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I've found many books which treats of the theoretical and conceptual part of the mathematical demonstration, but now I'm searching for a book with a plenty of demonstration of mathematical proofs. Almost a "mathematical demonstration cookbook", with all sorts of solutions of problems like:

prove that $10^n > n$, for every $n \geq 1$.

Anyone know something like it? Thanks in advance.

Gamma Function
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thiago
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  • Damn, thank you very much! Your answer in this second link probably has exactly what I'm looking for. I have a doubt: what's the difference between heuristic and discrete mathematics? Please, can you answer it like "for dummies"? – thiago Mar 02 '14 at 13:46
  • I'll take a look, thank you. – thiago Mar 02 '14 at 13:55
  • By all these books that you recommended in your answers I think that 2000 Solved Problems and the How to Think Like a Matheatician will be of great help. Thanks for your help. – thiago Mar 02 '14 at 14:22
  • I own How to Think Like a Mathematician and it is pretty good. It is similar, but I think slightly worse, than How to Prove It. Regardless, it is probably worth checking out (especially if you have it in your university library). – Gamma Function Mar 02 '14 at 15:58
  • Within mathematics, a heuristic is usually used as a synonym for a problem-solving strategy.

    Discrete mathematics, on the other hand, is a very big chunk of mathematics. Although some high schools have courses labeled "discrete mathematics" which is usually geared towards weaker students, discrete mathematics certainly is not "for dummies". Both number theory and combinatorics are within the purview of discrete mathematics. For books on these topics, see the last two books on my list. A book like How to Think Like a Mathematician or How to Prove It would prepare you well for these.

     – Gamma Function Mar 02 '14 at 16:08
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    Does this answer your question? Basic book about mathematical proofs – user1110341 Oct 07 '23 at 09:17

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I figure that you are an advanced high school student or beginning undergraduate. If you are not, please correct me. Here are some books you might want to look into. They are arranged in roughly in order of difficulty.

None of these books are cookbooks. I suspect that How to Prove It is most relevant to what you are looking for, but all four of the above books that will almost certainly pique your interest. It would probably be best that you look at a book like How to Prove It before looking at either of the last two books.

Gamma Function
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  • You're right, I'm a freshman on the physics course. I'm going to take a look on these books and if some of them seem help me I comment which one got it. Thank you very much! – thiago Mar 02 '14 at 13:22
  • I took a look and I think this How to Prove It will be better than a cookbook. Thanks for your help. – thiago Mar 02 '14 at 14:17