All numbers indicate sections from A Friendly Introduction to Number Theory -- 4rd Edition.
R is for the reading assignment
C is for exercises that are assigned and will be collected
NC is for exercises that are assigned but will not be collected
Tuesday |
Thursday |
| Jan. 30 Lecture #1: Guest Lecture: Adam Boocher Title: From Magic Squares to Polynomials |
Feb. 1 Lecture #2: Divisibility Division Algorithm GCD Homework Due: R Chapter 5 |
| Feb. 6 Lecture #3: Euclidean Algorithm Speed of Euclidean Algorithm Homework Due: R Chapter 6 |
Feb. 8 Lecture #4: Bezout's Theorem Solutions to Linear Diophantine Equations Homework Due: R Chapter 7 Written Homework #1: C 5.1,5.3 C Additional Problems NC 5.5 |
| Feb. 13 Lecture #5: Prime Numbers |
Feb. 15 Lecture #6: Prime Divisibility Theorem E-Zone Fundamental Theorem of Arithmetic Homework Due: R Chap. 8 Written Homework #2: C 6.1,6.2,6.5 C 7.1,7.2 C Additional Problems NC 6.6 |
| Feb. 20 Lecture #7: Factoring Congruence |
Feb. 22 Lecture #8: LCM Solving Congruent Equations Fermat's little Theorem Homework Due: R Chapter 9 Written Homework #3: C 7.4b,7.5cd C Additional Problems NC 7.2,7.3,7.6 |
| Feb. 27 Lecture #9: Euler's Theorem Homework Due: R Chapter 10 |
March 1 Quiz #1 Lecture #10: Computing φ Homework Due: R Chapter 11 Written Homework #4: C 8.1,8.2,8.3abe,8.4abe,8.6 C 9.1,9.4 C Additional Problems NC 8.3cd,8.4d,8.5 |
| March 6 Lecture #11: Proof of φ formula Chinese Remainder Theorem Homework Due: R Chapter 12 |
March 8 Lecture #12: Counting Primes Homework Due: R Chapter 13 Written Homework #5: C 10.2 C 11.1,11.2,11.5ac,11.12bc C Additional Problems NC 11.5b,11.11a,11.12a |
| March 13 Lecture #13: Mersenne Primes and Perfect Number σ function Homework Due: R Chapters 14 and 15 |
March 15 Exam 1 Topics Chapter 5-15 Written Homework #6: C 12.2 C 13.2,13.3,13.5,13.6a C 14.3 NC 13.1,13.4 |
| March 20 Lecture #14: Successive Squaring Computing roots mod m Homework Due: R Chap. 16 |
March 22 Lecture #15: RSA Homework Due: R Chapter 17 Written Homework #7: C 15.2,15.3abc,15.8ab C Additional Problems NC 15.3de,15.5 |
| March 27 Spring Break |
March 29 Spring Break |
| April 3 Lecture #16: Fermat Test for Primality Carmichael numbers Homework Due: R Chapter 18 and 19 C Peer Review |
April 5 Lecture #17: Rabin-Miller Test Quadratic Residues Homework Due: R Chapter 20 Written Homework #8: C 16.3,16.5 C 17.1 C Homework Sent to you C Additional Problems NC 16.1 |
| April 10 Lecture #18: Legendre Symbol Polynomial roots mod p Euler Criterion Homework Due: R Chapter 21 |
April 12 Quiz #2 Lecture #19: Gauss's Lemma When is 2 a Quadratic Residue Homework Due: R Chapter 22 Written Homework #9: C 19.3bdgh,19.4,20.3ab C Additional Problems C Homework Sent to you NC 19.4acefi,19.6c |
| April 17 Office hours Today: 3:30-5 Lecture #20: Quadratic Reciprocity!! Homework Due: R Chapter 23(optional- no quiz) |
April 19 Lecture #21: Jacobi Symbol Euler Witnesses Homework Due: Written Homework #10: C 21.1 C Additional Problems |
| April 24 Lecture #22: Solovay-Strassen Theorem Arithmetic Function revisited Homework Due: R Chapter 27 |
April 26 Exam 2 Topics TBA Homework Due: Written Homework #11: C Problem sent by email C Additional Problems |
| May 1 Lecture #23: Primitive roots Mod p Homework Due: R Chapter 28 |
May 3 Lecture #24: Index of a Primitive Root Diffie-Hellman Homework Due: R Chapter 29 Written Homework #12: C Additional Problems |
| May 8 Lecture #25: Finding primitive roots ElGamal |
May 10 Lecture #26: Questions for the Final Meet at secret location Homework Due: Written Homework #13: C Problems Emailed to You |