Kevin Milans : Teaching : Fall 2015 Math545

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: TuTh 2:15pm-3:15pm, W 10:00am-11:00am, and by appointment
Class Meetings: TuTh 1:00pm-2:15pm in Armstrong Hall 121
Home | Course Syllabus (PDF) | Homework

Course Schedule

-->
No. Date Class Summary Section(s) Quiz Quiz Soln Comments
1 Aug 18 Introduction; Induction 1.1,1.2 - - HW1 assigned.
2 Aug 20 Basis representation; Division definition 1.2,2.1 - - HW Workshop at 5pm
3 Aug 25 GCDs and integral linear combinations 2.2 - - -
4 Aug 27 Euclidean algorithm; Linear Diophantine equations 2.2,2.3 - - HW Workshop at 5pm
5 Sep 1 Fundamental Theorem of Algebra; Combinatorics 2.4,3.1 - - HW1 due; HW2 assigned.
6 Sep 3 Fermat's Little Theorem; Congruences 3.2,4.1 - - -
7 Sep 8 Residue Systems; Riffling 4.2,4.3 - - -
8 Sep 10 Linear Congruences; Fermat and Wilson 5.1-5.3 - - -
9 Sep 15 Chinese Remainder Theorem; Polynomial Recurrences; Euler's Phi Function 5.3,5.4,6.1 - - HW2 due; HW3 assigned this evening.
10 Sep 17 Inclusion/Exclusion; Arithmetic Functions 6.2,6.3 - - -
11 Sep 22 Arithmetic Functions; Mobius Inversion 6.3,6.4 - - -
12 Sep 24 Mobius Inversion; Primitive Roots 6.4,7.1 - - -
13 Sep 29 Primitive Roots II 7.1 - - HW3 due. HW4 assigned.
14 Oct 1 Existence of primitive roots modulo p; prime numbers 7.2,8.1 - - -
15 Oct 6 Midterm (Chapters 1 to 6) - - - -
16 Oct 8 Prime Numbers 8.2 - - -
17 Oct 15 Prime Numbers: Chebyshev's Theorem 8.2 - - HW5 posted.
18 Oct 20 Prime Numbers: Chebyshev's Theorem II 8.2 - - -
19 Oct 22 Prime Numbers: Bertrand's Postulate 8.2 - - -
20 Oct 27 Quadratic Reciprocity: Euler's Criterion and Gauss's Lemma 9.1,9.2 - - -
21 Oct 29 Quadratic Reciprocity: Legendre Symbols (-1/p) and (2/p) 9.3 - - -
22 Nov 3 Quadratic Reciprocity Law: Proof 9.3 - - HW5 due. HW6 assigned.
23 Nov 5 Quadratic Reciprocity Law: Proof II; quadratic congruences 9.3 - - -
24 Nov 10 Consecutive Residues 10.1-10.2 - - -
25 Nov 12 Consecutive Residues II; sums of two squares 10.2,11.1 - - -
26 Nov 17 Lagrange's four square theorem I 11.2 - - HW6 due.
27 Nov 19 Lagrange's four square theorem II 11.2 - - HW7 assigned (as of Tues. Nov 24).
28 Dec 1 Partitions; Euler's Partition Theorem 12 - - -
29 Dec 3 Generating Functions 13.1 - - -
30 Dec 8 Lattice Points 15 - - HW7 due.
- Dec 15 Final Exam: Tues. Dec 15, 3pm-5pm - - - -
milans@math.wvu.edu