# Kevin Milans : Teaching : Fall 2013 Math545

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: MW 1:30pm-2:30pm, Tues, 11am-noon, and by appointment
Class Meetings: MW 3:30pm-4:45pm in Armstrong Hall 203

Home | Course Syllabus (PDF) | Homework

### Course Schedule

 No. Date Class Summary Section(s) Quiz Quiz Soln Comments 1 Aug 19 Introduction; Induction; Basis representation 1.1,1.2 - - - 2 Aug 21 Basis representation; Divison lemma; Greatest common divisors 1.2,2.1 - - HW1 assigned. 3 Aug 26 Euclid's algorithm; Linear combinations 2.2 - - - 4 Aug 28 Linear Diophantine equations; Fundamental theorem of arithmetic; Combinatorics 2.3,2.4,3.1 - - - 5 Sep 4 Combinatorics; Fermat's Little Theorem 3.1,3.2 - - HW2 assigned. 6 Sep 9 Wilson's Theorem; Congruences 3.3,4.1 - - - 7 Sep 11 Residue Systems; Riffling 4.2,4.3 - - - 8 Sep 16 Linear Congruences; Fermat and Wilson II; Chinese Remainder Theorem 5.1-5.3 - - HW3 assigned. 9 Sep 18 Polynomial Recurrences; Euler's Phi Function 5.4,6.1 - - - 10 Sep 23 Arithmetic Functions; Mobius Inversion 6.2,6.3,6.4 - - - 11 Sep 25 Mobious Inversion; Primitive Roots 6.4,7.1 - - HW3 due. 12 Sep 30 Primitive Roots 7.1,7.2 - - Midterm assigned. 13 Oct 2 Prime Numbers 7.2,8.1 - - Midterm due. 14 Oct 7 Prime Numbers: Chebyshev's Theorem 8.1,8.2 - - - 15 Oct 9 Prime Numbers: Bertrand's Postulate - - - - 16 Oct 16 Quadratic Reciprocity: Euler's Criterion and Gauss's Lemma 9.1,9.2 - - HW4 assigned. 17 Oct 21 Quadratic Reciprocity: Legendre Symbols (-1/p) and (2/p) 9.3 - - - 18 Oct 23 Quadratic Reciprocity Law: Proof 9.3 - - - 19 Oct 28 Quadratic Reciprocity Law: Applications 9.4 - - HW4 due. 20 Oct 30 Quadratic Reciprocity Law: Proof 9.3 - - - 21 Nov 4 Distribution of Quadratic Residues 10.1,10.2 - - HW5 assigned. 22 Nov 6 Distribution of consecutive QR triples; Sums of squares 10.2,11.1 - - - 23 Nov 11 Sums of squares 11.1,11.2 - - - 24 Nov 13 Partitions 12 - - HW5 due. 25 Nov 18 Partitions II 12 - - - 26 Nov 20 Generating Functions 13.1 - - HW6 assigned. 27 Dec 2 Partition Generating Functions; Jacobi's Triple Product Identity 13.2 - - - 28 Dec 4 JTPI Proof; Euler's Pentagonal Number Theorem 13.2,14.2 - - - 29 Dec 18 Final Exam - - - -

milans@math.wvu.edu