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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/

sdfaewrFAAEA
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  • Not especially famous, long-open problems which anyone can understand https://mathoverflow.net/questions/100265/not-especially-famous-long-open-problems-which-anyone-can-understand – joro Dec 11 '15 at 17:31
  • 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. – sdfaewrFAAEA Dec 11 '15 at 17:34
  • So are you asking for OPEN, but not open for long? – joro Dec 11 '15 at 17:37
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    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. – Joseph O'Rourke Dec 11 '15 at 17:41
  • @Joseph: The second link is also in my post. Have you read my post/question? – sdfaewrFAAEA Dec 11 '15 at 17:44
  • (Sorry, I didn't recognize the URL.) – Joseph O'Rourke Dec 11 '15 at 17:45
  • Think about the constraints you are placing on this hypothetical problem list: the problems should be interesting enough for someone to collect and easy enough for an undergrad to solve, either too new or too obscure to be "long-standing", but miraculously not already solved by the people who collect such problems. I'm not saying no such list can exist, but I'd be surprised if it did. In any case, let me strongly recommend that you apply for a summer REU --- those are designed precisely for the sort of people you appear to be describing. – Vidit Nanda Dec 11 '15 at 18:38
  • @Vidit: Your comment answers my questions completely. Thanks. – sdfaewrFAAEA Dec 11 '15 at 18:50
  • I think the best source for the sort of problem you describe are the faculty members at your university. They probably already have a number of problems that fit into the "open but not too hard" category for any future/current phd students. I hope, certainly in some fields, they'd also be able to explain the problems in a way understandable to undergrads. – user62562 Dec 11 '15 at 19:05
  • For the record: I voted to close as "too broad," but I also think that this question is not fully within the scope of the site. –  Dec 11 '15 at 20:11
  • As this question is closed I recommend that you post it on MathSE. Then I will answer. – Alexandre Eremenko Dec 11 '15 at 20:34
  • This comment might end up under the fold forever, but perhaps the OP will see it -- my advice to them is not to ask such questions here, but to find an enthusiastic member of staff at their university and get them to give you an undergraduate research project. My university runs these and runs them well. There is even a small amount of money available for some people to do projects, and some staff (certainly not all, but more than zero) enjoy having the extra enthusiastic cheap labor available. I'd supervise you myself -- but not over the internet. I save my best puzzles for my own students:-) – eric Dec 12 '15 at 09:18

2 Answers2

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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

JMP
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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.

Jan-Christoph Schlage-Puchta
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