11/13: Reminder: Midterm II is Thursday, November 16.
11/13: Office hours for Midterm II: Wednesday November 15, 2:004:30pm, Krieger 412 (usual time but long hours).
10/4: Room change (tomorrow only): The classroom for tomorrow (October 5) will be Gilman 313, per registrar office.
10/4: Reminder: Midterm I is next Tuesday, October 10.
10/4: Extra office hours for Midterm I: Monday October 9, 2:003:30pm, Krieger 412.
9/26: For homework problem #14 in 3.1, here is a (3part) help video if you use induction. Note that there are other ways without using induction.
9/19: Office hours change: for tomorrow (9/20) only, office hours will be 3:004:30pm.
9/18: TA's office hours: Wednesday 6:00  7:00 pm. Krieger 211
9/1: Room change: Please note the new classroom for 110.304 Fall 2017 is Hodson 315, effective from first meeting on Tuesday September 5.
8/26: Please note that on the first class day August 31, classes meet according to Monday schedule. The first meeting of this class is on Tuesday September 5.
Date  Topic  Sections  Homework  Due Date 
Week 0  
Aug 31  No Class (Classes meet on Monday schedule)  No assignment  
Week 1  Sep 14  
Sep 5  Introduction. Mathematical Induction  1.1  1.1: 2, 7, 10, 12, 13, 15 1.2: 6, 7 2.1: 2, 4, 5, 7 

Sep 7  Basis representation theorem Euclid's division lemma 
1.2, 2.1  
Week 2  Sep 21  
Sep 12  Divisibility  2.2  2.2: 2, 10, 11, 12 2.3: 1(b), 4 2.4: 6(f), 8, 10, 12 

Sep 14  Linear Diophantine equations Fundamental theorem of arithmetic 
2.3, 2.4  
Week 3  Sep 28  
Sep 19  Permutations and combinations  2.4, 3.1  3.1: 3, 6, 7, 10, 13, 14 3.2: 3, 6 3.3: 2 3.4: 3, 5 

Sep 21  Fermat's little theorem.
Wilson's theorem Generating functions 
3.2, 3,3, 3.4  
Week 4  Oct 5  
Sep 26  Basic properties of Congruences Residue Systems 
4.1, 4.2 
4.1: 1(c), 6 4.2: 3 5.1: 1(b) 5.2: 3, 4, 6, 9, 11, 15, 21, 22 

Sep 28  Solving
Linear Congruences Euler's Theorem. Fermat and Wilson Theorem (using congruences). 
5.1, 5.2  
Week 5  Oct 12  
Oct 3  Chinese remainder theorem  5.3  5.3: 2, 4, 6 5.4: 3, 4, 5, 6, 7 

Oct 5  Polynomial congruences Review 
5.4  
Week 6  Oct 19  
Oct 10  Midterm I  6.1: 1, 4, 5, 8, 9, 10, 11, 15  
Oct 12  Combinatorial study of φ(n)  6.1  
Week 7  Oct 26  
Oct 17  Formulae for d(n) and σ(n) Multiplicative arithmetic functions 
6.2, 6.3  6.2: 2, 4, 5, 9, 15 6.3: 1 6.4: 2, 4, 5, 7, 8, 11, 12 

Oct 19  Möbius inversion formula  6.4  
Week 8  Nov 2  
Oct 24  Properties of reduced residue systems Primitive roots 
7.1, 7.2  7.1: 6, 7 7.2: 7, 8, 9, 10, 11, 12, 13, 14 

Oct 26  Elementary properties of π(x)  8.1  
Week 9  Nov 9  
Oct 31  Tchebychev's theorem  8.2  8.1: 1, 2, 3, 5, 6, 7, 9, 10, 18 8.2: 1 

Nov 2  Euler's criterion. Legendre Symbol  9.1, 9.2  
Week 10  Nov 16  
Nov 7  Gauss's Lemma. Quadratic reciprocity law  9.3  9.1: 1 9.2: 1, 2, 3 9.3: 1, 2, 5, 6 9.4: 1, 3, 4, 5 

Nov 9  Quadratic reciprocity law Applications of quadratic reciprocity law 
9.4  
Week 11  Nov 30  
Nov 14  Consecutive residues and nonresidues Review  10.1  10.1: 2, 4, 5, 6, 7  
Nov 16  Midterm II  
Week 12  
Nov 21  No Class (Thanksgiving holiday)  
Nov 23  
Week 13  
Nov 28  Consecutive triples of quadratic residues  10.2  
Nov 30  Sum of two squares  11.1  
Week 14  
Dec 5  Sum of four squares  11.2  
Dec 7  Review 