All numbers indicate sections from A Friendly Introduction ot Number Theory -- 3rd 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. 29 Lecture: Introduction to Number Theory Pythagorean Triples Homework: R Chap. 1,3-5 C 1.2,1.3,2.1,2.2 NC 1.1,1.4 |
Jan. 31 Lecture: Fermat's Last Theorem Divisibility Greatest Common Divisor (GCD) Homework: R Chap. 6-7 C 5.1,5.4,5.5a-b C Additional Problems NC 5.5c-e |
| Feb. 5 Lecture: Validity of Euclidean Algorithm Linear Combinations Solutions to Linear Diophantine Equations Homework: R Chap. 8 C 6.1,6.2,6.5 C Additional Problems NC 6.6 |
Feb. 7 Last Week's Homework Due Lecture: Prime Divisibility Theorem E-Zone Fundamental Theorem of Arithmetic Homework: R You get a break C 7.1,7.2,7.3cd,7.5 NC 7.3ab,7.4 |
| Feb. 12 Lecture: Uniqueness of Division Algorithm Congruences Homework: R Chap. 9 and 10 C 8.1,8.2,8.3,8.4abde,8.5ab,8.6ab NC 8.5c,8.6c |
Feb. 14 Homework Due: Last Week's Homework Quiz 1 Lecture: Fermat's Little Theorem Homework: R Chap. 11 C 9.1,9.2a,9.3,9.4 |
| Feb. 19 Lecture: Euler's Phi Function Euler's Theorem Multiplicative Arithmetic Functions Homework: R Chapter 12 C 10.3a,11.1,11.2,11.5,11.6,11.12ab C Additional Problems NC 11.12c |
Feb. 21 Homework Due: Last Week's Homework Lecture: Proof of Chinese Remainder Theorem Infinitely Many Prime Numbers Dirichlet's Theorem on Primes in Arithmetic Progressions Homework: R Chapter 13 and 14 C 7.2(again),11.9,11.10,11.11a,12.1,12.2 NC 11.11bc,12.3 |
| Feb. 26 Lecture: Prime Number Theorem Prime Number Conjectures Mersenne Prime Homework: R Chap. 15 C 13.1a, 13.2,13.3,13.4ac,13.5,13.6a NC 13.1b,13.4bd |
Feb. 28 Homework Due: Homework from Last Week Lecture: Mersenne Primes and Perfect Number Sigma Function Homework: R Chap. 16 and Chap. 17 C 15.2,15.3abc C Additional Problems NC 15.1, 15.4de,15.5 |
| March 4 Lecture: Computing Powers by successive squaring Computing Roots Questions for Exam Homework: C Study for exam |
March 6 Exam 1 Homework Due: Last Week's Homework You may turn it in on Friday Homework: C 16.1,16.3a,17.1,17.2a,17.4 C Additional Problems Click here to copy and paste the numbers. NC 16.3b,16.5,17.2b |
| March 11 Lecture: Cryptography Caesar Shifts Monographic Substitutions Homework: C Problems NC Problems |
March 13 Homework Due: Last Week's Lecture: Vigenere Cipher Playfair Cipher Hill Cipher Correction to Lecture Homework: R Chapter 18 C Problems NC Problems |
| March 18 Spring Break |
March 20 Spring Break |
| March 25 Lecture: Public Key Cryptography RSA Homework: R Chapter 19 C 18.1,18.4 Link to Book Website C Problems NC Problems |
March 27 Homework Due: Last Week's Homework (Really 2 weeks ago) Lecture: PGP ADFGVX Homework: R Chapter 21 (We are skipping a chapter) C 19.3acfghl, 19.4 C Problems NC 19.3(rest) |
| April 1 Lecture: Carmichael Numbers Rabin-Miller Test Homework: C 19.5,19.7 (use gp) C Problems Click here to copy and paste |
April 3 Homework Due: Last Week's Homework Lecture: Mobius Inversion Formula Sum of Phi Primitive Roots Homework: R Chapter 22 C 19.1,20.1,20.2a C Problems NC 20.3 |
| April 8 Lecture: Mobius Inversion Formula Existence of Primitive Roots Homework: R Chap. 23 C 21.2,21.4,21.6,21.8 C Problems NC 21.1,21.7 |
April 10 Lecture: Primitive Roots Index Homework: C Study for Exam |
| April 15 Exam 2 Chapters 17-21 Cryptography MAF's Homework Due: Last Week's Homework Homework: R Chapter 23 (again) C 22.1ad,22.2,22.3,22.6 NC 22.1bc,22.4 |
April 17 Homework Due: Last Week's Homework Lecture: Quadratic Residues Legendre symbol Homework: R Chapter 24 C 23.1,23.3 |
| April 22 Lecture: Gauss's Lemma When is 2 a Quadratic Residue? Homework: R Chapter 25 C 24.1ac,24.2(get a list of 10 numbers) C Problems NC 21.bc,24.3 |
April 24 Homework Due: Last Week's Homework Lecture: Quadratic Reciprocity Eisensein's Lemma Homework: C Problems C More Problems Click here to copy and paste |
| April 29 Lecture: Proof of Quadratic Reciprocity Jacobi Symbol Homework: R Chapter 33 C Problems NC Problems |
May 1 Homework Due: Last Week's Homework Lecture: Gaussian Integers Homework: R Chapter 34 (pg. 253-261) C 33.4a,33.5ac,33.6a C Problems NC 33.4b,33.5bd,33.6b |
| May 6 Lecture: Gaussian Primes Homework: NC Problems |
May 8 Homework Due: Last Week's Homework |