Date Planned |
Date Actual |
Topic |
Week 1 | 1-2 | Ch. 1: What is Number Theory? and Chs. 2-3: Pythagorean Triples |
Week 2 | Weeks 2-3 | Ch. 4: Sums of Higher Powers and Fermat’s Last Theorem and Ch. 5: Divisibility and the Greatest Common Divisor and Ch. 6: Linear Equations and the Greatest Common Divisor |
Week 3 | Weeks 3-4 | Ch. 7: Factorization and the Fundamental Theorem of Arithmetic and Ch. 8: Congruences |
Week 4 | Weeks 4-5 | Ch. 9-10: Congruences, Powers, Fermat’s Litle Theorem, and Euler’s Formula |
Week 5 | Weeks 5-6 | Ch. 11: Euler’s \(\phi\)-function and the Chinese Remainder Theorem and Ch. 12: Prime Numbers |
Test 1 through the middle of Chapter 11 | ||
Week 6 | Weeks 5-6 | Ch. 13: Counting Primes and Chs. 14-15: Mersenne Primes and Perfect Numbers |
Week 7 | Week 7 | Ch. 16: Powers Modulo \(m\) and Successive Squaring and Ch. 17: Computing \(k^{\textrm{th}}\) Roots Modulo \(m\) and Ch. 18: Powers, Roots, and “Unbreakable” Codes (aka RSA algorithm) |
Weeks 8-9 | Weeks 8-9 | Chs. 35-36: Gaussian integers and unique factorization and Ch. 37: Irrational and Transcendental Numbers (including Liousville’s Number) |
Test 2 emphasizes the Chinese Remainder Theorem, Chapters 12-18, and Chapters 35-37 (excluding anything related to the sums of two squares) |