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  
Sep 26  Basic properties of Congruences Residue Systems 
4.1, 4.2  
Sep 28  Solving Linear Congruences.  5.1  
Week 5  
Oct 3  Euler's Theorem. Fermat and Wilson Theorem (using congruences).  5.2  
Oct 5  Chinese remainder theorem Review 
5.3  
Week 6  
Oct 10  Midterm I  
Oct 12  Polynomial congruences  5.4  
Week 7  
Oct 17  Combinatorial study of φ(n)  6.1  
Oct 19  Formulae for d(n) and σ(n) Multiplicative arithmetic functions Möbius inversion formula 
6.2, 6.3, 6.4  
Week 8  
Oct 24  More on Möbius inversion formula Properties of reduced residue systems 
6.4, 7.1  
Oct 26  Primitive roots  7.2  
Week 9  
Oct 31  Elementary properties of π(x)  8.1  
Nov 2  Tchebychev's theorem  8.2  
Week 10  
Nov 7  Euler's criterion. Legendre Symbol  9.1, 9.2  
Nov 9  Quadratic reciprocity law Applications of quadratic reciprocity law 
9.3, 9.4  
Week 11  
Nov 14  Proof of quadratic reciprocity law. Review  9.3  
Nov 16  Midterm II  
Week 12  
Nov 21  No Class (Thanksgiving holiday)  
Nov 23  
Week 13  
Nov 28  Consecutive residues and nonresidues  10.1  
Nov 30  Consecutive triples of quadratic residues  10.2  
Week 14  
Dec 5  Sum of two squares  11.1  
Dec 7  Sum of four squares. Review  11.2 