Math 4802
Fall 2007
Combinatorics Problems (due Tuesday, October 30) 1. Dene a selsh set to be a set which has its own cardinality (number of elements) as an element. A selsh set is called minimal if
Math 4802
Fall 2007
Infinite Series Problems (due Tuesday, October 23) 1. Evaluate the innite sum
n=1
n2 . 2n
2. Suppose that a sequence a1 , a2 , a3 , . . . of positive real numbers satises an a2n +
Math 4802
Fall 2007
Probability Problems Due Tuesday, September 11: 1. Shue an ordinary deck of 52 playing cards, and then turn the cards face up one at a time. On average, how many cards are required
Math 4802
Fall 2007
Polynomial Problems (due Tuesday, October 16) 1. Determine all polynomials P (x) with complex coecients such that P (0) = 0 and P (x2 + 1) = (P (x)2 + 1. 2. Suppose the polynomial
Math 4802
Fall 2006
Pigeonhole Principle Problems In-class Problems: 1. Suppose that 17 playing cards are chosen at random from a standard deck of 52 cards. Show that these cards must contain a ush. 2
Math 4802
Fall 2007
Number Theory Problems 1. a. Find all positive integers n for which 7 divides 2n 1. b. Show that there is no positive integer n for which 7 divides 2n + 1. 2. Find all prime number
Math 4802
Fall 2007
Inequalities Problems (due Tuesday, November 6) 1. If a, b, c are positive real numbers, prove that a4 + b4 + c4 abc(a + b + c) . 2. Given that a, b, c, d, e are real numbers for w