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Mathematical Proof - Books

  1. May 28, 2012 #1

    Could anyone recommend a good introductory book for learning how to write mathematical proofs.

    Thank you.
  2. jcsd
  3. May 28, 2012 #2
    How to Prove It by Daniel Velleman

    I'd post a link to Amazon but I have less than 10 posts. It's cheap but well written.
  4. May 28, 2012 #3
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  5. May 28, 2012 #4

    Dr Transport

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  6. May 28, 2012 #5
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  7. May 28, 2012 #6
    Are those appropriate for first proofs or for people who have some proof experience already? I've done proofs in linear algebra, number theory, etc. but I've never taken a discrete math or mathematical logic class. I know induction, contradiction, contraposition, and such, but I'd like to have some more experience before I take more rigorous courses like algebra and analysis this fall. (It's a long story, but I'm doing transitional coursework in grad school, and my university teaches proofs in the advanced sequences rather than in a separate logic class.)
  8. May 29, 2012 #7
  9. Jun 3, 2012 #8


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    I second this book. I went from a novice to decent proof writer after reading Velleman's book.
  10. Jun 3, 2012 #9
    My proof writing class used Doing Mathematics: an introduction to proofs and problem solving by Steven Galovich.

    However, I didn't particularly like the class or the book (though there are a lot of fun problems at the back of the book), not because either one was bad, but I didn't like learning how to prove things for its own sake. I got a better experience with proofs from abstract algebra and topology classes.
  11. Jun 4, 2012 #10
  12. Jun 4, 2012 #11
    Elementary Analysis: The Theory of Calculus, by Kenneth A. Ross
  13. Jun 4, 2012 #12


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    "If yer gonna be stoopid, ya gotta be tough"

    I heard this as "life is hard; if you're stupid, it's really hard!"

    oh yeah, proofs: i agree it is best to learn actual proofs of interesting things, but a tiny basic amount of logic (propositional calculus) helped me, from Principles of mathematics, chapter one I think.
  14. Jun 19, 2012 #13
    Hello to all,

    Wow this thread has really taken off. Thanks for all the suggestions. I actually bought Velleman's book. I just finished the first three chapters. It's really well written.

    Good luck.
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