like, just diving into wikipedia, starting from high-level articles and taking your own notes might not be a terribly bad approach.

I actually expect that this is a very good way to approach learning world history.

There's a

lotof history. Something that covers both ancient and modern history is going to be something like Sapiens (my summary) or the Big History Project. But Sapiens is about a particular viewpoint of history / the general arc drawn through the datapoints, not the datapoints themselves.Consider, for example, a request for a book on

allof science. The only real thing that could be recommended is a book on the scientific method, or a general history of the most important scientific ideas, but nothing that could be considered "comprehensive." To just grab four history books off my shelf, I have a 300 page one on the history of materials and material science (and how that impacted economics and politics), a 420 page book detailing the evidence for evolution over the last ~500 years in Britain, a 900 page book that tersely describes important cultural works and events in Western civilization over the last 500 years, and another 900 page book that describes four distinct cultural groups in Britain that are the ancestors of the major cultural forces in the modern US.*2 points [-]Here's, for example, a textbook I was looking into: World History by Duiker & Spielvogel. The table of contents looks pretty much like what I was seeking, though there's less focus on geopolitics and more on the civilisational "big picture" than I would have liked. (Edit: and perhaps if it were thrice the page count it would have been closer to the level of detail I was trying to get.) I was interested in getting a comparison between, for instance, this book and others of the same type.

What I'm trying to remedy is a very poor knowledge of the most basic, boring kind of historical data: who ruled when, what were the major battles and their dates and locations, what political entities and subdivisions existed and when were they founded and ended/conquered, what major reforms were made, what people produced and traded etc. I too have and can find books on very specific historical matters, and take pleasure in reading them, but they would fit better in an understanding of the hard facts and data relevant to those historical circumstances.

Would you be willing to share the titles and authors of those books?

The Substance of Civilization by Stephen L. Sass

A Farewell to Alms by Gregory Clark (Note that many contest the claims on comparisons to China, claiming that the pressures detailed were even stronger there.)

From Dawn to Decadence by Jacques Barzun

Albion's Seed by David Hackett Fisher (there is a more recent book on a very similar subject that I have not yet read here, but it has fewer pages and covers more groups, so I imagine it has less details but may be worth reading with / instead of Albion's Seed.)

*2 points [-]Subject: Animal Behavior (Ethology)

Recommendation: Animal Behavior: An Evolutionary Approach (6th Edition, 1997) Author: John Alcock

This is an excellent, well organized, engagingly written textbook. It may be a tiny bit denser than the comparison texts I give below, but I found it to be far and away the most rewarding of the three (I've just read the three). The natural examples he gives to illustrate the many behaviors are perfectly curated for the book. Also, he uses Tinbergen's four questions to frame these discussions, which ensured a rich description of each behavior. The author gives a cogent defense of sociobiology in the last chapter, which was icing on the cake.

Other #1: Principles of Animal Behavior (1st Edition, 2003) Author: Lee Alan Dugatkin

This was one I had to read for a class; it's a bit shorter than Alcock, and maybe it has been improved upon since this inaugural edition, but I found the fluff-to-substance ratio to be concerningly high. It was much more basic than Alcock, perhaps better suited for a high school audience. The chapters were written like works of fiction and the author maintained this style throughout, which I found distracting (though others may like it). Bottom line: If you have had a decent college level class in biology, you would definitely be better off going straight to an older edition of Alcock.

Other #2: Animal Behavior: An Evolutionary Approach (9th Edition, 2009) Author: John Alcock

I read through this edition too (I think there's a 10th out now) while writing my undergraduate thesis to make sure I hadn't missed any important updates in the field (I hadn't). The new edition had ~100 fewer pages; it was long on pictures (quite a few more than its predecessor) and short on content. It's been several years now and I can't remember exactly the ways in which it differed, but “watered down” comes to mind. I would highly recommend picking up an older edition unless this one is specifically required.

