Catalogue Syllabus: Properties of the natural numbers, congruences, diophantine equations, prime numbers and elementary arithmetical functions.
| Week | Lecture dates | Sections | topics |
|---|---|---|---|
| 1 | 9/3 (Thurs) | 1.1-1.2 | Numbers and Sequences, sums and products |
| 2 | 9/8(T), 9/10 | 1.3-1.5; 2.1-2.2 | Induction, Fibonacci numbers, Division Algorithm
Integer Representations and Operations |
| 3 | 9/14, 9/17 | 2.3, 3.1-3.2 | Complexity, Prime Number & their distribution |
| 4 | 9/21, 9/24 | 3.2-3.4 | GCDs and the Euclidean Algorithm |
| 5 | 9/28, 10/1 | 3.5, 4.1-4.2 | Fundamental Theorem, Congruences |
| 7 | 10/5, 10/8 | 4.3, 4.5, 4.6 | Chinese Remainder Thm, Factoring numbers (ρ method) |
| 7 | 10/12, 10/15 | Review, Midterm | Chapters 1-4 |
| 8 | 10/19, 10/22 | 6.1-6.2 | Wilson's Theorem, Fermat's Little Theorem, pseudo-primes |
| 9 | 10/26, 10/29 | 6.3, 7.1-7.2 | Euler's φ function, Euler's Theorem, Sum and Number of Divisors |
| 10 | 11/2, 11/5 | 7.3-7.4 | Perfect numbers, Möbius inversion |
| 11 | 11/9, 11/12 | 9.1-9.4 | Primitive roots, Discrete Logarithms, Quadratic Residues |
| 12 | 11/16, 11/19 | 10.1-10.2 | El Gamal cryptosystem, Review |
| 13 | 11/23 (Mon) | Midterm | Chapters 6,7,9 |
| 14 | 11/30, 12/3 | 11.1-11.2 | Legendre symbols, Quadratic Reciprocity |
| 15 | 12/7, 12/10 | 13.1-13.2 | Pythagorean triples, Fermat's Last Theorem |
| 14 | 12/18 (Friday) | Final Exam 8-11 AM | |
| Due date | Homework Section/Problems |
|---|---|
| 9/14/09 | 1.4 #4,16; 1.5 #5a,8,24,27 |
| 9/21/09 | 2.2 #14,16; 2.3 #4,14,16 |
| 9/24/09 | 3.1 #3,6,16(c),19,21; 3.2 #6(d),10(a),12,20(a) |
| 10/1/09 | 3.3 #2f,10,22 3.4 #2bc,4bc,25 3.5 #2,6,10,16 |
| 10/8/09 | 4.1 #4,6(bcde),8,22,28(a); 4.2 #2(abc),8,10 |
| 10/15/09 | 4.3 #4(abc),8,12,17a,18; 4.5 #2a,4,10a,11a; 4.6 #2(b,d) |
| 10/29/09 | 6.1 #3,4,10,12,26; 6.2 #1,2,7 |
| 11/5/09 | 6.3 #2,6,16; 7.1 #2,4(bc),12,20,30; 7.2 #2(de),10,12 |
| 11/12/09 | 7.3 #2,4(c),18; 7.4 #2(g),8,10,15,24,30,31; 9.1 #2(bd),6,8 |
| 11/19/09 | 9.2 #2(b,c),6,10; 9.3 #2,6(a),8(b); 9.4 #2(a),4,8 |
| 12/3/09 | 11.1 #2(a,d), 4, 8, 20 |
| 12/10/09 | 11.2 #1, 2, 4, 13(a,b,d); 13.1 #2, 4, 12 |
Charles Weibel / Fall 2009