Fall 2012 : MATH381 Discrete Mathematics

General information

• Lectures: Tuesday and Thursday 9:30-10:45am in room Phillips 224
• Instructor: Justin Sawon, Chapman 441
• Office hours: Monday 1:30-2:30pm, Tuesday and Thursday 11am-12noon
• Email: sawon -at- email -dot- unc -dot- edu

Course prerequisite

You must have earned a passing grade in MATH232 (or an equivalent) to register for this class.

Textbook

 Kenneth H. Rosen "Discrete mathematics and its applications", 7th edition, McGraw Hall, 2012.

A paperback version customized for UNC is available from the university bookstore. There are answers to the odd-numbered problems at the back of the textbook. For more detailed solutions to the odd-numbered problems, you may wish to consult the student's solutions guide.

 "Student's solutions guide", prepared by Jerrold Grossman, 7th edition, McGraw Hall, 2012.

Homework and exams

Homework assignments will be posted on Sakai each Tuesday. Of course you are free to work together on these problems, but please write out your own solutions (due the following Tuesday). One of the main objectives of this course is for you to learn to communicate clearly using the language of mathematics. Some problems will ask for a proof, others will ask for a calculation, but in all cases you should formulate your statements using complete sentences.

There will be two midterms, held in class on Tuesday 25th September and Tuesday 30th October. The final exam will be a two hour exam on Tuesday 11th December at 8am.

Grading scheme

Your overall score will be composed of homework (15%), midterms (25% each), and the final exam (35%). Corresponding grades are: A = 90-100, B = 80-89, C = 70-79, D = 60-69, F = 59 or below.

Course syllabus

The syllabus below may be adjusted as the semester progresses.

 Week Material covered Additional notes Aug 20-24 Chapter 1 : Logic and proofs 1.1 Propositional logic 1.3 Propositional equivalences Aug 27-31 1.4 Predicates and quantifiers 1.5 Nested quantifiers Sep 3-7 No class Monday Labor day 1.6 Rules of inference 1.7 Introduction to proofs Sep 10-14 1.8 Proof methods and strategy Chapter 2 : Sets and functions 2.1 Sets Sep 17-21 2.2 Set operations 2.3 Functions Sep 24-28 Midterm one : Tuesday 25th September 2.3 Functions (continued) Oct 1-5 Chapter 4 : Number theory and cryptography 4.1 Divisibility and modular arithmetic 4.2 Integer representations and algorithms 4.3 Primes and greatest common divisors Oct 8-12 4.3 Primes and greatest common divisors (continued) Chapter 5 : Induction and recursion 5.1 Mathematical induction Oct 15-19 No classes Thu-Friday Fall break 5.2 Strong induction Oct 22-27 5.2 Strong induction (continued) Chapter 9: Relations 9.1 Relations and their properties Oct 29- Nov 2 Midterm two : Tuesday 30th October 9.3 Representing relations Nov 5-9 9.5 Equivalence relations Chapter 6: Counting 6.1 Basics of counting Nov 12-16 6.3 Permutations and combinations 6.4 Binomial coefficients Nov 19-23 No classes Wed-Friday Thanksgiving 6.5 Generalized permutations and combinations Nov 26-30 Chapter 7 : Discrete probability 7.1 An introduction to discrete probability 7.2 Probability theory Dec 3-7 Wednesday is the last day of classes Review Final exam : Tuesday 11th December at 8am

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