*2 points [-]For someone who currently has a teacher's-password understanding of physics and would like a more intuitive understanding, without desiring to put in the work to obtain a

technicalunderstanding (i.e. learning the math), I would recommend Brian Green'sFabric of the Cosmos, which I feel does for physics (and the history of physics) whatAn Intuitive Explanation of Bayes Lawdoes for Bayesian probability. It goes through history, starting with Newton and ending with modern day, explaining how the various Big Names came up with their ideas, demonstrates how those ideas can explain reality incrementally better than the previous ideas by using easy-to-envision thought experiments, and also contains a skippable explanation of the mathematic principles behind the new ideas for those who want that, although the book is valuable even without these sections. In this way, it's like a popular science book with an optional textbook component.It has a couple weaknesses, like taking M-theory seriously, but in general I would say that it accomplishes its goal of imparting an intuitive understanding better than other popular physics books with similar goals, like Hawking's

A Brief History of Time,The Universe in a Nutshell, or Green'sThe Elegant Universe.*2 points [-]Question: what are the recommended books on the following topics?

*Entrepreneurship

*Innovation management

*Inspiration (how to get inspiration for yourself and for others)

*Social Science research methods

Cheers!

There is a thread on calculus textbook recommendations here. And here are some useful textbook recommendations on mathematical logic, math foundations and computability theory, courtesy of Vladimir_M.

*2 points [-]On the basics of (normative) decision theory, I recommend Peterson's

An Introduction to Decision Theoryover Resnik'sChoices: An Introduction to Decision Theoryand Luce & Raiffa'sGames and Decisions. Peterson's book has clearer explanations and is more up to date than these others. It's main failing is to ignore the work on decision theory in computer science and in Bayesian statistics, but the other two standard decision theory textbooks (Resnik; Luce & Raiffa) skip those subjects, too.In statistical decision theory you've got Chernoff & Moses and Berger, but they're kinda out of date now and perhaps too difficult for the beginner.

*2 points [-]This guy reviewed 5 freely available calculus textbooks and chose Elementary Calculus: An Approach Using Infinitesimals by Jerome H. Keisler as his favorite. Note that the book uses a nonstandard approach.

Here are some physics and quantum mechanics recommendations that may not meet the "read three books" requirement.

Another strategy for finding good textbooks is to surf around Amazon and see what seems to have good reviews.

For organic chemistry, all the textbooks have more or less the name "Organic Chemistry", The best, if most rigorous, is by Clayden, Greeves, Stuart Warren (main author) and Wothers. Much less rigorous are the books by McMurray, or Jan Smith or many others. I find the Wm. Brown book well written but rather similar to all the rest. The market requires that the book prepare one for the MCATs which means all chemistry discovered after about 1980 is omitted. Perhaps that is why Clayden is good, it is English. Modesty prevents me from naming the one I wrote, but I would suggest that if you want to organize your thoughts, writing a textbook is not a bad way to do it.

For transport phenomena (momentum, mass, heat) I recommend Bird, Stewart, Lightfoot over Welty, Wicks, Wilson, Rohrer or Deen. WWWR is good if you need a quick reference and Deen is great for mathematical treatments, but nothing beats BSL if you are trying to actually learn transport phenomena.

For Physical Chemistry, McQuarrie and Simon is better than Atkins.

For basic Calculus, James Stewart has the best treatment.

I need book titles, please.

Subject: Criminal Justice Recommendation: Criminal Justice: Mainstream and Crosscurrents/John R. Fuller

Reason: The other intro texts on the subject are somewhat dry and tend to be just recitations of the Uniform Crime Reports and other government documents, with little interpretation. There are books by several authors (Neubauer and Albanese are two), but Fuller's book takes a critical view of the system without demonizing the system or those who work in it. Fuller's writing is also better, making reading a pleasure, which is an unusual trait for textbook. Nearly all CJ intro books delve into criminological theory, which students (including me) hate, but Fuller makes the theories clear and easier to understand. He also introduces a bit more history. Personally, I like to know where criminal justice practices come from and why. So much of it is based on common law, custom, and precedent!

