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Methematics its Method, Conecpets and Meaning

  1. Oct 30, 2007 #1
    My question is does anyone know of some good books at getting a well rounded understanding of math?

    And the explanation of my question is as follows: (Any suggestions would be awesome)

    I have some complicated circumstances that have ultimately left me 22 and with a wholly unsatisfactory if not sad understanding of Mathematics. I am enthralled with the threadbare understanding of mathematics I have now. I wish to only evolve that understanding as much as I can. My problem is that I don’t have the time or cash to go to college right now and no education since the 6th grade. I want to learn these things and I don’t care how hard it will be. So I have begun trying to teach myself these things.

    I have selected few books to start as a general framework to make it to an understanding that allows me to dive far deeper into Mathematics in order to give myself the proper tools to understand physics..
    Mathematics: Its Content, Methods and Meaning or M:ICMM by A. D. Aleksandrov, A. N. Kolmogorov, and M. A. Lavrent'ev
    and as a supplement Dictionary of Mathematics Terms (Barron's Business Dictionaries) by Douglas Downing Ph.D

    My problem is that around page 72 of M:ICMM I lost steam and floundered. This was about the time in the book a jump was made from geometry and basic algebra in rapid succession. After reviewing the circumstances I made the determination that the problem was that I had missed several or more pieces of information that would allow me to understand the material in question. This is thing as I haven’t had any real formal education in math since I was 10 years old. Since that time I have not had the opportunity to gain a lot of the fundamentals of almost every discipline of math. I can read and understand the material in the first book I mentioned without much difficulty.
  2. jcsd
  3. Oct 30, 2007 #2

    Chris Hillman

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    Sorry to hear you didn't like the book coauthored by Kolmogorov (one of the greatest mathematicians, also one of the greatest teachers, of the last century... mumble mumble 2Co4:3)

    Here (mumble mumble Jn16:24) are some more classic popular books:

    Hilbert and Cohn-Vossen, Geometry and the Imagination, Chelsea, 1952 (translation of German language classic; still in print)

    E. T. Bell, Men of Mathematics, Simon & Schuster, 1937 (still in print in new editions)

    Edward Kasner, Mathematics and the Imagination, Simon and Schuster, 1940

    E. T. Bell, The Development of Mathematics, Dover, 1992 (reprint of 1945 original)

    Richard Courant and Herbert Robbins, What is Mathematics?, Oxford University Press, 1948 (reprinted by Dover).

    E. T. Bell, Mathematics: Queen and Servant and Science, McGraw-Hill, 1951

    James R. Newman, The World of Mathematics, four volumes, Simon & Schuster, 1956 (I believe that at least some volumes have been reprinted).

    Hans Rademacher and Otto Toeplitz, The Enjoyment of Mathematics, Princeton University Press, 1957

    Mark Kac and Stanislaw M. Ulam, Mathematics and Logic, Praeger, 1968

    Ian Stewart, The Problems of Mathematics, 2nd edition, Oxford University Press, 1992
    Last edited: Oct 30, 2007
  4. Oct 30, 2007 #3

    Thank you very much for that list. I am in the process of purchasing a few right now.

    I found the The World of Mathematics: Edited by James R. Newman released by Dover in 2003. Amazon Page

    I probably wasn't clear enough in my post. M:ICMM has been the most helpful resource I have found so far. I am looking for books of the same caliber. I love the book, sadly though I am missing the pieces of information that would help me to better understand his work.

    I am glad that I picked the right author to read :)
    Last edited: Oct 30, 2007
  5. Nov 1, 2007 #4


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    i myself have seldom found it helpful to read surveys of mathematics. on the same principle that caused gurdjieff to say "if a man can even make a cup of coffee, you can talk to him" and a famous magic teacher to say "if you can do one trick well, you are a magician", i suggest learning a small topic in mathematics well, and then progressing to another one.

    there are exceptions. the book by courant and robbins listed above by chris succeeds in being both a survey and a deep discussion of particulars. read whatver you can understand and try to advance to harder books.

    good luck.
  6. Nov 1, 2007 #5
    Choose a topic: calc, linear algrbra, whatever you can understand.

    Get some books, read them and take notes then do the problems.

    When you get stuck post questions here.

    Try to get in to a course, you might be able to try auditing a course.

    Don't give up!
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