MAT 418-01 Tentative Schedule

Emphasis on tentative! The instructor reserves the right to change schedules and topic, depending on the class’s needs and other events!

Date Planned

Date Actual

Topic

Week 11-2Ch. 1: What is Number Theory? and
Chs. 2-3: Pythagorean Triples
Week 2Weeks 2-3Ch. 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 3Weeks 3-4Ch. 7: Factorization and the Fundamental Theorem of Arithmetic and
Ch. 8: Congruences
Week 4Weeks 4-5Ch. 9-10: Congruences, Powers, Fermat’s Litle Theorem, and Euler’s Formula
Week 5Weeks 5-6Ch. 11: Euler’s \(\phi\)-function and the Chinese Remainder Theorem and
Ch. 12: Prime Numbers
Test 1 through the middle of Chapter 11
Week 6Weeks 5-6Ch. 13: Counting Primes and
Chs. 14-15: Mersenne Primes and Perfect Numbers
Week 7Week 7Ch. 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 8-9Weeks 8-9Chs. 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)