This article showed up on the front page of HackerNews and on the front page of metafilter today.

*2 points [-]Logic:

--mathematical

Enderton, "A mathematical introduction to logic" then Shoenfield's classic "Mathematical logic"

Cori and Lascar, "Mathematical logic: a course with exercise" for exercises for self-study

Manin, "A course in mathematical logic" for additional enrichment

--computational

Van Dalen's "Logic and Structure" and then Fitting, "First Order Logic and Automated theorem proving" to fill in the gaps

--philosophical

From Frege to Goedel: a sourcebook in mathematical logic

additional works by Frege and Cantor in dover reprints or in the original.

"Goedel's Proof" by Nagel

"Goedel, Escher and Bach" by Hofstadter

--modal and fuzzy

Goldblatt, "Logics of Time and Computation" (Introduction to modal logic through temporal logic)

Bergmann, "An introduction to many valued and fuzzy logic"

Calculus:

Apostol, "Calculus" 2 volumes (Still a classic)

Demidovich, "Problems in mathematical analysis" (Classic drill book)

Topology:

Viro, "Elementary Topology Problem Textbook" (Based on a classic course)

Modern Abstract Algebra:

Jacobson, "Basic Algebra" volumes 1 and 2

History of Western Philosophy:

Basic primary sources in western philosophy (Not a textbook!)

*2 points [-]Recommendation requests: Intro to calculus. I know about derivatives and I can use them and I sort of understand integrals but my knowledge is very fragmented. For instance, I don't know what half of the notation is supposed to actually represent. Also, I want strategies for solving problems rather than being given a bunch of (apparently) unrelated tools and told to just figure it out.... yea, I didn't have a good math teacher

Set theory and other discrete mathematics.

Psychology.

Something or other on the scientific method (how to design experiments)

Biology. General, human, micro, intro or advanced... Just trying to make the list more comprehensive

Chemistry. See above.

Physics. There are already some here but I want more topics (thermodynamics is the first that comes to mind).

In recommendations, I would suggest another criteria be added related to learning type. Some books are being praised for their concreteness and others for their topical comprehensiveness and others for their pedagogical comprehensiveness (addresses most common misconceptions etc.) and other sometimes mutually exclusive traits. Just a way of systematizing this and making it easier for people to get the type of book that they are looking for.

Edit:Another topic: writing. I have read elements of style but I haven't read anything else on the subject. I would like to see how it compares to other (newer?) books.Re: how to design experiments:

Look into statistics. Most experiments have a statistical or hidden statistical basis.

See my suggestions above for calculus.

*1 point [-]I've got a recommendation for experimental design/general inference:

Experimental and Quasi-Experimental Designs for Generalized Causal Inference, by Shadish, Cook, and Campbell (2001)Admittedly, this is the only textbook I've ever used that was expressly for experimental design, but I really do think it is superb. Does anyone else have comparison texts for this kind of thing? The validity typology alone is heroic; statistical conclusion validity, internal validity, construct validity, and external validity are each covered in great detail, as are common threats to each of these types of validity.

Subject: Automated Theorem ProvingRecommendation: Harrison, Handbook of Practical Logic and Automated ReasoningReason: Afraid I'm going to break the rules here, I haven't read any other books on the subject but as there's nothing posted here on ATPs I thought this might be useful to someone. The book is an excellent introductory text for someone who has a CS background but not in logic, and who wants to learn about theorem provers for from a practical perspective.*2 points [-]I would like to request a recommendation for a text that provides a comprehensive introduction to Lisp, preferably one with high readability.

Structure and Implementation of Computer Programs

How to design Programs

The Little Schemer

HTDP teaches Scheme, SICP teaches computer science concepts using Scheme.

Request for textbook suggestions on the topic of Information Theory.

I bought Thomas & Cover "Elements of Information Theory" and am looking for other recommendations.

MacKay's Information Theory, Inference, and Learning Algorithms may not be exactly what you're looking for. But I've heard it highly recommended by people with pretty good taste, and what I've read of it is fantastic. Also, the pdf's free on the author's website.

