Home Page: CSci 2312 - Discrete Structures II - Fall 2016 - The George Washington University

Location: Lectures: Discussion Section: 410 Tompkins Hall

Schedule: Lectures: Tuesday and Thursday, 4:45pm-6:00pm, SEH 1300-1400
Discussion Section: Monday, 12:45-2:00 pm (PHIL 109) or Wednesday, 9:00-10:15 am (TOMP 303) from 12 September onwards

Instructor: Poorvi Vora, SEH 4610. Office Hours: Tuesday and Thursday: 12:00-1:00 pm, from 6 September onwards

Graduate Teaching Assistants: Cheng Tang and Maya Shende.
Office Hours:
Cheng: TBD
Maya: TBD

University Teaching Fellow: Katherine Walker

Text: Susanna Epp, "Discrete Mathematics with Applications", 4th Edition, 2011.

Course Content: Proofs, algebraic structures, number theory, graph theory (coloring and planar graphs), asymptotics.

Prerequisites: CSci 1311 (Discrete Structures I) or equivalent discrete mathematics; Math 1231/1221 or single-variable calculus.

Grading: HWs (20%), quizzes and participation in lectures and online on Piazza (20%), 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, Course Syllabus, Course Outcome Form,

Planned Schedule (note that this is very fluid and will change after each lecture, based on what we were able to complete or not)

29 August, 31 August: No Discussion Section 30 August
Lecture 1: An exercise in what one can do with numbers: simple cryptography
1 September
Lecture 2: Divisibility

Reading Assignment for this weekend (you will be tested on this next week)

Sections 4.1, 4.2, Divisibility notes.

5 and 7 September: No Discussion Section 6 September
Lecture 3: Conditional statements and fallacies.
8 September Lecture 4: Divisibility and Modular Arithmetic: Theorem 25. Definition of congruence modulo m. Congruence modulo m as an equivalence relation.

HW 1 due

Quiz 1

Reading Assignment for this week

Chapter 4, all the way to, and including, 4.2.2 and Modular Arithmetic Notes I

Reading Assignment for next week:

Practice problems:

12, 14 September: Discussion Section
13 September
Lecture 5: Lemmas 26 and 27.
15 September
Lecture 6: Cancelation modulo a prime and multiplicative inverses: Lemma 28 and Corollary 29.

Little Quiz 1

HW 2 due

Quiz 2

Reading assignment for lecture 6: sections up to and including 4.3.2, Modular Arithmetic Notes I, Understanding Modular Arithmetic, Modular Arithmetic Notes II. Reading assignment for next week: Up to and including section 4.3.4.

19, 21 September: Discussion Section
20 September
Lecture 7: Corollary 30 and Theorem 31 (Fermat's Theorem).
22 September
Lecture 8: Complete Fermat's Theorem

Little Quiz 2

HW 3 due

Quiz 3

Reading assignment for lecture 8: up to and including section 4.3.6 Reading assignment for next week: Euclidean algorithm for GCD . Practice Problems, GCD

26, 28 September: Discussion Section
GCD definition. Euclidean algorithm for the GCD.
27 September
Test 1: Number theory: lectures 1-8. No GCD.
29 September
Lecture 9: GCD. Euclidean algorithm for the GCD. Inverses modulo p.

Reading assignment for next week:

3 October, 5 October: Discussion Section:
Test review
4 October
Lecture 10: Return test
6 October

Lecture 11:

Little Quiz 3

Quiz 4
Reading assignment for next week: