Spring 2012 : MATH381 Discrete Mathematics

  1. General information
  2. Course prerequisite
  3. Textbook
  4. Homework and exams
  5. Grading scheme
  6. Course syllabus

General information

Course prerequisite

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

Textbook

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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.

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

Homework and exams

Homework assignments will be posted here (next to the syllabus) and 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 three midterms, held in class on Thurday 2nd February, Thursday 1st March, and Thursday 12th April. The final exam will be a two hour exam on Saturday 28th April at 4pm.

Grading scheme

Your overall score will be composed of homework (16%), midterms (18% each), and the final exam (30%). Corresponding grades are: A = 90-100, B = 80-89, C = 60-79, D = 45-59, F = 44 or below.

Course syllabus

The syllabus below will be updated as the semester progresses.

Week

Material covered

Homework

Jan 9-13

Chapter 1 : Logic and proofs

  • 1.1 Propositional logic
  • 1.3 Propositional equivalences

1.1, exercises 6bce, 12cde, 22aeg, 32ade.
1.3, exercises 8ab, 10bc, 12c, 24, 32, 40.
Due Tuesday 17th January.

Jan 16-20
No class Monday
MLK day

  • 1.4 Predicates and quantifiers
  • 1.5 Nested quantifiers

1.4, exercises 10, 18bde, 34, 44, 48b.
1.5, exercises 10, 24, 32, 40, 46.
Due Tuesday 24th January.

Jan 23-27

  • 1.6 Rules of inference
  • 1.7 Introduction to proofs

1.6, exercises 10acd, 14abd, 16abd, 24, 28.
1.7, exercises 6, 8, 16, 24, 30, 38.
Due Tuesday 31st January.

Jan 30-Feb 3

  • 1.8 Proof methods and strategy
Midterm one : Thursday 2nd February

1.8, exercises 4, 10, 22, 24, 36, 44.
Due Tuesday 7th Feburary.

Feb 6-10

Chapter 2 : Sets and functions

  • 2.1 Sets
  • 2.2 Set operations

2.1, exercises 8, 20, 22, 42.
2.2, exercises 12, 14, 18c, 24, 28a, 30, 50c.
Due Tuesday 14th February.

Feb 13-17

  • 2.3 Functions
Chapter 4 : Number theory and cryptography
  • 4.1 Divisibility and modular arithmetic

2.3, exercises 6abd, 12, 14, 20, 36, 64, 74bcd.
4.1, exercises 6, 10aceg, 14ace, 28, 38.
Due Tuesday 21st February.

Feb 20-24

  • 4.2 Integer representations and algorithms
  • 4.3 Primes and greatest common divisors

4.2, exercises 2ab, 4abc, 21bc, 26, 28.
4.3, exercises 4, 12, 16bc, 18, 24, 30, 32cde.
Due Tuesday 28th February.

Feb 27-Mar 2

  • 4.3 Primes and greatest common divisors (cont.)
Midterm two : Thursday 1st March

4.3, exercises 40cdefg, 42, 44, 50, 54.
Due Tuesday 13th March.

Mar 5-9

Spring break - no classes

Mar 12-16

Chapter 5 : Induction and recursion

  • 5.1 Mathematical induction
  • 5.2 Strong induction

5.1, exercises 4, 6, 10, 18, 20, 26, 32, 62.
5.2, exercises 6, 10, 12, 30.
Due Tuesday 20th March.

Mar 19-23

Chapter 9: Relations

  • 9.1 Relations and their properties
  • 9.3 Representing relations

9.1, exercises 4, 6, 10, 32, 34acdfh, 36, 50abe.
9.3, exercises 2ac, 14, 20, 26, 32 (ignore irreflexive and asymmetric).
Due Tuesday 27th March.

Mar 26-30

  • 9.5 Equivalence relations
Chapter 6: Counting
  • 6.1 Basics of counting

9.5, exercises 2, 16, 22, 24, 28ad, 40, 46.
6.1, exercises 8, 18, 22, 26, 32, 40, 44, 46.
Due Tuesday 3rd April.

Apr 2-6

  • 6.3 Permutations and combinations
  • 6.4 Binomial coefficients

6.3, exercises 10, 14, 16, 18, 22, 26, 30, 32.
6.4, exercises 8, 10, 16, 22, 28.
Due Tuesday 10th April.

Apr 9-13

  • 6.5 Generalized permutations and combinations
Midterm three : Thursday 12th April

6.5, exercises 4, 10, 16, 20, 30, 32, 46.
Due Tuesday 17th April.

Apr 16-20

Chapter 7 : Discrete probability

  • 7.1 An introduction to discrete probability
  • 7.2 Probability theory

7.1, exercises 12, 16, 26ab, 30, 34, 36.
7.2, exercises 8, 12, 16, 18, 24, 38a.
Due Tuesday 24th April.

Apr 23-27
Wednesday is the
last day of classes

Revision
Final exam : Saturday 28th April at 4pm

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