I highly recommend this book, but then it's currently my introduction to both Information Theory and Bayesian Statistics, and I haven't read any others to compare it to. I find it difficult to imagine a better one though.

Clear, logical, rigorous, readable, and lots of well chosen excellent exercises that illuminate the text.

Thank you for this post. It is profoundly useful. I noted it when it first appeared and recently had the need for a textbook on a subject. Came over here and found a great one.

I would like to

request a book on Game Theory. I went to my school's library and grabbed every book I could find, and so I haveIntroduction to Game Theoryby Peter Morris,Game Theory 2nd Editionby Guillermo Owen,Game Theory and Strategyby Philip Straffin,Game Theory and Politicsby Steven Brams,Handbook of Game Theory with Economic Applicationsedited by Aumann and Hart,Game Theory and Economic Modelingby David Kreps, andGaming the Voteby William Poundstone because I also like voting theory.My brief glances make

Game Theory and Strategylook like a fun, low level read that I'll probably start with to whet my appetite for the subject.Introduction to Game Theorylooks like a good, well written intro textbook, but it was written in 1940 and was only updated once in 1994, and I would hope something new would have happened in that time.Game Theory 2nd Editionlooks like a good, moderately modern (1982) and incredibly boring book. The others look worse.I'll read at least portions of all of them and at least two or three completely unless somebody suggests anything. If no one does before I read them I'll post an update.

On systems theory, I'll recommend "Thinking in Systems: A Primer" is a great general audiences book, with a great nontechnical approach.If you are looking for something more mathematical, you'll need to ask someone else; I'm just not well read enough. (Despite being a math major back in school.)

"The Fifth Discipline: The Art & Practice of The Learning Organization" is a great book, but not as useful for systems theory in general, it's a more domain specific book. (I would recommend it, but not as the best book on the subject generally)

"Introduction to Systems Thinking" by Kim is just not as good; it's a fine book, but small and not at all comprehensive.

There are some great, slightly more technical books on the subject, like An Introduction to General Systems Thinking by Weinberg, as well, I am sure, as others. I haven't read enough of them to say that that specifically stands out among technical books on the subject. (If anyone has recommendations on the technical side, I'd love to hear them, as I would like to see more.)

Added the recommendations by joshkaufman, realitygrill, and alexflint.

Thanks, gang! Keep 'em coming.

I would like to request a recommendation for a text that introduces one to Utilitarianism.

*4 points [-]I don't read much on normative ethics, but Smart & Williams'

Utilitarianism: For and Againsthas some good back-and-forth on the major issues, at least up to 1973. The other advantage of this book is that it's really short.But there are probably better books on the subject I'm just not aware of.

For elementary economics: "Macroeconomics" by Mankiw, is without a doubt the best on the market. It is incredibly well written, and it's so good once you've read the book it fools you into thinking you understand absolutely everything on the topic! "Intermediate Microeconomics" by Varian, is arguably the one to get. It can be a tad dry, and he uses lots of maths. If you don't like the idea of that then "Microeconomics" by Katz and Rosen is a very readable and less mathematical, though not quite as comprehensive as Varian.

That's a weird feature to claim for a book you say is both good and only covers elementary knowledge.

Software engineering: everything by Andrew Tanenbaum. The standard texts in the field for good reason.

Tannenbaum wrote some Operating System books (including one on networking). He's not so much concerned with software engineering.

I've not finished reading either book, but Tanenbaum's OS book seemed very dry to me compared to "Operating System Concepts" (which has just been delightful to read!).

the absolutely wonderful thing about textbooks is that you can often pick up older editions for the price of a paperback novel.

In college, I found most of the time that the professor's lecture notes contain almost everything of value that both the textbook and the lecture contains, but they contain ten times less text. This led me to believe that textbooks are a terribly inefficient way to convey facts, by comparison to the format of lecture notes. Books are words, words, words, flowery metaphors, digressions, etc. Hell, I don't know what they spend all those words on. But I know that, potentially, lecture notes are one fact after another.

