Location: TOMP 203

Schedule: Tuesday, Thursday, 4:45pm-6:00pm

Instructor: Poorvi Vora, poorvi@gwu.edu, 706 Philips Hall. Office Hours: Tues, 1-4 pm, Wed: 2-5 pm

Grader: Bowu Zhang, bowuzh@gwu.edu.

Text: Grimaldi, “Discrete and Combinatorial Mathematics”. Class Notes.

Course Content: Complex Numbers, Linear Algebra, Algorithmic Number Theory, with applications to media compression, audio-video processing and computer security

Prerequisites: CSci 123 (Discrete Structures I) or equivalent discrete mathematics, Math 31 or single-variable calculus

Grading: HWs (30%), best 10 quizzes (15%), two tests (15% each), final (25%). HWs are due by 6 pm on the due date. Late HWs are not allowed.

224 and 124 will be graded separately. If you are an undergrad, please consult your adviser before choosing to take 224; graduate credit for 224 is not automatic for undergrads, but all those enrolled in 224 will be graded together.

Course Outline

Slides and notes on this website are not in final form till one week after the lecture covering the material. I often update notes and slides during and after the lecture

Planned Schedule

2 September 2008 Lecture 1: Divisibility and a review of Mathematical Induction.	4 September 2008 Lecture 2: Shift and Affine Ciphers. Notes, sections 1-3 Quiz 1
9 September 2008 Lecture 3: Modular Arithmetic. Notes, section 4	11 September 2008 Lecture 4: Rings Quiz 2
16 September 2008 Lecture 5: Rings: Chapter 14.1 from text HW 1 assigned. Due 25 September, 6 pm.	18 September 2008 Lecture 6: Rings: Chapter 14.1 from text completed Quiz 3
23 September 2008 Lecture 7: Rings: Chapter 14.2 from text	25 September 2008 Lecture 8: GCD: Euclidean algorithm Quiz 4
30 September 2008 Lecture 9: GCD: Euclidean algorithm	2 October 2008 Lecture 10: Euclidean algorithm for inverse mod m Quiz 5
7 October 2008 Test	9 October 2008 Lecture 12: Units and zero divisors. See additional notes on groups. HW 2 assigned. Due 23 October, 6 pm on Blackboard.
14 October 2008 Lecture 13: Proof of correctness of euclidean algorithm. See complete description of euclidean algorithm updated 16 October. Notes on units.	16 October 2008 Lecture 14: Fast exponentiation mod m Notes, Practice Quiz 6 Test 1 Solutions
21 October 2008 Lecture 15: Chinese Remainder Theorem Notes	23 October 2008 Lecture 16: Groups: Homomorphisms and isomorphisms Notes Quiz 7
28 October 2008 Lecture 17: Gaussian Elimination Notes HW 3 assigned. Due 4 November	30 October 2008 Lecture 18: Complete gaussian elimination. Quiz 8
4 November 2008 Lecture 19: Vector Spaces, definition. Notes Quiz 7 solutions, Quiz 8 solutions,	6 November 2008 Lecture 20: Test on Lectures 12-18
11 November 2008 Lecture 21: Spans. Notes	13 November 2008 Lecture 22: Basis. HW 4 assigned. Due 26 November on Blackboard HW 3 solutions Quiz 9
18 November 2008 Lecture 23: Basis. Notes. Inner Products, section 1 from notes	20 November 2008 Lecture 24: Complete Inner Products and Orthogonality. Quiz 10
25 November 2008 Lecture 24: Gauss-Jordan Matrix Inverse and Determinants notes HW 5 assigned. Due 4 December, 6 pm., in instructor mailbox or in class.	27 November 2008 Holiday: Thanksgiving
2 December 2008 Lecture 26: Cramer's Rule notes Extra Credit HW assigned. Due 16 December, 6 pm., on Blackboard.	27 November 2008 Lecture 27: Matlab Quiz 11