Discrete Math (V63.0120)
Instructor information
- Ashish Myles
- e-mail: mailto:amyles@cs.nyu.edu
- office: 715 Broadway, Room 1213
- hours: Tuesday & Thursday, 4:30-5:30pm
Prerequisites
Goals and Topics
Our major goal will be to familiarize ourselves with some of the important tools of discrete mathematics.
- Mathematical language, logic, writing, and proof
- Set theory
- Functions and Relations
- Combinatorics and discrete probability
- Graph theory and trees
Course Details
Class
- Meeting times: Tuesday & Thursday, 2pm–3:50pm
- Location: SILV 709
Textbook and Materials
Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games
by Douglas E. Ensley and J. Winston Crawley.
ISBN 0-471-47602-1
Homework
Homework will be assigned weekly and collected on Thursdays. In fairness to the other students in the course, late homework will generally not be accepted. We will, however, drop the lowest homework score in computation of final grades. Please talk to the instructor in cases of emergency.
Homework problems will each be worth 3 points and will be graded according to the following rubric.
Points | Description of Work |
---|---|
3 | Work is completely accurate and essentially perfect. Work is thoroughly developed, neat, and easy to read. Complete sentences are used. |
2 | Work is good, but incompletely developed, hard to read, unexplained, or jumbled. Answers which are not explained, even if correct, will generally receive 2 points. Work contains the "right idea" but is flawed. |
1 | Work is sketchy. There is some correct work, but most of the work is incorrect. |
0 | Work minimal or non-existent. Solution is completely incorrect. |
Exams
Quizzes
There will be five 15-20 minute quizzes. Quizzes will start at the beginning of class. We will also drop the lowest quiz.
Midterms
There will be an in-class midterm examination as indicated in the schedule below.
Final
The cumulative final examination for this course is noted on the schedule below. We will not be able to accommodate early finals for nonacademic, non-emergency reasons. Please plan your travel schedule accordingly.
Make-ups
Make-up quizzes and exams are allowed only for the following.
- A documented medical excuse.
- A religious holiday.
- Extreme hardship such as a family emergency.
Those make-ups not arising from emergencies must be taken before the date of the quiz/exam. If the make-up needs to be taken after the date/time of the quiz/exam, it should be taken early as possible. In all cases, contact the instructor immediately.
Cheating
Don't cheat. It is the only fair and respectful option to your classmates and me. If you are caught, you might find me breathing down your neck through the rest of the semester in addition to suffering whatever penalty I deem fit for the transgression.
Grading policy
Grades will be computed by a weighted average:
Homework | 10% |
Quizzes | 20% |
Midterm | 30% |
Exam | 40% |
Final scores will be converted to letter grades beginning with the following scale:
93 | A |
90 | A- |
87 | B+ |
83 | B |
80 | B- |
75 | C+ |
65 | C |
50 | D |
As for a curve, these cutoffs might be adjusted, but only in the downward direction (to make letter grades higher).
Tentative Calendar
Week | Day | Book Section | Topic and Notes |
---|---|---|---|
1 | Tue 01/25 | 1.1, 1.2 | First Examples, Number Puzzles and Sequences |
Thu 01/27 | 1.3 | Truth-tellers, Liars, and Propositional Logic | |
2 | Tue 02/01 | 1.4 | Predicates |
Thu 02/03 | 1.5 | Implications | |
3 | Tue 02/08 | 1.6 | Quiz 1; Validity of Arguments |
Thu 02/10 | 2.1 | Mathematical Writing | |
4 | Tue 02/15 | 2.2 | Proofs about Numbers |
Thu 02/17 | 2.3 | Mathematical Induction | |
5 | Tue 02/22 | 2.5 | Quiz 2; Contradiction and the Pigeonhole Principle |
Thu 02/24 | 3.1, 3.2 | Set Definitions and Operations | |
6 | Tue 03/01 | 3.3 | Proving Set Properties |
Thu 03/03 | 3.4 | Boolean Algebra | |
7 | Tue 03/08 | Review | |
Thu 03/10 | Midterm | ||
8 | Tue 03/15 | Spring Break | |
Thu 03/17 | Spring Break | ||
9 | Tue 03/22 | 4.1, 4.2 | Definitions of Functions, Diagrams, Relations, and Inverses, Composition |
Thu 03/24 | 4.3 | Properties of Functions and Set Cardinality | |
10 | Tue 03/29 | 4.4 | Properties of Relations |
Thu 03/31 | 4.5 | Equivalence Relations | |
11 | Tue 04/05 | 5.1, 5.2 | Quiz 3; Introduction to Combinatorics, Basic Rules for Counting |
Thu 04/07 | 5.3 | Combinations and the Binomial Theorem | |
12 | Tue 04/12 | 5.4 | Binary Sequences |
Thu 04/14 | |||
13 | Tue 04/19 | 6.1, 6.2 | Quiz 4; Introduction to Probability, Sum, and Product Rules |
Thu 04/21 | 6.3 | Probability in Games of Chance | |
14 | Tue 04/26 | 7.1, |
Graph Theory, |
Thu 04/28 | 7.3 | Isomorphism and Planarity | |
15 | Tue 05/03 | Quiz 5; Review | |
Thu 05/05 | Final Exam |