12/19: Course grades posted to SIS. Happy holidays!
12/19: Final exam solutions posted.
12/8: Extra office hours for the final exam: Thursday December15, 25pm.
12/8: Reminder: The Final Exam is Friday December 16, 9am12noon in Gilman 55 (the regular classroom).
10/5: Extra office hours for Midterm I: Monday October 10, 24pm.
10/5: Reminder: Midterm I is on Tuesday October 11.
8/26: The first meeting is on Thursday September 1.
Date  Topic  Sections  Homework  Due Date 
Week 1  
Sep 1  Introduction Principle of mathematical induction 
1.1  No assignment  
Week 2  Sep 15  
Sep 6  Basis representation theorem Euclid's division lemma 
1.2, 2.1  1.1: 2, 7, 10, 11, 13, 15 1.2: 6, 7 2.1: 2, 4, 5, 6 

Sep 8  Divisibility  2,2  
Week 3  Sep 22  
Sep 13  Fundamental theorem of arithmetic  2.4  2.2: 2, 10, 11, 12 2.3: 1(b), 4 2.4: 6(f), 8, 10, 12 

Sep 15  Linear Diophantine equations Permutations and combinations 
2.3, 3.1  
Week 4  Sep 29  
Sep 20  Fermat's little theorem. Wilson's theorem  3.2, 3.3  3.1: 3, 6, 7, 10, 13, 14 3.2: 3, 6 3.3: 2 3.4: 3, 5 

Sep 22  Generating functions  3.4  
Week 5  Oct 6  
Sep 27  Basic properties of Congruences Residue Systems 
4.1, 4.2 
4.1: 1(b), 6 4.2: 3 5.1: 1(c) 5.2: 3, 4, 6, 9, 11, 15, 21, 22 

Sep 29  Solving
Linear Congruences. Euler's Theorem. Fermat and Wilson Theorem (using congruences). 
5.1, 5.2  
Week 6  Oct 13  
Oct 4  Chinese remainder theorem  5.3  5.3: 2, 4, 6 5.4: 3, 4, 5, 6, 7 

Oct 6  Polynomial congruences Review 
5.4  
Week 7  Oct 27  
Oct 11  Midterm I  6.1: 1, 4, 5, 8, 9, 10, 11, 15  
Oct 13  Combinatorial study of φ(n)  6.1  
Week 8  Oct 27  
Oct 18  Formulae for d(n) and σ(n) Multiplicative arithmetic functions Möbius inversion formula 
6.2, 6.3, 6.4  6.2: 2, 4, 5, 9, 15 6.3: 1 6.4: 2, 4, 5, 7, 8, 11, 12 

Oct 20  No Class (classes meet on Monday schedule) 

Week 9  Nov 3  
Oct 25  More on Möbius inversion formula Properties of reduced residue systems 
6.4, 7.1  7.1: 6, 7 7.2: 7, 8, 9, 10, 11, 12, 13, 14 

Oct 27  Primitive roots  7.2  
Week 10  Nov 10  
Oct 1  Elementary properties of π(x)  8.1  8.1: 1, 2, 5, 6, 7, 9, 10, 12, 16 8.2: 1, 7 

Nov 3  Tchebychev's theorem  8.2  
Week 11  Nov 17  
Nov 8  Euler's criterion. Legendre Symbol  9.1, 9.2  9.1: 1 9.2: 1, 2, 3 9.3: 1, 2, 5, 6 9.4: 1, 3, 4, 5 

Nov 10  Quadratic reciprocity law Applications of quadratic reciprocity law 
9.3, 9.4  
Week 12  
Nov 15  Proof of quadratic reciprocity law. Review  9.3  No Assignment  
Nov 17  Midterm II  
Week 13  
Nov 22  No Class (Thanksgiving holiday)  No Assignment  
Nov 24  
Week 14  Not Due  
Nov 29  Consecutive residues and nonresidues  10.1  10.1: 1, 2, 3, 4, 5, 6, 7 11.1: 1, 2 11.2: 9 

Dec 1  Consecutive triples of quadratic residues  10.2  
Week 15  
Dec 6  Sum of two squares  11.1  No Assignment  
Dec 8  Sum of four squares. Review  11.2 
Midterm I Solutions
Midterm II Solutions
Final Exam Solutions