11/5: Reminder: Midterm II is next Thursday, November 14.
10/1: Extra office hours for Midterm I: Monday October 8, 2:003:30pm, Krieger 412.
10/1: Reminder: Midterm I is next Tuesday, October 9.
9/30: TA's new hours in Math Helproom will be Thursday 79pm. Also you can usually find him in his office (Krieger 201) Tuesday 34pm.
9/23: 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.
9/6: TA's office hours: Thursday 45pm, Krieger 201. TA also will be in Math Helproom Tuesday 35pm.
8/16: Please note that on the first class day August 29, classes meet according to Monday schedule. The first meeting of this class is on Tuesday September 3.
Date  Topic  Sections  Homework  Due Date 
Week 0  
Aug 29  No Class (Classes meet on Monday schedule)  No assignment  
Week 1  Sep 12  
Sep 3  Introduction. Mathematical Induction  1.1  1.1: 1, 7, 10, 11, 13, 15 1.2: 6, 7 2.1: 2, 4, 5 

Sep 5  Basis representation theorem Euclid's division lemma 
1.2, 2.1  
Week 2  Sep 19  
Sep 10  Divisibility Linear Diophantine equations 
2.2, 2.3  2.2: 3, 10, 11, 12 2.3: 1(f), 4 2.4: 6(f), 8, 10, 12 

Sep 12  Fundamental theorem of arithmetic  2.4  
Week 3  Sep 26  
Sep 17  Permutations and combinations Fermat's little theorem 
3.1, 3.2  3.1: 3, 6, 7, 10, 14 3.2: 3, 6 3.3: 2 3.4: 3, 5 

Sep 19  Wilson's theorem. Generating functions  3.3, 3.4  
Week 4  Oct 3  
Sep 24  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, 6, 9, 11, 15, 21, 22 

Sep 26  Solving
linear congruences Euler's Theorem. Fermat and Wilson Theorem (using congruences). 
5.1, 5.2  
Week 5  Oct 10  
Oct 1  Chinese remainder theorem  5.3  5.3: 4, 5, 6 5.4: 1(c), 3, 4, 5, 6 

Oct 3  Polynomial congruences. Review 
5.4  
Week 6  Oct 17  
Oct 8  Midterm I  6.1: 1, 4, 5, 8, 9, 10, 11 6.2: 2, 4, 5 

Oct 10  Combinatorial study of φ(n) Formulae for d(n) and σ(n) 
6.1, 6.2  
Week 7  Oct 24  
Oct 15  Multiplicative arithmetic functions Möbius inversion formula 
6.3, 6.4  6.2: 9, 15 6.3: 1 6.4: 2, 4, 5, 6, 7, 11, 12 

Oct 17  Properties of reduced residue systems  7.1  
Week 8  Oct 31  
Oct 22  Primitive roots  7.2  7.1: 6, 7 7.2: 7, 8, 9, 10, 11, 12, 13, 14 

Oct 24  Elementary properties of π(x)  8.1  
Week 9  Nov 7  
Oct 29  Tchebychev's theorem  8.2  8.1: 1, 2, 5, 6, 7, 9, 10, 16, 18 8.2: 1 

Oct 31  Euler's criterion. Legendre Symbol  9.1, 9.2  
Week 10  Nov 14  
Nov 5  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 

Nov 7  Applications of quadratic reciprocity law  9.4  
Week 11  Nov 21 (Last HW due) 

Nov 12  Consecutive residues and nonresidues Review  10.1  10.1: 2, 4, 5, 6, 7  
Nov 14  Midterm II  
Week 12  
Nov 19  Consecutive triples of quadratic residues  10.2  
Nov 21  Sum of two squares  11.1  
Week 13  
Nov 26  No Class (Thanksgiving holiday)  
Nov 28  
Week 14  
Dec 3  Sum of four squares  11.2  
Dec 5  Review 