Kevin Milans : Teaching : Fall 2017 Math545: Number Theory 1

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: MW 11:30am-12:30pm, and by appointment
Class Meetings: TuTh 1:00pm-2:15pm in Armstrong Hall 313

Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Sections(s) Comments
1 Aug 17 Introduction; Induction; the sum 1 + ... + n 1-1 HW1 assigned.
2 Aug 22 Basis representation 1-2
3 Aug 24 Euclid's Division Lemma; GCDs; Integer Combinations 2-1 -
4 Aug 29 Extended Euclidean Algorithm; primes 2-2 -
5 Aug 31 Linear Diophantine Eqns; Fundamental Theorem of Arithmetic 2-3,2-4 HW1 due; HW2 assigned.
6 Sep 5 Permutations and Combinations 3.1,3.2 -
7 Sep 7 Fermat's little theorem; Wilson's theorem 3.2,3.3 -
8 Sep 12 Congruences; Complete and Reduced Residue Systems 4.1,4.2 -
9 Sep 14 Riffling (congruence application); Linear congruence relations 4.3,5.1 HW2 due; HW3 assigned.
10 Sep 19 Euler's Theorem; Fermat and Wilson II 5.2 -
11 Sep 21 Systems of congruences; Chinese remainder theorem; Polynomial congruences 5.3,5.4 -
12 Sep 26 Combinatorial study of Euler's phi function 6.1 -
13 Sep 28 Multiplicative functions; Dirichlet product 6.2-6.4 HW3 due; HW4 assigned.
14 Oct 3 Mobius inversion 6.4 -
15 Oct 5 Midterm Exam (coverage up to and including Thurs Sept 28) - Midterm (pdf)
16 Oct 10 Orders modulo m and primitive roots 7.1 -
17 Oct 12 Existence of primitive roots modulo a prime; prime counting function 7.2,8.1 -
18 Oct 17 Divergence of Sum 1/p, Chebychev's Thm 8.2 HW4 due.
19 Oct 19 Bertrand's postulate; Euler's Criterion 9.1 HW5 assigned.

milans@math.wvu.edu