01:640:356 Theory of Numbers Fall 2017 Syllabus

(Revised 11/29/17) All numbers refer to sections of Rosen's Elementary Number Theory.

Week 1
- Thursday, September 7
  - History and Review
  - Why Number Theory? Some Historical Background and Applications
  - 1.1 Numbers and Sequences
  - 1.3 Induction and the pigeon hole principle
- Monday, September 11
  - 1.4 Fibonacci Numbers
  - 1.5 Divisibility
Week 2
- Thursday, September 14 Homework 1 Due
  - 3.1 Prime Numbers
  - 3.2 Distribution of Primes
  - 3.3 Greatest Common Divisors
  - 3.4 The Euclidean Algorithm
- Monday, September 18
  - 3.5 The Fundamental Theorem of Arithmetic
  - 3.7 Linear Diophantine Equations
Week 3
- Thursday, September 21 Homework 2 Due
  - 4.1 Introduction to Congruences
  - 4.2 Linear Congruences
- Monday, September 25
  - 4.3 The Chinese Remainder Theorem
  - 4.4 Solving Polynomial Congruences
Week 4
- Thursday, September 28 Homework 3 Due
  - 4.5 Systems of congruences
  - 4.6 Factoring via Pollard rho method
- Monday, October 2
  - 5.1 Divisibility Checks
  - 5.5 Check Digits
Week 5
- Thursday , October 5 Homework 4 Due
  - 6.1 Wilson's Theorem and Fermat's Little Theorem
  - 6.2 Pseudoprimes
- Monday, October 9
  - 6.3 Euler's Theorem
  - 7.1 The Euler Phi-Function
Week 6
- Thursday, October 12 Homework 5 Due
  - 7.1 Multiplicative functions
- Monday, October 16
  - Exam 1
Week 7
- Thursday, October 19 Homework 6 Due
  - 7.2 The Sum and Number of Divisors
  - 7.3 Perfect Numbers
- Monday, October 23
  - 7.4 Mobius Inversion
Week 8
- Thursday, October 26 Homework 7 Due
  - 7.5 Partitions and generating series
- Monday, October 30
  - 7.5 Partitions and Euler's pentagonal number formula
Week 9
- Thursday, November 2 Homework 8 Due
  - 9.1 The Order of an Integer and Primitive Roots
  - 9.2 Primitive Roots for Primes
- Monday, November 6
  - 9.3 The Existence of Primitive Roots
  - 9.4 Index Arithmetic
Week 10
- Thursday, November 9 Homework 9 Due
  - 9.3 Primitive Roots
- Monday, November 13
  - 9.4 Index Arithmetic
Week 11
- Thursday, November 16 Homework 10 Due
  - 9.4 More Index Arithmetic
- Monday, November 20
  - 8.4. 10.2 Applications of number theory to cryptography
- Tuesday, November 21 (Thursday schedule at Rutgers due to holiday)
  - Exam 2
Week 12
- Thursday, November 30 Homework 11 Due
  - 11.1 Quadratic residues
- Monday, December 4
  - 11.2 Quadratic reciprocity
Week 13
- Thursday, December 7 Homework 12 Due
  - 11.2, 11.3 More quadratic reciprocity, The Jacobi symbol
- Monday, December 11
  - Review for final exam
Week 14
- Thursday, December 14
  - Office hours 10:30-11:30 in Hill 546
- Monday, December 18
  - Final Exam : Monday 12/18/17 8:00-11:00AM SEC-217