I find all those extra words surrounding the bare facts in textbooks to be highly useful. That's what helps me not just memorize the teacher's password but really

understandthe material at a gut level.I usually find that (good) textbooks can let you learn the subject matter by yourself, whereas lecture notes are excellent reference material but, if you didn't attend the lectures, they're just not going to make for good building material on their own.

I join NihilCredo and lukeprog in this. Textbooks usually have less text than what I would find ideal, not more. Lecture notes (and many textbooks which seemingly obey the even formula to text ratio) take me more time to read than a book which contains the same number of formulas and four times as much text. I can't continue reading after having stumbled upon something which looks like an inconsistency, non-sequitur or counterintuitive definition (that usually first happens on page 5 or so) and then have to spend time trying to find out what is wrong (and if I fail, then must spend some more time persuading myself that it doesn't matter and reading can continue). On the other hand, if the author spends some time and pages explaining, such events occur much less frequently.

Just so you know, the title of Spivak's book has been misspelled as

'Caclulus.'Another attempt to do something like this thread: Viva la Books.

*1 point [-]Subject:Written style and compositionRecommendation:Rhetorical Grammar: Grammatical Choices, Rhetorical Effects, by Martha Kolln and Loretta GrayReason:After reading Pinker'sThe Sense of Style, I wanted a meatier syllabus in the mechanics of writing well. My follow-up reading wasRhetorical Grammarand Joseph Williams'Style: Ten Lessons in Clarity and Grace.I would actually recommend reading all three.

Rhetorical Grammaris the most textbook-y of the recommendations, andThe Sense of Styleis more like a weighty, popular book on the subject, withTen Lessonsbeing more of an extended exposition/workbook on (you will be unsurprised to learn) ten broad principles of clear writing. All three books have similar messages and convergent positions on the subject matter.Rhetorical Grammarwins out for being the book I imagine one would learn most from.Does anyone know some good textbooks for animal anatomy and ecology? I haven't found any good ones so far...

For Introduction to Computational Fluid Dynamics, the book I would recommend is "Numerical Heat Transfer and Fluid Flow" by S. V. Patankar.

Most common Finite Volume codes used for incompressible flows are based on a method (SIMPLE) originally created/invented by the author, Patankar and this book has a from-the-horse's-mouth appeal and doesn't disappoint. The book is somewhat limited because everything builds up to explain the SIMPLE algorithm and the focus is narrow. However it does this very well. Another limitation is that it is short on worked out examples thought it does have end of the chapter problems. The other issue is that the last edition is from early 80s and so there is very little coverage of anything that has happened in this field since then, which is quite a lot. Still, the book is very good for what it does and quite short too.

Other books that address some of the shortcomings of Patankar's book are:

1A) "An introduction to computational fluid dynamics: The finite volume method" by HK Versteeg and W Malalasekera. This contains a lot of nice worked out examples that help explain the concepts well. I would happily recommend this book as a replacement for Patankar's book - it was a tossup. They keep adding more stuff to each edition though and you should get this book too.

2) "Computational Methods for Fluid Dynamics" by Joel Ferziger and Milovan Peric - this is an excellent book too. It is more of a general CFD book and covers much more of the subject that the first 2 books, though not with as much detail on any one subject. There are little or no worked out examples in this book.

3) One of the standard books for CFD is the book "Computational Fluid Mechanics and Heat Transfer" by Richard Pletcher , John C. Tannehill , Dale Anderson. It is a classic.

4) Numerical Methods for Internal and External Flows by C Hirsch is quite comprehensive too.

Would love to hear from others on what books they use, both from academics and people in the industry.

*1 point [-]These two books are great for those who want to study Computer Sciense in a breadth-first manner. While each topic is not discussed in great details, the number of covered topics is mind-boggling. From trivial ones such as Sorting and Searching to more esoteric matter like Pricing Algorithms for Financial Derivatives, etc.

