Lectures |
Sections in Text |
Brief Description |
9/20 |
1.4 |
Introduction: History of Number Theory, Leonardo Fibonacci |
9/22 |
1.3, 1.5 |
Mathematical Induction, Divisibility |
9/25 |
2.3, 3.1 |
Complexity of Integer Operations, Introduction to Prime Numbers |
9/27 |
3.2, 3.3 |
Distribution of Primes, Greatest Common Divisor |
9/29 |
3.4 |
Euclidean Algorithm |
10/2 |
3.5, 3.6 |
Fundamental Theorem of Arithmetic, Factorization & Fermat |
10/4 |
4.1 |
Introduction to Congruences |
10/6 |
4.2, 4.3 |
Linear Congruences, Chinese Remainder Theorem |
10/9 |
4.3, 4.4 |
More on CRT, Polynomial Congrences |
10/11 |
4.4, 5.1 |
More Polynomial Congruences, Tests for Divisibility |
10/11 |
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Midterm Exam #1 handed out |
10/13 |
5.1, 5.2 |
Applications: Tests for Divisibility, Perpetual Calendar |
10/16 |
5.5 |
Application: Check Digits |
10/18 |
6.1, 6.2 |
Wilson's Theorem, Fermat's Little Theorem, Pseudoprimes |
10/20 |
6.2 |
Pseudoprimes, Carmichael Numbers |
10/23 |
6.2, 6.3 |
Primality Tests, Euler's Theorem |
10/25 |
7.1, 7.2 |
Euler's φ-function, σ- and τ-functions |
10/25 |
7.2, 7.3 |
More on the σ- and τ-functions, Perfect Numbers |
10/27 |
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No Class |
10/30 |
7.3, 7.4 |
Mersenne Primes, Möbius Inversion |
10/31 |
Supplement |
Euler, Fermat and 17th/18th Century Mathemtaics |
11/1 |
8.1, 4.5 |
Character Ciphers, Systems of Linear Congruences |
11/3 |
8.2 |
Block and Stream Ciphers |
11/3 |
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Midterm Exam #2 handed out |
11/6 |
8.2, 8.3 |
Exponentiation Ciphers |
11/8 |
8.4, 8.5 |
Public Key Cryptography, Knapsack Ciphers |
11/10 |
8.5, Supplement |
Misc. Cryptology Topics |
11/13 |
11.1 |
Introduction to Quadratic Residues |
11/15 |
11.1, 11.2 |
Law of Quadratic Reciprocity |
11/17 |
11.2 |
More on Quadratic Reciprocity |
11/20 |
11.3, 11.4 |
The Jacobi Symbol, Euler Pseudoprimes |
11/27 |
3.7, 13.1 |
Diophantine Equations |
11/29 |
13.2 |
Introduction to Fermat's Last Theorem
|
11/29 |
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Final Exam Handed Out |
12/4 |
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Final Exam Due, 12:00pm |