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Syllabus

NOTE: This is a tentative syllabus, and is subject to change.
However, the study information given on the homework page will always be accurate.

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 --- 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 --- 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 --- 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 --- Final Exam Handed Out
12/4 --- Final Exam Due, 12:00pm