3/13: Office hours change for Wednesday 3/14 only: 3:455:15pm.
3/6: Office hours change for Wednesday 3/7 only: 121pm.
2/28: Reminder: Midterm I is on Tuesday March 6.
2/20: 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.
2/7: TA's office hours: Tuesday 12pm. Krieger 211.
1/16: The first meeting of this class is on Tuesday January 30.
Date  Topic  Sections  Homework  Due Date 
Week 1  Feb 8  
Jan 30  Introduction. Mathematical Induction  1.1  1.1: 1, 7, 10, 11, 13, 15 1.2: 6, 7 2.1: 2, 4, 5 

Feb 1  Basis representation theorem Euclid's division lemma 
1.2, 2.1  
Week 2  Feb 15  
Feb 6  Divisibility  2.2  2.2: 2, 10, 11, 12 2.3: 1(d), 4 2.4: 6(f), 8, 10, 12 

Feb 8  Linear Diophantine equations Fundamental theorem of arithmetic 
2.3, 2.4  
Week 3  Feb 22  
Feb 13  Permutations and combinations Fermat's Theorem 
3.1, 3.2  3.1: 3, 6, 7, 13, 14 3.2: 3, 6 3.3: 1, 2 3.4: 3, 5 

Feb 15  Wilson's theorem Generating functions 
3,3, 3.4  
Week 4  Mar 1  
Feb 20  Basic properties of Congruences Residue Systems 
4.1, 4.2 
4.1: 1(a), 6 4.2: 3 5.1: 1(c) 5.2: 3, 4, 5, 9, 11, 15, 21, 23 

Feb 22  Solving
Linear Congruences Euler's Theorem. Fermat and Wilson Theorem (using congruences). 
5.1, 5.2  
Week 5  Mar 8  
Feb 27  Chinese remainder theorem  5.3  5.3: 2, 4, 6 5.4: 3, 4, 5, 6, 7 

Mar 1  Polynomial congruences Review 
5.4  
Week 6  Mar 15  
Mar 6  Midterm I  6.1: 1, 4, 5, 8, 9, 10, 11, 13  
Mar 8  Combinatorial study of φ(n)  6.1  
Week 7  Mar 29  
Mar 13  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, 11, 12 

Mar 15  Möbius inversion formula  6.4  
Week 8  
Mar 20  No Class (spring break)  
Mar 22  
Week 9  
Mar 27  Properties of reduced residue systems Primitive roots 
7.1, 7.2  
Mar 29  Elementary properties of π(x)  8.1  
Week 10  
Apr 3  Tchebychev's theorem  8.2  
Apr 5  Euler's criterion. Legendre Symbol  9.1, 9.2  
Week 11  
Apr 10  Gauss's Lemma. Quadratic reciprocity law  9.3  
Apr 12  Quadratic reciprocity law Applications of quadratic reciprocity law 
9.4  
Week 12  
Apr 17  Consecutive residues and nonresidues Review  10.1  
Apr 19  Midterm II  
Week 13  
Apr 24  Consecutive triples of quadratic residues  10.2  
Apr 26  Sum of two squares  11.1  
Week 14  
May 1  Sum of four squares  11.2  
May 3  Review 