4/15: Office hours for Midterm II: Wednesday April 17 23:30pm.
4/15: Reminder: Midterm II is on Thursday April 18.
2/28: Extra office hours for Midterm I: Monday March 4, 23:30pm.
2/26: Reminder: Midterm I is next Tuesday March 5.
2/19: 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.
2/12: School opens at 10am. No class today (Read 3.2 and 3.3).
2/4: TA's office hours: Monday 11:00am12:00pm.
1/16: The first meeting of this class is on Tuesday January 29.
Date  Topic  Sections  Homework  Due Date 
Week 1  Feb 7  
Jan 29  Introduction. Mathematical Induction  1.1  1.1: 1, 8, 10, 12, 13, 15 1.2: 6, 7 2.1: 2, 4, 5 

Jan 31  Basis representation theorem Euclid's division lemma 
1.2, 2.1  
Week 2  Feb 14  
Feb 5  Divisibility  2.2  2.2: 2, 4, 10, 11, 12 2.3: 1(d), 4 2.4: 8, 10, 12 

Feb 7  Linear Diophantine equations Fundamental theorem of arithmetic Permutations and combinations 
2.3, 2.4, 3.1  
Week 3  Feb 21  
Feb 12 
No class (school opens at 10am). Read 3.2 and 3.3 
3.1: 3, 6, 7, 10, 13, 14 3.2: 3, 6 3.3: 2 3.4: 3, 5 

Feb 14  Fermat's Theorem. Wilson's theorem Generating functions 
3.2, 3.3, 3.4  
Week 4  Feb 28  
Feb 19  Basic properties of Congruences Residue Systems 
4.1, 4.2 
4.1: 6 4.2: 3 5.1: 1(b), 3 5.2: 3, 4, 6, 9, 11, 15, 21, 23 

Feb 21  Solving
Linear Congruences Euler's Theorem. Fermat and Wilson Theorem (using congruences). 
5.1, 5.2  
Week 5  Mar 7  
Feb 26  Chinese remainder theorem Polynomial congruences 
5.3  5.3: 2, 5, 6 5.4: 1(a), 3, 4, 5, 6 

Feb 28  Review  5.4  
Week 6  Mar 14  
Mar 5  Midterm I  6.1: 1, 2, 4, 5, 8, 9, 10, 11, 13  
Mar 7  Combinatorial study of φ(n)  6.1  
Week 7  Mar 28  
Mar 12  Formulae for d(n) and σ(n) Multiplicative arithmetic functions 
6.2, 6.3  6.2: 2, 5, 9, 15 6.3: 1 6.4: 2, 4, 5, 7, 10, 11, 12 

Mar 14  Möbius inversion formula  6.4  
Week 8  
Mar 19  No Class (spring break)  
Mar 21  
Week 9  Apr 4  
Mar 26  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 

Mar 28  Elementary properties of π(x)  8.1  
Week 10  Apr 11  
Apr 2  Tchebychev's theorem  8.2  8.1: 1, 2, 3, 5, 6, 7, 10, 13, 16 8.2: 1 

Apr 4  Quadratic Residues. Legendre Symbol  9.1, 9.2  
Week 11  Apr 18  
Apr 9  Gauss's Lemma Quadratic reciprocity law 
9.3  9.1: 1 9.2: 1, 2, 3 9.3: 5, 6 9.4: 1, 3, 4, 5 

Apr 11  Applications of quadratic reciprocity law  9.3, 9.4  
Week 12  Apr 25 (Last HW Due) 

Apr 16  Consecutive residues and nonresidues Review 
10.1  10.1: 3, 4, 5, 6, 7  
Apr 18  Midterm II  
Week 13  
Apr 23  Consecutive triples of quadratic residues  10.2  
Apr 25  Sum of two squares  11.1  
Week 14  
Apr 30  Sum of four squares  11.2  
May 2  Review 