Homework assignments will be posted here
Tips for writing solutions to mathematics problems
1. The Integers
1.3 Mathematical induction 1.3
1.5 Divisibility 1.5
3 Primes and Greatest Common Divisors
3.1 Prime numbers
3.2 The distribution of primes
3.3 Greatest common divisors
3.4 The Euclidean algorithm
3.5 The fundamental theorem of arithmetic
3.7 Linear Diophantine equations
4 Congruences.
4.1 Introduction to congruences
4.2 Linear congruences
4.3 The Chinese Remainder Theorem
5 Applications of Congruences
5.1 Divisibility tests
5.2 The perpetual calendar (will not be covered on final exam)
5.5. Check digits (ISBN code only)
6 Some Special Congruences
6.1 Wilson's Theorem and Fermat's Little Theorem
6.2 Pseudoprimes
6.3 Euler's Theorem
7 Multiplicative Functions
7.1 The Euler phi-function
7.2 The sum and number of divisors
7.3 Perfect numbers and Mersenne primes
8 Cryptology.
8.1 Character ciphers
8.4 Public key cryptography
8.6 Cryptographic protocols and applications (digital signatures only)
If time permits, additional topics from Chapters 9, 10 or 11.