15/17: Course grades posted to SIS. Have a great summer!
5/17: Final exam solution posted.
5/1: Office hours for Final Exam: Tuesday May 15, 1:004:00pm, Krieger 412.
5/1: Reminder: The Final Exam is Wednesday, May 16, 9:00 am 12:00 noon, Maryland 104.
4/17: Office hours for Midterm II: Wednesday April 18 24:30pm.
4/10: Reminder: Midterm II is on Thursday April 19.
3/6: Office hours change for Wednesday 3/7 only: 121pm.
2/28: Reminder: Midterm I is on Tuesday March 6.
2/20: 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.
2/7: TA's office hours: Tuesday 12pm. Krieger 211.
1/16: The first meeting of this class is on Tuesday January 30.
Date  Topic  Sections  Homework  Due Date 
Week 1  Feb 8  
Jan 30  Introduction. Mathematical Induction  1.1  1.1: 1, 7, 10, 11, 13, 15 1.2: 6, 7 2.1: 2, 4, 5 

Feb 1  Basis representation theorem Euclid's division lemma 
1.2, 2.1  
Week 2  Feb 15  
Feb 6  Divisibility  2.2  2.2: 2, 10, 11, 12 2.3: 1(d), 4 2.4: 6(f), 8, 10, 12 

Feb 8  Linear Diophantine equations Fundamental theorem of arithmetic 
2.3, 2.4  
Week 3  Feb 22  
Feb 13  Permutations and combinations Fermat's Theorem 
3.1, 3.2  3.1: 3, 6, 7, 13, 14 3.2: 3, 6 3.3: 1, 2 3.4: 3, 5 

Feb 15  Wilson's theorem Generating functions 
3,3, 3.4  
Week 4  Mar 1  
Feb 20  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, 5, 9, 11, 15, 21, 23 

Feb 22  Solving
Linear Congruences Euler's Theorem. Fermat and Wilson Theorem (using congruences). 
5.1, 5.2  
Week 5  Mar 8  
Feb 27  Chinese remainder theorem  5.3  5.3: 2, 4, 6 5.4: 3, 4, 5, 6, 7 

Mar 1  Polynomial congruences Review 
5.4  
Week 6  Mar 15  
Mar 6  Midterm I  6.1: 1, 4, 5, 8, 9, 10, 11, 13  
Mar 8  Combinatorial study of φ(n)  6.1  
Week 7  Mar 29  
Mar 13  Formulae for d(n) and σ(n) Multiplicative arithmetic functions 
6.2, 6.3  6.2: 2, 4, 5, 9, 15 6.3: 1 6.4: 2, 4, 5, 7, 11, 12 

Mar 15  Möbius inversion formula  6.4  
Week 8  
Mar 20  No Class (spring break)  
Mar 22  
Week 9  Apr 5  
Mar 27  Properties of reduced residue systems  7.1  7.1: 6, 7 7.2: 7, 8, 9, 10, 11, 12, 13, 14 

Mar 29  Primitive Roots  7.2  
Week 10  Apr 12  
Apr 3  Elementary properties of π(x)  8.1  8.1: 1, 2, 5, 6, 7, 10, 12, 16 8.2: 1, 7 

Apr 5  Tchebychev's theorem Quadratic Residues 
8.2, 9.1  
Week 11  Apr 19  
Apr 10  Legendre Symbol. Gauss's Lemma Quadratic reciprocity law 
9.2, 9.3  9.1: 1 9.2: 1, 2, 3 9.3: 5, 6 9.4: 1, 3, 4, 5 

Apr 12  Applications of quadratic reciprocity law  9.4  
Week 12  Apr 26 (Last HW Due) 

Apr 17  Proof of quadratic reciprocity law Review 
9.3  10.1: 3, 4, 5, 6, 7  
Apr 19  Midterm II  
Week 13  Not Due  
Apr 24  Consecutive residues and nonresidues  10.1  10.2: 2 11.1: 1, 2 11.2: 9 

Apr 26  Consecutive triples of quadratic residues  10.2  
Week 14  
May 1  Sum of two squares  11.1  
May 3  Sum of four squares Review 
11.2 