MA5440 Combinatorics and Number Theory
Combinatorics: Numbers and counting, partitions and permutations, principle of inclusion and exclusion, pigeon hole principle, recurrence relations, generating Functions.
Number Theory: Primes, divisibility and the fundamental theorem of arithmetic, prime number theorem, Euclidean algorithm, congruences, ring of integers mod n, chinese remainder theorem, arithmetic functions, Fermat's last theorem, Mobius inversion formula, quadratic residues, quadratic reciprocity law, binary quadratic forms, continued fractions, Pell's equation, Diophantine equations.
1. J. L. Mott, A. Kandel, and T. P. Baker, Discrete Mathematics for Computer Scientists and Mathematicians, PHI Learning, 2003.
2. I. Niven, H.S. Zuckerman, and H.L. Montgomery. An Introduction to the Theory of Numbers, Wiley, 1991.
1. T. Koshy, Discrete Mathematics with Applications, Elsevier, 2004.
2. K.F. Ireland and M.I. Rosen, A Classical Introduction to Modern Number Theory, Springer, 1990.