What are possible research problems in mathematics for an undergraduate thesis?

Answer 1

you could solve one of the 6 remaining Millennium Prize problems.
http://www.claymath.org/millennium/

Answer 2

I could suggest that you try to solve the Odd Perfect Number (OPN) Problem. A positive integer N is said to be perfect if S(N) = 2N, where S(N) equals the sum of all the positive divisors of N, including 1 and N itself. So far, only 43 perfect numbers are known, and all of these are even. Even perfect numbers are in one-to-one correspondence with Mersenne primes M_p = 2^p - 1, since an even perfect number takes the form N = [(M_p)(M_p + 1)]/2. No one has produced an example for an odd perfect number, and it is known (see: http://www.oddperfect.org) that if one exists, then it must be greater than 10^500. Also, an odd perfect number must be a sum of two squares and must have at least nine (9) distinct prime factors. Lastly, it is known that the arithmetic/natural/asymptotic density of odd perfect numbers is equal to zero (0).

The topic of odd perfect numbers lends itself well to an undergraduate thesis preparation simply because the problem is very simple to state, yet very difficult to solve. Judging by the temerity with which the problem has resisted the efforts of numerous mathematicians since antiquity, as well as the hundreds of research papers written on the subject, an aspiring undergraduate thesis advisee could (potentially) write an exposition on one or two papers devoted to solving the OPN problem, in the hope that some (previously undiscovered) inspiration would ignite one's mathematical imagination to conclusively solve the problem.

Answer 3

hi ... I suggest probability things for texas holdem poker ... The game is very popular on tv etc...but some of the probabilities are not known.. for high stakes games there is bluffing which is hard to deal with in probability... but i think you could do a study that could throw more light on that game... leo

Answer 4

runga kuttah methods for stiff problems