| This schedule dates from when MAT 421 was a summer class. You can estimate the spring schedule by multiplying the week number by 1.5. |
|
Date Planned |
Date Actual |
Topic |
| Week 1 | Ch. 1: What is Number Theory? and Chs. 2-3: Pythagorean Triples |
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| Week 2 | 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 |
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| Week 3 | Ch. 7: Factorization and the Fundamental Theorem of Arithmetic and Ch. 8: Congruences |
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| Week 4 | Ch. 9-10: Congruences, Powers, Fermat’s Litle Theorem, and Euler’s Formula | |
| Week 5 | 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 | Ch. 13: Counting Primes and Chs. 14-15: Mersenne Primes and Perfect Numbers | |
| 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 | 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) | ||