01:640:356 Theory of Numbers Fall 2018 Syllabus

(Revised 11/7/18) All numbers refer to sections of Rosen's Elementary Number Theory.

Week 1
- Thursday, September 6
  - 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 10
  - 1.4 Fibonacci Numbers
  - 1.5 Divisibility
Week 2
- Thursday, September 13 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 20 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 27 Homework 3 Due
  - 4.5 Systems of congruences
  - 4.6 Factoring via Pollard rho method
- Monday, October 1
  - 5.1 Divisibility Checks
  - 5.5 Check Digits
Week 5
- Thursday , October 4 Homework 4 Due
  - 6.1 Wilson's Theorem and Fermat's Little Theorem
  - 6.2 Pseudoprimes
- Monday, October 8
  - 6.3 Euler's Theorem
  - 7.1 The Euler Phi-Function
Week 6
- Thursday, October 11 Homework 5 Due
  - 7.1 Multiplicative functions
- Monday, October 15
  - Exam 1 ( Sample Exam 1)
Week 7
- Thursday, October 18 Homework 6 Due
  - 7.2 The Sum and Number of Divisors
  - 7.3 Perfect Numbers
- Monday, October 22
  - 7.4 Mobius Inversion
Week 8
- Thursday, October 25 Homework 7 Due
  - 7.5 Partitions and generating series
- Monday, October 29
  - 7.5 Partitions and Euler's pentagonal number formula
Week 9
- Thursday, November 1 Homework 8 Due
  - 9.1 The Order of an Integer and Primitive Roots
  - 9.2 Primitive Roots for Primes
- Monday, November 5
  - 9.3 The Existence of Primitive Roots for certain moduli
Week 10
- Thursday, November 8 Homework 9 Due
  - 9.3 Primitive Roots
  - 9.4 Index Arithmetic
- Monday, November 12
  - 9.4 More Index Arithmetic
Week 11
- Thursday, November 15 Homework 10 Due
  - 8.4 Applications of number theory to cryptography
- Monday, November 19
  - 8.4. 10.2 Applications of number theory to cryptography
Week 12
- Tuesday, November 20 Homework 11 Due (Thursday schedule at Rutgers due to holiday)
  - Exam 2
- Monday, November 26
  - 11.1 Quadratic residues
Week 13
- Thursday, November 29 Homework 12 Due
  - 11.2 Quadratic reciprocity
- Monday, December 3
  - 11.2 More Quadratic reciprocity, Pepin's test
Week 14
- Thursday, December 6 Homework 13 Due
  - 11.2, 11.3 Quadratic reciprocity, The Jacobi symbol
- Monday, December 10
  - Catchup and Review for Final Exam
- Monday, December 17
  - Final Exam : Monday 12/17/18 8:00-11:00AM SEC-217