Instructor(s): Tristan Phillips

Course on canvas.dartmouth.edu.

Syllabus

Week Class Day  Topics  Textbook Chapters
Week 1 9/15 (M)

What is number theory?

Pythagorean Triples

1, 2
9/17 (W) Pythagorean Triples and the Unit Circle 2, 3
9/19 (F) Divisibility, Greatest Common Divisor, and Linear Equations  5,6
Week 2 9/22 (M) Factorization, the Fundamental Theorem of Arithmetic, and Congruences 7,8
9/24 (W) Congruences, Powers, and Fermat's Little Theorem 8,9
9/26 (F) Fermat's Little Theorem and Euler's Formula 9,10
Week 3 9/29 (M) Euler's Phi Function and Primes 11, 12
10/1 (W) Primes and Counting Primes 12, 13
10/3 (F) Prime Conjectures and Mersene Primes 13, 14
Week 4 10/6 (M) Mersenne Primes and Perfect Numbers 15
10/8 (W) Successive Squaring and k-th Roots Modulo m 16, 17
10/10 (F) Exam I
Week 5 10/13 (M) "Unbreakable" Codes 18
10/15 (W) Primality Testing and Carmichael Numbers 19
10/17 (F) Square-Triangular Numbers 31
Week 6 10/20 (M) Pell Equations and Diophantine Approximation 32, 33
10/22 (W) Diophantine Approximation and Pell Equations 33, 34
10/24 (F) Continued Fractions 34, 47 (online Links to an external site.)
Week 7 10/27 (M) Continued Fractions 47 (online Links to an external site.)
10/29 (W) Continued Fractions and Pell Equations 48 (online Links to an external site.)
10/31 (F) Exam II
Week 8 11/3 (M)
11/5 (W)
11/7 (F)
Week 9 11/10 (M) Project Presentations
11/12 (W) Project Presentations
11/14 (F) Project Presentations
Week 10 11/17 (M) Project Presentations