Location: Lectures: 205 Corcoran Hall; Discussion Section: 410 Tompkins Hall

Schedule: Lectures: Tuesday, Thursday, 4:45pm-6:00pm; Discussion Section: Monday, 12:45-2:00 pm

Instructor: Poorvi Vora, poorvi@gwu.edu, 714 Philips Hall. Office Hours: Tues, Thurs: 12-2 pm, 3-4 pm

TA: Nadezhda (Nadya) Radeva, 102 Staughton Hall, Office Hours: Wed., 11am-2pm

Text: None. 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 (10%), two tests (15% each), final (25%), discussion session (5%). HWs are due by 6 pm on the due date. Late HWs are not allowed.

Course Outline This outline replaces the earlier one, 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

30 August Discussion Session 1: Problems on Induction On your own, review of Mathematical Induction.	31 August Lecture 1: Divisibility.	2 September Lecture 2: Shift and Affine Ciphers: Notes, read sections 1-3 before class. Modular Arithmetic.
6 September Labor Day	7 September Lecture 3: Modular Arithmetic Proofs.	9 September Lecture 4: Group Definition. HW 1 assigned.
13 September Discussion Session 2. Problems Quiz 1	14 September Lecture 5: Groups, examples.	16 September Lecture 6: Subgroups and rings: definitions.
20 September Discussion Session 3. Complete problems from session 2 Quiz 2	21 September Lecture 7: Complete subgroups and rings.	23 September Lecture 8: Euclidean algorithm for GCD . Practice Problems, GCD.
27 September Discussion Session 4: Problems Original list modified at 11:16 pm on Friday, 24 September Quiz 3	28 September Lecture 9: Euclidean algorithm for multiplicative inverses. Practice Problems. GCD as a linear combination	30 September Lecture 10: Proofs of correctness of euclidean algorithms HW 1 Solutions
4 October Discussion Session 5: Complete problems from Session 4	5 October Lecture 11: Complete euclidean algorithm correctness. Begin gcd as a linear combination.	7 October Test 1
11 October Discussion Session 6: Begin homomorphisms and isomorphisms Quiz 4	12 October Lecture 12: Complete condition for multiplicative inverse. HW 2 assigned. Due 22 October.	14 October Lecture 13: Return test. Homomorphisms and Isomorphisms.
18 October Discussion Session 7: Gaussian Elimination Quiz 5	19 October Lecture 14: Complete Part I: Groups and Rings and applications. Notes for existence of multiplicative inverse.	21 October Lecture 15: Complete Gaussian Elimination.
25 October Discussion Session 8: Problems on Gaussian Elimination Quiz 6	26 October Lecture 16: Vector Spaces: Definitions and Examples	28 October Lecture 17: Vector Spaces: Spans and Examples HW 3 assigned. Due 12 November.
1 November Discussion Session 9: Matlab examples for vector spaces and spans Quiz 7	2 November Lecture 18: Vector Spaces: Gaussian elimination as a way of solving questions on spans. Section 1.1 from handout. Inner Products, sections 1 and 3.	4 November Lecture 19: Vector Spaces: Inner Products, complete.
8 November Discussion Session 10: Inner Products: problems	9 November Test 2	11 November Lecture 20: Return Test 2. Begin Linear Independence
15 November Discussion Session 11: Continue: Linear Independence HW 4 assigned. Due 29 November 2010 Quiz 8	16 November Lecture 21: Vector Spaces: Bases and Dimension: Sections 4, 5 and 6 of Linear Independence Notes.	18 November Lecture 22: Orthogonality and Bases
22 November Discussion Session 12: Fourier Series as a basis with applications to audio signals. Problems on linear independence and bases from notes. Problems on inner products and bases Quiz 9	23 November Lecture 23: Inner Products	25 November No class, Thanksgiving
29 November Discussion Session 13: Complete inner products. Convolution and Polynomial Multiplication Quiz 10	30 November Lecture 23: Matrix Inverses HW 5 assigned. Due 10 December, 6:00 pm Extra credit HW assigned. Due 15 December, 6:00 pm	2 December Lecture 24: Complex Numbers
6 December Discussion Session 14: Fast Fourier Transform. Quiz 11	7 December Make-Up Day for all classes; no class in CS 124	9 December Lecture 23: Review
Friday, 17 December Final Exam; from 12:40 - 2:40 in regular classroom: COR 205