MATH 256 - Elementary Number Theory

3 units (fi 6)(FIRST, 3-0-0)

Divisibility, prime numbers, congruences, quadratic residues, quadratic reciprocity, arithmetic functions and diophantine equations; sums of squares. Prerequisites: MATH 125 or 127.

MATH 325 - Linear Algebra III

3 units (fi 6)(SECOND, 3-0-0)

Hermitian and unitary matrices, spectral theorem. Jordan canonical form. Cayley-Hamilton Theorem. Bilinear forms, positive-definiteness, Sylvester's Law of inertia, geometric lattices. Numerical methods. Application to discrete system evolution, matrix exponentials and differential equations. Prerequisite: MATH 225. Note: This course may not be taken for credit if credit has already been obtained in MATH 227.