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I just finished my second year as a mathematics student at university. At university, we learn about advanced mathematics and problems. However, I'm also interested in some problems that doesn't acquire deep results from mathematics or a certain theory to solve them.

Now I'm looking for a good guide to learn more about this type of problem-solving. I want some pdf or a book that gives some brief introduction to a problem solving technique and after that a large bunch of problems. I don't want these problems to be too easy but I also don't want them to be too hard so that I have to know much modern results in mathematics to understand them.

Does anyone of you knows such a guide at my level (university student)?

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    $\begingroup$ The Putnam exams might interest you. $\endgroup$
    – Git Gud
    Jun 24, 2013 at 20:15
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    $\begingroup$ I forget if Polya's "How to Solve It" has problems, but it was the go-to recommendation for this sort of thing when I was young. $\endgroup$ Jun 24, 2013 at 20:17
  • $\begingroup$ Maybe try - ''Mathematical circles''. Just take a look at problems from chapters like - invariants . I think it might be too easy for you? $\endgroup$ Jun 23, 2021 at 7:42

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I like "The Art and Craft of Problem Solving" by Paul Zeitz

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Problem-Solving Strategies

Arthur Engel

http://www.amazon.com/Problem-Solving-Strategies-Problem-Books-Mathematics/dp/0387982191

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  • $\begingroup$ I was going to recommend the same book. $\endgroup$
    – Ed Pegg
    Jun 25, 2013 at 14:08
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I have just the thing for you: "The Top-Down Approach to Problem Solving", by Eduardo Corpeño (yours truly), ISBN 979-8464073296. You can find it on amazon as paperback and ebook. I hope it helps.

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