Tentative hour exam dates: Hour Exam #1: Week of March 5, 2002 Hour Exam #2: Week of April 16, 2002 Here is a rough plan showing the topics we might cover during the semester. Week of Text sections Topics JAN 29 1.1 - 1.3 Primes and the Prime Number Theorem, the Euclidean algorithm and GCDs FEB 5 1.3, 1.4 The Binomial Theorem, generating functions FEB 12 2.1, 2.2 Congruences in prime and prime-power moduli, systems of distinct representatives, pseudoprimes, Carmichael numbers FEB 19 2.3 - 2.5 More prime-power congruences, systems of congruences, Fermat's little theorem, the Euler phi function, public-key cryptography FEB 26 2.6 - 2.7 More prime-power congruences, p-adic numbers, the Fundamental Theorem of Algebra MAR 5 2.8 Primitive roots, primality testing MAR 12 2.10, 2.11 Groups, rings, fields, and number theory MAR 19   Spring break MAR 26 3.1 - 3.3 Quadratic residues and quadratic reciprocity, the Jacobi symbol APR 2 4.2, 4.3 Arithmetic functions and Möbius inversion APR 9 5.3, 5.4 Pythagorean triples and other Diophantine equations APR 16 5.6, 5.7 Rational points on curves, elliptic curves APR 23 7.1 - 7.3 Continued fractions APR 30 7.3 - 7.7 More continued fractions