I'd like to request a book on

Mathematical Economicsthat teaches you the basics of building and solving utility based microeconomic models (without strategic behavior).Fundamental Methods of Mathematical Economics by Alpha C. Chiang is a sufficient basis for entering a graduate programme in Economics. Mathematics for Economists by Carl P. Simon and Lawrence Blume is a higher level book. For miroeconomics as such you probably want to start with Intermediate Microeconomics by Hal Varian, and if you need more you can go to Microeconomic Analysis by same. David D. Friedman's Price Theory is absolutely fine and on his website, free as well.

Could you clarify what you are looking for? When I think of mathematical micro models without strategic behavior, my mind goes to general equilibrium models with a continuum of agents. Your use of 'building' suggests you are thinking of something else though.

Can anyone think of a good textbook on research in nursing? The one I have is abysmal and I literally cannot read it, thus I have a C in the class. Something in English might help. (I'm taking the class in French and although I'm almost equally fluent in both, I do find it harder work to read in French.)

Any recommendations for a textbook on cryptography?

The math, or application thereof?

For the latter, Applied Cryptography, by Bruce Schneier is the standard response, and surprisingly readable. I've read other books in the field, but nothing I can think of that's quite as much a "textbook", so this recommendation may or may not officially count.

And of course, a caveat applies to any book on cryptography: don't read it and start coding your own algorithms - anyone can invent a cryptosystem he can't break himself. If you're planning on doing development, the only safe way to handle this stuff is to use well reviewed, well maintained libraries. A textbook will give you a sense of what's available and how things might fit together.

Updated again. Thanks, people! Keep 'em coming!

I haven't had much success with textbooks. I have found them to be mostly boring and riddled with errors. I interpret boredom to mean that I'm not learning anything.

Here's a possible explanation for the boringness. Are you familiar with the experience of not being able to understand how you didn't get something, right after you've got it? The same presumably applies in the minds of professors.

It's hard for them to imagine not understanding the ideas. One can't know what the reader knows and doesn't know and what his misconceptions are. Teaching generations of students helps, but not much, and it won't help at all with tacit knowledge communicated face-to-face, but not via text.

Incidentally, that's probably why textbooks are so full of mistakes: not only do they contain arcane symbols which cause typos, but, being boring, nobody reads them anyway and the errors remain uncorrected.

The solution I think is to make two texts: one main text, which can be edited online to fix errors, and accompanying notes

written by readers, with links to better material wherever possible.If textbooks don't work for you very often, what

doeswork for you?*1 point [-]I would like to

request a book recommendation on probability theory.Following the rules if possible.

*6 points [-]Feller comes in two volumes, and goes from extremely introductory to measure theory in the second volume. It's a classic and Feller is famous for his writing style, and so this is probably the best book. I remember finding it confusing once upon a time, but that was probably because I was too young and not because of the book.

Ross is elementary, and isn't a measure-theoretic approach, and has lots of applications (e.g. to queuing theory and operations). It's handy as a "gimme the facts" kind of book -- if you want to look up common distributions and formulae you'll find them in Ross faster than anywhere else -- but it doesn't have all the mathematical foundations you might want.

Koralov and Sinai is a measure-theory based probability course. The second half of the book has stochastic processes, martingales, etc. If you don't know any probability at all (let's say... haven't seen the Bernoulli distribution derived) or if you haven't seen measure theory, it's probably not intuitive enough to be your first textbook. I had no complaints with the presentation; it was all straightforward enough.

Basically, I'd split the difference between elementary and advanced by using Feller; he includes EVERYTHING so you can safely skip what you know and read what you don't.

Feller is very good, though I haven't even finished vol1. I also like Tijms for real beginners - easy and fun, good examples. http://www.amazon.com/Understanding-Probability-Chance-Rules-Everyday/dp/0521701724/ref=sr_1_1?ie=UTF8&qid=1296163232&sr=8-1

The best introductory book I've read is

Chance in Biology: Using Probability to Explore Natureby Mark Denny and Steven Gaines. While most introductory books have mainly examples from games of chance, this book uses examples from physics, chemistry and biology. It's very accessible and it takes you very fast from the basic rules of probability theory to useful examples.I would also recommend Jaynes' lectures. They're more informal than the book (and also free :D). These I think are the best for quickly understanding the "subjectivist" approach to probability theory.

