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
Monday |
Wednesday |
Friday |
| Aug. 29 |
Aug. 31 Lecture #1: Introduction to Number Theory Divisibility |
Sept. 2 Lecture #2: GCD Division Algorithm Homework Due: R Chapter 5 |
| Sept. 5 Labor Day |
Sept. 7 Lecture #3: Proof of Division Algorithm Euclidean Algorithm Speed of Euclidean Algorithm Homework Due: Written Homework #1: C 5.1,5.3 C Additional Problems NC 5.5 |
Sept. 9 Lecture #4: Bezout's Theorem Homework Due: R Chapter 6 |
| Sept. 12 Lecture #5: Linear Diophantine Equations Homework Due: R Chapter 7 |
Sept. 14 Lecture #6: Prime Numbers Prime Divisibility Theorem Homework Due: Written Homework #2: C 6.1, 6.2 C Additional Problems |
Sept. 16 Lecture #7: E-Zone Fundamental Theorem of Arithmetic Factoring |
| Sept. 19 Lecture #8: Sieve of Eratosthenes Congruence Homework Due: R Chapter 8 (pg 55-59) |
Sept. 21 Lecture #9: Divisibility Rules Solving Congruent Equations Homework Due: Written Homework #3: C 8.1 C Additional Problems NC 6.5,7.2,7.3,7.4 |
Sept. 23 Lecture #10: Finding Incongruent Solutions Inverses |
| Sept. 26 Lecture #11: Find Inverse mod Fermat's Little Theorem Homework Due: R Chapter 9 |
Sept. 28 Lecture #12: Proof of Fermat's Little Theorem Euler's Theorem Homework Due: R Chapter 10 Written Homework #4: C 8.2,8.3abe,8.4abe,8.6 C 9.1,9.4 C Additional Problems NC 8.3cd,8.4d,8.5 |
Sept. 30 Lecture #13: Proof of Euler's Theorem Euler φ Function |
| Oct. 3 Lecture #14: Arithmetic Functions Proof of φ formula Chinese Remainder Theorem Homework Due: R Chapter 11 |
Oct. 5 Lecture #15: Proof of Chinese Remainder Theorem Homework Due: Written Homework #5: C 10.2 C 11.1,11.2,11.5ac,11.12bc C Additional Problems NC 9.2,9.3,10.1 NC 11.5b,11.11a,11.12a |
Oct. 7 Exam 1 Topics: Chapters 5-11 |
| Oct. 10 Lecture #16: Complexity of Computing φ Prime Numbers Homework Due: R Chapter 12 |
Oct. 12 Lecture #17: Prime Number Conjecture Counting Primes Primes of the form an-1 Homework Due: R Chapter 13 Written Homework #6: C 11.7 C Additional Problems |
Oct. 14 Lecture #18: Mersenne Primes Perfect Numbers Sigma Function Homework Due: R Chapter 14 |
| Oct. 17 Lecture #19: Proof of Euler-Euclid Theorem Homework Due: R Chapter 15 R Chapter 16 |
Oct. 19 Lecture #20: Successive Squaring Euler's Theorem and congruence Homework Due: R Chapter 17 Written Homework #7: C 12.2 C 13.2,13.3,13.5 C Additional Problems NC 13.1,13.4,13.6 |
Oct. 21 Lecture #21: Computing roots mod m Homework Due: R Chapter 18 |
| Oct. 24 Lecture #22: RSA RSA in groups |
Oct. 26 Lecture #23: RSA in practice Generating Primes Homework Due: R Chapter 19(129-136) Written Homework #8: C 16.3,16.5 C 17.1 C Additional Problems NC 16.1 |
Oct. 28 Lecture #24: Fermat Test for Primarily Carmichael numbers |
| Oct. 31 Lecture #25: Polynomials Homework Due: R Chapter 8 (60-62) |
Nov. 2 Lecture #26: Arithmetic Function Revisited Property of Phi-Function Order of integer mod p Homework Due: R Chapter 27 Written Homework #9: C In our Shared Directory |
Nov. 4 Lecture #27: Primitive roots Mod p Existence of Primitive Root Homework Due: R Chapter 28 (211-217) |
| Nov. 7 Lecture #28: Proof Korselt's Criterion Squares Modulo p |
Nov. 9 Lecture #29: Legendre Symbol Homework Due: R Chapter 20 Written Homework #10: C In Shared Folder |
Nov. 11 Exam 2 Chapter 8,12-19,27-28 |
| Nov. 14 Lecture #30: Euler Criteria When is -1 a Quadratic Residue Primes congruent to 1 mod 4 Homework Due: R Chapter 21 (148-153) |
Nov. 16 Lecture #31: Gauss's Lemma When is 2 a Quadratic Residue Quadratic Reciprocity!! Homework Due: R Chapter 21 (154-157) Written Homework #11: C In shared Folder |
Nov. 18 Lecture #32: Eisenstein's Lemma Proof of Quadratic Reciprocity (Fun) Homework Due: R Chapter 22 |
| Nov. 21 Lecture #33: Jacobi Symbol Homework Due: R Chapter 23(optional- no quiz) |
Nov. 23 Thanksgiving Break |
Nov. 25 Thanksgiving Break |
| Nov. 28 Lecture #34: Properties of Jacobi Symbol Euler Witnesses |
Nov. 30 Lecture #35: Solovay-Strassen Theorem Homework Due: Written Homework #12: C In shared Folder |
Dec. 2 Lecture #36: Index of a Primitive Root Discrete Log Problem Finding a Primitive Root Homework Due: R Chapter 29 |
| Dec. 5 Lecture #37: Diffie-Hellman Key Exchange ElGamal Encryption system |
Dec. 7 Lecture #38: Practice with ElGamal |
Dec. 9 Lecture #39: Live From a secret location Homework Due: Written Homework #13: C In shared Folder |