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Studying Self-studying mathematics - Discussion

  1. Mar 21, 2015 #1
    Are you self-studying mathematics? Do you have any questions on how to handle it? Anything you want to share? Do so here!
  2. jcsd
  3. Mar 21, 2015 #2
    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!
  4. Mar 22, 2015 #3
    What textbooks are the best ?
    Last edited: Mar 22, 2015
  5. Mar 22, 2015 #4
    That will be something for the following posts :)
  6. Mar 22, 2015 #5
    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.
  7. Mar 22, 2015 #6
  8. Mar 22, 2015 #7
    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?
  9. Mar 22, 2015 #8
    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.
  10. Mar 22, 2015 #9
    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?
  11. Mar 22, 2015 #10
    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 :-p ), 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.
    Last edited: Mar 22, 2015
  12. Mar 22, 2015 #11
    Do you have experience about self-studying physics ?
  13. Mar 22, 2015 #12
    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/Classical-Mechanics-R-Douglas-Gregory/dp/0521534097 I'm sure a physicist will look at these things completely different. For example, many physicists prefer Kleppner: https://www.amazon.com/Introduction-Mechanics-Kleppner-Daniel/dp/0070350485 (be sure to buy the first edition, not the later ones).

    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.

    Why don't you post the problems here on PF? Wouldn't that be easier for you?

    I agree his text could use some more problems. I like text with a lot of problems.

    No, I do not. Hence why my guide is only about mathematics. Although I'm sure many tips also hold true for physics.
    Last edited by a moderator: May 7, 2017
  14. Mar 22, 2015 #13
    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?)
  15. Mar 22, 2015 #14
    Certainly, but don't like post 10 questions at once. Only post like 3 questions at once and more questions if they get resolved.

    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.
  16. Mar 22, 2015 #15
    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? ;)
  17. Mar 22, 2015 #16
    Thanks for the good advice! I will be sure to start posting my proofs here.
  18. Mar 22, 2015 #17
    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.
  19. Mar 22, 2015 #18
    Dear friends, as it was nearly 4 decades since I studied mathematics as part of my german high school and as part of the mechanical engineers study my mathematical abilities have strongly eroded and besides that mathematics has had quite a development in this time. I am surprised reading the contributions to this thread totally ignore what I consider the most valuable resource available for self study, not just in mathematics! In many countries around the world universities are making their courses available in the Internet for free. This has the advantage that you can choose a lecture from a professor whose style fits best to your personal learning preferences. For engölisch speaking people like you in this forum I would highlight the offering from the MIT in Boston through its program "OpenCourseWare". You can search through the courses offered, all for free by going to this place! I even prefer to go to this place, where courses are listed by course number, where Mathematics appears under department 18. If you go to department 18 on the left most column of the table and select it by clicking on it, you find the course numbers listed on the center column and on the bottom half of the screen a scrollable list of all the courses availble. If you focus on those that have the letters "SC" at the end of the course number you find the most complete offerings for self paced courses. To get my eroded mathematical skills up to speed I have chosen to go through the courses of "Calculus Single variable, 18.01SC and Calculus Multivariable, 18.02SC. Clicking in the course 18.01SC on the right column you see that the course is as taught in fall 2010! Clicking on the "RESULTS" offered below you get here! Same is true for 18.02SC where I offer you the link to here! Similar by the way can be found for physics courses! get a view of what the courses offer, I believe excelent videos of the lectures and assignments, excellent reading and exercises in the book to read, which is also available for free from Gilbert Strang, the professor who offers an excellent lecture about "Linear Algebra, also offered here, whose recorded course was held in 2011! Analysis 1 and 2 I prefer it following the book from "Terence tao", on whose personal page in the Internet you get download the books that are the reading for the Analysis course with honors he teaches on the UCLA! As video recorded lecture I personally prefer the recorded lecture from a german Professor, Groh, who teaches at the university in the city of Tübingen, Germany, but following the books of Terence Tao.
  20. Mar 22, 2015 #19
    How many subjects do you like to self study at a given time? Do you focus on one subject or a few at a time?
  21. Mar 22, 2015 #20
    I am currently self-studying 6 subjects at a time. But I'm a bit extreme. I think 3 should be a decent number.
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