Location: Lectures: DUQUES 361; Discussion Section: TOMP 410

Schedule: Lectures: Tuesday, Thursday, 4:45pm-6:00pm; Discussion Section: Wed., 2:20-3:10 pm

Instructor: Poorvi Vora, poorvi@gwu.edu, 706 Philips Hall. Office Hours: Tues: 1-2 pm, 6-8:30 pm, Thurs: 1:30-4 pm

TA: Nadezhda (Nadya) Radeva, nradeva@gwmail.gwu.edu, Staughton Hall 309. Office Hours: Mon: 10am-1pm

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%), Quizzes (15%), two tests (15% each), final (25%). HWs are due by 6 pm on the due date. Late HWs are not allowed.

Course Outline, Course Description, Course Outcome Form,

Discussion Session Outline and Syllabus

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

1 September 2009 Lecture 1: Review of Mathematical Induction.	2 September 2009 Discussion Session 1: Problems on Induction	3 September 2009 Lecture 2: Divisibility. Quiz 1
8 September 2008 Lecture 3: Shift and Affine Ciphers: Notes, read sections 1-3 before class. Modular Arithmetic. These notes were modified at 1:50 pm on Thursday, 10 September.	9 September 2009 Discussion Session 2: Modular Arithmetic Proofs	10 September 2009 Lecture 4: Rings. Group Definition and section 14.1 from text HW 1 assigned. Due September 25, 6 pm. Quiz 2
15 September 2009 Lecture 5: Rings: Chapter 14.1 from text	16 September 2009 Discussion Session 3: Problems on Rings, Proofs	17 September 2008 Lecture 6: Rings: Chapter 14.1 from text completed Quiz 3
22 September 2009 Lecture 7: Properties of rings	23 September 2009 Discussion Session 4: Euclidean algorithm for GCD and inverse	24 September 2009 Lecture 8: Continue euclidean algorithm for gcd. Practice Problems, GCD, Practice Problems, Multiplicative inverses. HW 2 assigned. Originally due 9 October, 6 pm. Deadline extended to October 16, 6 pm. Quiz 4
29 September 2009 Lecture 9: Units in the integers modulo m.	30 September 2009 Discussion Session 5: Rings: Complete chapter 14.2 from text	1 October 2009 Lecture 10: Units in the integers modulo m. Quiz 5
6 October 2009 Lecture 11: Complete: Units in the integers modulo m. HW 2 Deadline extended to October 16, 6 pm.	7 October 2009 Discussion Session 6: Complete assigned problems	8 October 2009 Lecture 12: Proof of correctness of euclidean algorithms. Quiz 6
13 October 2009 Test 1	14 October 2009 Discussion Session 7: Break affine and shift ciphers	15 October 2009 Lecture 14: Begin Homomorphisms
20 October 2009 Lecture 15: Complete Homomorphisms and isomorphisms. Return and discuss test.	21 October 2009 Discussion Session 8: Homomorphisms: Problems	22 October 2009 Lecture 16: Vector Spaces: Definitions and Examples HW 3 assigned on 23 October. Due 6 November, 6 pm. Quiz 7
27 October 2009 Lecture 17: Spans	28 October 2009 Discussion Session 9: Gaussian Elimination	29 October 2009 Lecture 18: Spans: Examples Quiz 8
3 November 2009 Lecture 19: Section 1.1 from Gaussian Elimination notes. Inner Products: Sections 1 and 3. Homomorphisms and Isomorphisms, Notes	4 November 2009 Discussion Session 10: Inner Products	5 November 2009 Lecture 20: Linear Independence. Quiz 9
10 November 2009 Test 2	11 November 2009 Discussion Session 11: Matlab: Signal and Image Processing, Fourier Transforms	12 November 2009 Lecture 22: Bases and Dimension.
15 December 2009 Final Exam: 3-5 pm Duques 361