01:640:356 Theory of Numbers Summer 2011 Tentative Lecture Schedule

Tentative lecture schedule for the course, which is subject to change as need dictates. All numbers refer to sections of Rosen's Elementary Number Theory.

Note: Students must attend a majority of class meetings since the previous exam, otherwise they will not be allowed to take the next exam.

Week 1
- Wednesday, June 1
  - History and Review
  - Why Number Theory? Some Historical Background and Applications
  - 1.1 Numbers and Sequences
  - 1.3 Induction
- Thursday, June 2
  - 1.4 Fibonacci Numbers
  - 1.5 Divisibility
  - 3.1 Prime Numbers
  - 3.2 Distribution of Primes
Week 2
- Monday, June 6
  - 3.3 Greatest Common Divisors
  - 3.4 The Euclidean Algorithm
- Wednesday, June 8 Homework 1 Due
  - 3.5 The Fundamental Theorem of Arithmetic
  - 3.7 Linear Diophantine Equations
- Thursday, June 9
  - 4.1 Introduction to Congruences
  - 4.2 Linear Congruences
Week 3
- Monday, June 13
  - 4.3 The Chinese Remainder Theorem
  - 4.4 Solving Polynomial Congruences
- Wednesday, June 15 Homework 2 Due and Midterm 1
  - 5.1 Divisibility Checks
  - 5.5 Check Digits
- Thursday, June 16
  - 6.1 Wilson's Theorem and Fermat's Little Theorem
  - 6.2 Pseudoprimes
Week 4
- Monday, June 20
  - 6.3 Euler's Theorem
  - 7.1 The Euler Phi-Function
- Wednesday, June 22 Homework 3 Due
  - 7.2 The Sum and Number of Divisors
  - 7.3 Perfect Numbers
- Thursday, June 23
  - 7.4 Mobius Inversion
  - 9.1 The Order of an Integer and Primitive Roots
Week 5
- Monday, June 27
  - 9.2 Primitive Roots for Primes
  - 9.3 The Existence of Primitive Roots
- Wednesday, June 29 Homework 4 Due and Midterm 2
  - 9.4 Index Arithmetic
- Thursday, June 30
  - 11.1 Quadratic Residues and Nonresidues
  - 11.2 The Law of Quadratic Reciprocity
Week 6
- Monday, July 4 Lecture cancelled due to holiday.
- Wednesday, July 6 Homework 5 Due
  - 11.5 Zero-Knowledge Proofs
  - Topics from Chapters 8
  - 10.2 The ElGamal Cryptosystem
  - Review
  - Final Comments
- Thursday, July 7 Final Exam, 6-9 PM