10/2: Reminder: Midterm I is next Tuesday, October 9.
10/2: Extra office hours for Midterm I: Monday October 8, 3:004:30pm, Krieger 412.
9/24: 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.
9/17: Office hour change (this week only): This week's office hours will be Tuesday 9/18 (tomorrow) 2:003:30pm. There will be no office hours this Wednesday.
9/8: TA's office hour: Thursday 4:005:00pm in Krieger 211. Please note that the TA will also be in math Helproom Wednesday 5:007:00pm.
8/26: Please note that on the first class day August 30, classes meet according to Monday schedule. The first meeting of this class is on Tuesday September 4.
Date  Topic  Sections  Homework  Due Date 
Week 0  
Aug 31  No Class (Classes meet on Monday schedule)  No assignment  
Week 1  Sep 13  
Sep 4  Introduction. Mathematical Induction  1.1  1.1: 1, 7, 10, 12, 13, 15 1.2: 6, 7 2.1: 2, 3, 4, 5 

Sep 6  Basis representation theorem Euclid's division lemma 
1.2, 2.1  
Week 2  Sep 20  
Sep 11  Divisibility Linear Diophantine equations 
2.2, 2.3  2.2: 3, 10, 11, 12 2.3: 1(d), 4 2.4: 6(f), 8, 10, 12 

Sep 13  Fundamental theorem of arithmetic Permutations and combinations 
2.4, 3.1  
Week 3  Sep 27  
Sep 18  Fermat's little theorem. Wilson's theorem  3.2, 3.3  3.1: 3, 6, 7, 13, 14 3.2: 3, 6 3.3: 2 3.4: 3, 5 

Sep 20  Generating functions Basic properties of congruences 
3.4, 4.1  
Week 4  Oct 4  
Sep 25  Residue systems. Solving linear congruences 
4.2, 5.1 
4.1: 1(b), 6 4.2: 3 5.1: 1(c) 5.2: 3, 4, 5, 9, 11, 15, 21, 22 

Sep 27  Euler's Theorem. Fermat and Wilson Theorem (using congruences).  5.2  
Week 5  Oct 11  
Oct 2  Chinese remainder theorem  5.3  5.3: 4, 5, 6 5.4: 1(1), 3, 4, 5, 6 

Oct 4  Polynomial congruences. Properties of φ(n) Review 
5.4, 6.1  
Week 6  Oct 18  
Oct 9  Midterm I  6.1: 1, 4, 5, 8, 9, 10, 11 6.2: 2, 4, 5 

Oct 11  Combinatorial study of φ(n) Formulae for d(n) and σ(n) Multiplicative arithmetic functions 
6.1, 6.2, 6.3  
Week 7  
Oct 16  Möbius inversion formula  6.4  
Oct 18  Properties of reduced residue systems  7.1  
Week 8  
Oct 23  Primitive roots  7.2  
Oct 25  Elementary properties of π(x)  8.1  
Week 9  
Oct 30  Tchebychev's theorem  8.2  
Nov 1  Euler's criterion. Legendre Symbol  9.1, 9.2  
Week 10  
Nov 6  Gauss's Lemma. Quadratic reciprocity law  9.3  
Nov 8  Quadratic reciprocity law Applications of quadratic reciprocity law 
9.4  
Week 11  
Nov 13  Consecutive residues and nonresidues Review  10.1  
Nov 15  Midterm II  
Week 12  
Nov 20  No Class (Thanksgiving holiday)  
Nov 22  
Week 13  
Nov 27  Consecutive triples of quadratic residues  10.2  
Nov 29  Sum of two squares  11.1  
Week 14  
Dec 4  Sum of four squares  11.2  
Dec 6  Review 