Syllabus discrete spring 2019 PDF

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Discrete Mathematics MA-UY 2314 Spring 2019

Course Information Course: Discrete Mathematics MA-UY 2314 Class Dates: Monday January 28, 2019 - Monday May, 13 2019 Class Times: MW 10:30am-11:50am or MW 2:30pm-3:50pm Class Location: The 10:30am-11:50am class meets in DIBN room LC400 and the 2:30pm-3:50pm class meets in RGSH room 315. Recitation: (a) Yuhong Yu: 9:30-10:20, 10:30-11:20, 11:30-12:20, in RGSH room 304; 1:30-2:20 in JABS room 673. (b) Anam Waheed: 9:30-10:20, 11:30-12:20, in RGSH room 339; 1:302:20 in RGSH room 604. Instructor Information: • Name: Jose Diaz-Alban. Office: RGSH 305K Office Hours: MW 4:00pm-5:30pm. Other times available, just ask. Email: [email protected] (Please do not email me at my cims.nyu.edu account). • Name: Yuhong Yu Office: RGHS room 303 Office Hours: W 12:30-1:30 Email: [email protected] • Name: Anam Waheed Office: 2 Metro Tech room 10.038 (10th floor) Office Hours: T 4-5. Email: [email protected]

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Learning Objectives This course is a one-semester introduction to discrete mathematics with an emphasis on the understanding, composition and critiquing of mathematical proofs.

Homework There will be problems to write up on paper each week and turn in. Written homework will be posted in the Resources section of NYU Classes. One of the major goals of in this class is to move students from computational processes to conceptual thinking and communication. By all means you may work in groups on the homework assignments. Collaboration is a big part of learning and of scholarship in general. However, each student must turn in his or her own write-up of the solutions. Homework is collected via Gradescope. The due date will be advertised on the homework. Late homework is not accepted. Note that your lowest homework score is dropped. Extra Credit on homework. If you are willing to type the homework using Latex, you will get 30% bonus of that particular homework score. Note that all problems must be typed to receive the bonus. Just to make sure we are all on the same page, here is an example. Homework 0 is worth 21 points. If you get a perfect score and you type the homework, you will have 27.3/21 for your homework 0 score. If you get 18/21 on homework 0 and you type the homework, you will have 23.4 for your homework 0 score. If you get a perfect score, and you decide to type solutions for 6 out of the 7 problems, you will have 21/21 for your homework 0 score. Either type the entire assignment, or don’t bother. Grading of Written Homework: Each problem will be worth 3 points. If a particular problem has multiple parts, then each part will be worth 3 points. For example, if problem 1 has parts (a), (b), and (c), then problem 1 is worth 9 points. If problem 1 has no parts, then it is simply worth 3 points. Graders will be expecting you to express your ideas clearly, legibly, and completely, often requiring complete English sentences rather than merely just a long string of equations or unconnected mathematical expressions. This means you could lose points for unexplained answers, or poorly prepared and presented papers. Each problem is graded according to the following rubric Points 3 2 1 0

Description of Work Work is completely accurate and essentially perfect. Work is thoroughly developed, neat, and easy to read. Complete sentences are used. Work is good, but incompletely developed, hard to read, unexplained, or jumbled. Work contains right idea but is flawed. Work is sketchy. There is some correct work, but most of work is incorrect. Work minimal or non-existent. Solution is completely incorrect.

Note there are no half points

Textbook and Materials 2

Scheinerman, E. Mathematics: A Discrete Introduction. 3rd Edition. Please be aware of the University’s policy on illegal downloading of copyrighted material: DON’T

Quizzes/Midterm/Final All quizzes/exams will contain a mixture of computational and conceptual problems. Some of them will resemble homework problems, while some will be brand new to you. Quizzes: There is a 20-30 minute quiz given in recitation almost weekly. There are no make-ups for the quizzes. Your lowest quiz scores will be dropped. I will give notice well in advance regarding the topics the quiz will cover. In general, they will cover material on the previous week’s homework. See the Calendar section of the syllabus for the quiz schedule. Midterm1: The midterm exam is on Friday March 8. Time is 9:00am-10:50am in JABS room 474. Midterm2: The midterm exam is on Friday April 19. Time is 9:00am-10:50am in JABS room 474. Final: The final exam is given on a university scheduled date. More information about the final exam TBA. Registered students are required to sit for the course examinations on the scheduled day and time. Failure to do so will result in forfeiture of the percentage credit due for that component Policies for Exams, Quizzes, and Homeworks: If you have missed, or will need to miss an exam and want a make-up, please refer to the full make-up exam policy online: https://math.nyu.edu/tandon/policy.html It is University policy that an out-of-sequence exam can be administered only if there is prior authorization by the Mathematics Department or the Office of Student Affairs. If you miss an exam for a medical, religious, or family emergency reason, you must provide written documentation to the Math Department at [email protected] in order to schedule a make-up exam within 2 days of the missed exam, or upon your first day returning to class if the documentation excuses a longer absence. Make-ups will not be granted to students who do not notify the Math Department in a timely manner. Students may be asked to seek additional approval from the Office of Student Affairs. We cannot accommodate out-of-sequence exams, quizzes, and finals for reasons of convenient travel, even if you have already purchased tickets. Please note carefully the date of your exams and final and plan your travel schedule accordingly.

Academic Integrity: No cell phones, iPads or other devices that can communicate with the internet or with others may be used. Any such equipment found with the power on may well be interpreted as ”cheating”. The Department of Mathematics

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reserves the right to impose the strongest academic sanctions for violations of Academic Integrity.

Calculator Question Using calculators on homework is permitted. No particular calculator is endorsed. No calculators will be permitted on quizzes/exams.

Advice This is a fun, but challenging course. It will require a constant persistence on your part to succeed in the course. While it may seem that a variety of disjoint topics are being covered, you will soon find that they are all intertwined. If you get behind early, it may not be possible to catch up. Stay on top of things. Come to office hours. Do not get behind with the material.

Grades The grade will be determined as follows Written Homework Quizzes Midterm 1 Midterm 2 Final

10% 10 % 25 % 25 % 30 %

The following grade scale is used when assigning letter grades: Cutoff 93 90 87 83 80 75 65 50

Letter grade A AB+ B BC+ C D

These cutoffs may be adjusted, but only to your advantage.

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Calendar Spring 2019 Calendar (subject to change) Week 1 2 3 4 5 6 6 7 8 9 10 11 12 12 13 14 15

Sections 1-7 (notice that we essentially started with section 3) List, Factorial, Sets I (sectins 8-10) Quantifiers, Sets II, Combinatorial Proof (sections 11-13) Relations, Equivalence Relations (sections 14, 15) Partitions, Binomial Coefficients (sections 16, 17) Contradiction, Smallest Counterexample (sections 20, 21) Midterm 1 Friday March 8 Induction, Recurrence Relations, Functions (sections 22 -24) Spring Break Pigeonhole Principle, Composition (sections 25, 26) Permutations, Assorted Notation (sections 27, 29) Fundamentals of Graph Theory, Subgraphs (section 47, 48) Connections, Trees (sections 49, 50) Midterm 2 Friday April 19 Eulerian Graphs, Coloring (sections 51, 52) Dividing, Greatest Common Divisor (sections 35, 36) Review/Catch up

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Quiz No Recitation No Quiz Quiz 1 Quiz 2 Quiz 3 No Quiz Quiz 4 No Quiz Quiz 5 Quiz 6 No quiz Quiz 7 Quiz 8 Quiz 9 (TBD)...