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Are you self-studying mathematics? Do you have any questions on how to handle it? Anything you want to share? Do so here!
That will be something for the following posts :)What are the best textbooks ?
Yes, Rudin is a difficult book. It's not really suitable for self-study because of these things. It's better for a class textbook so the professor can give some extra explanations. But you can of course always ask here if you have a problem with anything.I just started going through Walter Rudin's Real and Complex Analysis. The hardest part for me is that he often says "A clearly follows from B," but I don't see how it clearly follows. After reading the problem in question 3 or 4 times over the span of a few days, I get it. But that takes a lot of time!
[emoji4][emoji2]That will be something for the following posts :)
From this post and your more extensive one, it seems you've had a lot of experience self-studying. What do you study, and why?Yes, Rudin is a difficult book. It's not really suitable for self-study because of these things. It's better for a class textbook so the professor can give some extra explanations. But you can of course always ask here if you have a problem with anything.
Right now I am studying some probability theory and some analysis. But most of my experience comes from guiding people who self-study. So now I am just writing down my experiences.From this post and your more extensive one, it seems you've had a lot of experience self-studying. What do you study, and why?
It really depends on what physics and math you already know. But as a mathematician, I have always enjoyed this book: https://www.amazon.com/dp/0521534097/?tag=pfamazon01-20 I'm sure a physicist will look at these things completely different. For example, many physicists prefer Kleppner: https://www.amazon.com/dp/0070350485/?tag=pfamazon01-20 (be sure to buy the first edition, not the later ones).Hey Micromass, I don't know whether this will be addressed in your textbook thread so I'll ask here just in case - which physics texts do you recommend for self-study by a prospective (i.e. undergrad) mathematician with an interest in the subject?
LADW is an extremely good text. It contains about everything one should know about linear algebra, and he does it the way I would do it. Not that it matters to me, but the book is completely free which is awesome.I am self-studying linear algebra using Sergei Treil's "Linear Algebra Done Wrong". I have to say that, *despite its name* (everyone has to add this one ), it is a wonderful book. I also discovered that I enjoy the abstraction in his approach, especially the treatment of vectors not as "something that has both magnitude and direction" but as elements of a set satisfying some definite axioms - a very enlightening and new approach to me. The only drawback is that there is no solution manual anywhere and in order to get feedback on the validity of my solution/proof I have to extensively search Google to hopefully find a similar problem solved somewhere (and I do not always find). Also, some more problems could be helpful.
On another note, I really like the idea of a thread dedicated to self-study. Great idea as I feel this topic should receive more attention here and in general.
No, I do not. Hence why my guide is only about mathematics. Although I'm sure many tips also hold true for physics.Do you have experience about self-studying physics ?
Definitely. It's just that often it takes time to write these posts. I should probably do so more often though (can I shamelessly bombard the questions section with lots of small problems?)Why don't you post the problems here on PF? Wouldn't that be easier for you?
Certainly, but don't like post 10 questions at once. Only post like 3 questions at once and more questions if they get resolved.can I shamelessly bombard the questions section with lots of small problems?
Thanks for the good advice! I will be sure to start posting my proofs here.In my opinion, proofs can be learned best by letting somebody critique your proof. So ask somebody to rip apart your proof completely. It is really the only way to learn. Watching somebody else's proof doesn't teach you much. Computational problems are very different though.
It's very tricky to learn it well. You can always read a proof book, but I don't like that option very much. Much better is finding somebody who is willing to critique your proofs. That way, you can start any math book (like analysis, algebra, discrete math) and start doing proofs. First you will suck, but if you keep asking for advice, then your proof abilities will get better fast. After a short while, you'll be very good at it.Apologies if this is slightly off-topic but what would you say helped you most in getting to grips with the nature of mathematical proof? Was there a particular class or text you can pinpoint as being of critical importance? Did it just come to you with time, experience and growth in mathematical maturity? Or were you one of those very lucky few who seem to be born with an innate understanding of mathematics and her methods? ;)
I have used a few of the Rudin books in classes, and I suggest that you read the exposition quickly the first time, marking but not dwelling on roadblocks like the one you mentioned above. Then as you do the exercises, go back to the exposition and study a proof further if you need some of the techniques used to solve a particular problem.I just started going through Walter Rudin's Real and Complex Analysis. The hardest part for me is that he often says "A clearly follows from B," but I don't see how it clearly follows. After reading the problem in question 3 or 4 times over the span of a few days, I get it. But that takes a lot of time!