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How to write proofs

  1. Apr 21, 2008 #1
    I searched around and I found some books on how to write proofs. There are so many of them that got good review and I have no idea which to choose. Here are some books I am considering:

    How to Solve It, by Polya
    An Introduction For Mathematical Reasoning, by Eccles
    The Nuts and Bolts of Proofs, by Cupillari
    How to Read and Do Proofs, by Solow

    Which one should I get? They all seem relatively expensive. Are these books much better than free online books and are they worth the price?
  2. jcsd
  3. Apr 21, 2008 #2
    You can learn a lot online, but if either of those are real "text books" then they have a lot of information, easily packaged and sectioned so you know which parts to learn first, second, etc.

    If you have a book store nearby that for some reason has text books, I'd look over them and see which ones you think would be better to learn from.
  4. Apr 22, 2008 #3
    What do you mean expensive? Both Polya and Solow are under $20! Cupillari is about $30, and Eccles is about $50. For textbooks these are relatively inexpensive.
  5. Apr 22, 2008 #4
    It's the $50 book that is kind of expensive. I want to know if it is worth the money. I wouldn't mind spending $50 if it is that good. Actually, I could get it for much less if I buy it used, but still, I want to get something good.
  6. Apr 22, 2008 #5
    the best way to learn to write proofs is to get them checked.
  7. May 15, 2008 #6
    How to Solve it won't really teach you to write proofs. Its sort of different.

    A better book is How to Prove it by Velleman. Its the best of all the proof books.
  8. May 24, 2008 #7


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    i myself learned from "principles of mathematics", by allendoerfer and oakley. i also recommend the first edition of geometry, a high school book by harold jacobs, yes i am serious. this is a good choice for most college students today, but not the current third edition.

    I.e. high schoolbooks from the 60's are adequate college books for today, but current high school books are not rigorous enough.

    [college has finally become high school, and high school become grade school i suppose.]

    I dislike many of the books suggested above (Eccles, Solow, Velleman), (I do not fault polya, but agree it has a different purpose), and will use instead:

    An Introduction to mathematical thinking, by William J. Gilbert and Scott A. Vanstone,

    in my proofs course this fall.

    uhoh! apparently this book is popular, and costs over $40 USED!

    here we go:

    Principles of Mathematics
    Allendoerfer, C. B. [and] Oakley, C. O.
    Bookseller: K&R's FIRSTEDITIONS
    (Colorado Springs, CO, U.S.A.)
    Bookseller Rating:
    Price: US$ 2.90
    [Convert Currency]
    Quantity: 1 Shipping within U.S.A.:
    US$ 4.70
    [Rates & Speeds]
    Book Description: McGraw-Hill, New York, 1955. Hardcover. Book Condition: Good. 1st Edition. Hardcover in good condition. Bookseller Inventory # A2H6802FEB

    this book covers proofs, sets, countability and uncountability, boolean algebra, groups (Only trivially), analytic geometry, complex numbers, some calculus, and probability. a great bargain.

    as always, do your own research in the library to find one you can understand. Since those of us recommending do not agree, you may not agree either.
    Last edited: May 24, 2008
  9. Sep 7, 2008 #8
    I requested the book you suggested mathwonk, I really need help in my Abstract Algebra class. Hope it's good, thanks :)
  10. Sep 7, 2008 #9
    May I ask why you dislike Velleman? You are an authority on the subject, so I am in no position to question you, but I have used Velleman and can only say it made theoretical math easier. You frequently suggest Oakley. I took your advice as a freshman, but I must say Oakley doesn't prepare one for proofs, it merely provides a survey. I find Oakley's presentation of logic inferior to that found in Velleman. In essence, Velleman discusses the proof aspects of Oakley in greater depth and constantly emphasizes binary logic. Oakley rushes through the principles and applies them to elementary math. Again, you are the expert, so I was wondering why you (and other mathematicians) hate Velleman.

    I can send you a copy if you'd like to re-evaluate Velleman.
  11. Sep 16, 2008 #10
    What is the difference between Principles of Mathematics by Allendoerfer & Oakley and the one by Russell? Does it have a dust jacket?

    The second edition of Geometry by Jacobs is also pretty good and you can find a teacher's manual as well for it.

    I have the book by Vellman and I plan on using it to ease myself into proofs.
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