All of AnatoliP's Comments + Replies

That's an interesting idea, although the discussion was about studying. I assume it can also be applied as a studying technique: Read small chunks of material and solve a lot of problems for feedback.

My point was that you cannot overlook the fundamentals.

AnatoliP-40

Perhaps RERO is the right way to develop software, but it will fail you in math.

4gjm
I suspect it might work quite well in collaborative mathematics. Publish (internally, to your collaborators) when you get a new idea, have a rough sketch of a proof, find a plausible conjecture, think of a good way of presenting something, etc. Eventually, of course, you'd need to clean it all up and get the bugs out, but frequent informal known-buggy "releases" might be an excellent way to get from zero to a high-quality research paper.
-4Shmi
Tell that to Zuckerberg, a big fan of RERO.

Check out Tricki.

It's a repository of useful mathematical techniques. From my experience, many skills can be developed through practice.

For calculus I strongly recommend Rudin. Reading the book (~ half of it) line by line and doing the great exercises was very difficult but gave me a real insight into calculus and mathematical thinking in general.

0JMiller
Thanks, I'll check em out.
5Shmi
Suggesting Rudin to an engineering or a programming student not already mathematically inclined is like offering a text in metallurgy or forest management to an apprentice lumberjack. They will learn nothing and give up in frustration almost immediately. Stewart calculus is plenty, and in some ways overkill.

That's a good question.

Many estimates can be easily checked when you have access to a data source (encyclopedia or the Internet), e.g. object heights, distances, populations etc.

Other estimates are more complicated to check (e.g. probabilities). In that case you can attempt to estimate the same thing using different techniques. This is useful for debugging and may give a general idea of your accuracy (if 3 independent estimates are close to one another, you are likely not mistaken by too much).

Also, its easier when a few people independently estimate the ... (read more)

Great examples. Next step is calibrating the confidence range based on multiple experiments.

Even 10% of all the children is many. I wonder what percentage was familiarized with numbers in that context. My guess is < 2%.

3Gunnar_Zarncke
I remember doing simple arithmetic with my father as 'bed time story' - and having fun with it. I'm just passing this on to my children who mostly like it. But then math an numbers and patterns and experiments are very present at their home, so at least some interest is to be expected. I have been asked how I'd feel if they later abandon math for e.g. following (or becoming) a guru. And I thought: Why not. My intention was always to teach knowledge instead of values. Values can only be lived. And all rules trained will become continegnt during puberty anyway. But knowledge - like math - cannot be lost. You cannot unbecome a scientist.

It looks like you are doing a good job with your kids.

There is also a whole set of questions dealing with probabilities. For example: "what is the chance I'll meet someone I know when going on a weekend trip?". These kind of questions often require more than one step.

Thanks. I wonder if there are more games like this.

3Gunnar_Zarncke
The Fermi Box is not really a 'game'. If you go on weekend trips with your children you can do lots of such games in the train (or car) because there are often large numbers of cars trees, animals, houses going by which easily promt the question how many of these are there during the trip, in view, in the city...

Did you do this spontaneously, or did your parents or teachers encourage you to?

My parents definitely encouraged me, although some inner disposition was probably there as well.

but I will

Glad to hear that.

I graduated a couple of years ago in Engineering. (Israel)

In general, it took more effort with large intro class sizes.

I think the main reason for this is not the size itself but the fact that for a large number of students these classes are not very relevant to their future profession (or so they thought). For example, math for engineering/computer science students. I think the motivation of the class in general is more important to your experience.

Regarding your other questions, the experience did not affect my career decisions and in most of the classes the use of technology was restricted to a class website.

I graduated a couple of years ago in Engineering. (Israel) In general, it took more effort with large intro class sizes. I think the main reason for this is not the size itself but the fact that for a large number of students these classes are not very relevant to their future profession (or so they thought). For example, math for engineering/computer science students. I think the motivation of the class in general is more important to your experience.

Regarding your other questions, the experience did not affect my career decisions and in most of the classes the use of technology was restricted to a class website.

10 decibans means 1:10 odds (~90%), 100 decibans 1:100 odds (~99%)

I think you have a typo there, shouldn't it say 20 decibels.

0DataPacRat
That's one of the more embarrassing typos I've made this week. :)
0OnTheOtherHandle
Wow, thank you. I'll check it out.
AnatoliP100

Hello, I stumbled upon LW a few months ago. Some of the stuff here I find extremely interesting. Really like the quality of the articles and discussions here. I studied math and engineering, currently working as a s/w developer, also very much interested in economics and game theory.

Cheers!

Very interesting.

It always amazes me how insightful scientists sometimes are, even more so when you consider the technological capabilities of their time.

To put it another way: its amazing how little we have progressed on the fundamental issues despite the exponential growth in computing power.