MATH 332 Algebra and Number Theory

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Schedule for Math 332, Fall 2007 (tentative) (in pdf format, ready to print) Week Day Ch. Topics 8/23 – 24 1 Introduction 8/27 – 8/31 2 1 Numbers, induction, divisibility and primes 3 The Euclidean algorithm 9/3 – 9/7 4 The linear diophantine equation 5 2 Congruences, divisibility tests 9/10 – 9/14 6 Linear congruences, solving them 7 Chinese Remainder Theorem and applications 9/17 – 9/21 8 3 Fermat's little theorem and Wilson's theorem 9 Euler's theorem and the Euler Φ-function 9/24 – 9/28 10 Rings and Fields – Z/mZ 11 5 Quadratic congruences 10/1 – 10/5 12 Quadratic residues and the law of Quadratic Reciprocity 13 Quadratic Reciprocity 10/8 – 12 FALL BREAK 14 6 Order of an integer modulo p 10/15 – 19 15 Primitive roots, power residues, indices 16 Existence of primitive roots 10/22 – 26 17 7 Primes: Eratosthenes, perfect and Fermat numbers, Mersenne 18 The prime number theorem, Dirichlet's thm., Goldbach conjecture 10/29 – 11/2 19 8 Diophantine equations: pythagorean triples and Fermat Last Thm. 20 Sums of two squares 11/5 – 9 21 9 Continued fractions: finite and infinite 22 Periodic continued fractions 11/12 – 16 23 Rational approximations to irrational numbers 24 10 Pell's equation 11/19 – 23 25 Pell's equation (continued) THANKSGIVING 11/26 – 30 26 11 Gaussian integers 27 Other quadratic extensions