5/17: Course grades posted to SIS. Have a great summer!
5/17: Final exam solution posted.
5/1: Office hours for Final Exam: Wednesday May 15, 3:305:30pm, Krieger 412.
5/1: Reminder: The Final Exam is Thursday, May 16, 2:005:00pm.
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  Not Due  
Apr 23  Consecutive triples of quadratic residues  10.2  10.2: 2 11.1: 1 11.2: 9 

Apr 25  Sum of two squares  11.1  
Week 14  
Apr 30  Sum of four squares  11.2  
May 2  Review 