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 much faster 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 significant amounts 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
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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).
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:
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.
Subject: Cognitive Science
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 02-25-2017):