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Suppose:

  • I am a 'problem-solver' rather than a 'theory-builder'
  • I am an undergraduate student
  • I have a passion for solving mathematical problems
  • The homework I get is not satisfying (in the sense that the problems are computing-problems rather than problems that require creative thinking), and I get far too little homework

Where can I find interesting problems (that require creative thinking) if I want to have fun solving mathematical problems and to practice problem-solving? Are there lists/books of such problems?

Furthermore, suppose I want to know how it is to do research.

Are there lists of the kind "open problems which can be understood by undergraduates". I guess these open problems should be in the fields of "discrete mathematics/combinatorics" and "graph theory".

I only found: http://dimacs.rutgers.edu/~hochberg/undopen/

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  • $\begingroup$ Not especially famous, long-open problems which anyone can understand mathoverflow.net/questions/100265/… $\endgroup$
    – joro
    Commented Dec 11, 2015 at 17:31
  • $\begingroup$ I think, "long-open" questions are not the kind of problems I am searching for. Is it realistic for an undergraduate to solve "long-open" problems. In general, I would say no. Maybe there are some geniuses. $\endgroup$
    – sdfaewrFAAEA
    Commented Dec 11, 2015 at 17:34
  • $\begingroup$ So are you asking for OPEN, but not open for long? $\endgroup$
    – joro
    Commented Dec 11, 2015 at 17:37
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    $\begingroup$ This MSE posting might help: "Undergraduate Mathematics Research." To supplement the list you found, DIMACS Open problems for undergraduates, there is The Open Problems Project, the latter not specifically oriented to undergraduates. $\endgroup$
    – Joseph O'Rourke
    Commented Dec 11, 2015 at 17:41
  • $\begingroup$ @Joseph: The second link is also in my post. Have you read my post/question? $\endgroup$
    – sdfaewrFAAEA
    Commented Dec 11, 2015 at 17:44

2 Answers 2

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Richard Guy compiled a list of open problems in combinatorial game theory, available at http://library.msri.org/books/Book29/files/unsolved.pdf . His book "Unsolved problems in number theory" also contains parts which are more combinatorial in nature. In the realm of Davenport's constant there are many open problems, some of which are probably non-trivial but doable.

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There's a big list of open problems at:

Open Problem Garden

and a smaller list at:

Unsolved Problems and Rewards

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