*1 point [-]I was just about to ask the same question, specifically for a measure theoretic treatment of probability theory. I've only read/still am reading Measure Theory and Probability Theory by Athreya and Lahiri for the second of a two course sequence and am not too impressed. For one, there are many typos that decrease the readability unless you're already familiar with measure theory and functional analysis (I was not). I haven't read any other texts of this nature, so I can't make any comparisons.

*1 point [-]But what exactly do you want to learn? If you study widely, surely you are trying to learn something different from what specialists in their respective fields try to learn. They might for example forgo a general understanding for specialist knowledge, because that is how they could best hope to contribute something unique to their field and hence reap the rewards of status. They might overemphasize certain methods of their fields since only discoveries through the use of such methods can hope to contribute results to their field.

An example:

from here

Perhaps it's better to have textbooks written for

otheracademics outside of a specialty, since such textbooks are forced to be tolerable/comprehensible to outsiders they are less susceptible to disciplinary navel gazing. They might aim to show off their specialty to others, instead of showing off the author's prowesswithinthe specialty, but even this is an improvement, since they must achieve that through appealing to a wider audience with diverse interests/aptitudes.What would be a general solution? Michael Vassar's idea of 'lightness of curiosity' helps I think. You should always make sure your curiosity tracks your goals. Do not rely on Schmidhuber's notion of curiosity as compression, because a discipline can hoodwink you by introducing difficult and enticing subproblems within the field which only practitioners would be interested in solving.

sark,

Yes, that's something I learned only recently. My earlier studies touched on all kinds of subjects, without a clear focus on where I was going or why I needed to spend time thinking about certain problems. These days, my study is tightly focused on the subjects that interest me, with the additional burden of occasionally reading philosophy of religion as well so that I can keep things interesting at my blog 'Common Sense Atheism.'

It seems to me that some sort of rudderless exploration is necessary to get a large enough set of potential problems for you to select a good one to focus on. After all, outside of very limited contexts you can't say "best possible," just "best I've seen."

I think that it pays to be rationally ignorant. It is an economic fact that the more people specialize, the more they get paid and the chance of making a significant contribution in their particular field increases. You can't achieve your best in being a doctor if you spend valuable time reading textbooks about Western philosophy or quantum computing instead of reading textbooks about diseases. There is a saying capturing this thought: "jack of all trades and master of none". Sure, there are some fields such as AI at the intersection of many sciences - however, I doubt that most people on this blog (including me) are capable of handling that much information while producing new results in the field in a reasonable amount of time.

So, instead of reading the intro textbook of each field/science (I bet there are more such fields than anyone can handle in a normal, no-singularity lifespan), the best approach for me is to learn a little about each field in my free time - just enough so that I will not be ignorant to the point of making serious mistakes about the nature of reality, and sufficiently easy on the mind so that I maintain the processing power for the main work: digging as deep as possible into the field of my choice.

So, I disagree with the author and think that Teaching Company courses are more useful than textbooks... except for the textbooks pertaining to your chosen specialty.

There is a real danger in becoming more absorbed with the exploration of rationality and science than with focusing on, and excelling in, your own field. I myself am guilty of this.

I have a gut feeling that there are

lotsof low-hanging fruit that could be picked by people reading more widely and applying the tools of one discipline into another. For instance, Aubrey de Grey claims that because he had a computer science background, he was able to start contributing new content to biology after studying for the field for only a very short time. There might be simple, obvious ways of expanding a field by bringing in new tools of analysis from another field, but none of this happens because most people only specialize in their own field.I'm also reminded of this discussion:

Working on the intensive margin seems to me to be what happens if you specialize too deeply in just one field or two (economics and math in this example), while work on the extensive margin requires you to read widely or otherwise become familiar of new areas to which your standard tools to be applied to.