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Fall 2010 : 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

rosen.jpg

Kenneth H. Rosen "Discrete mathematics and its applications", 6th edition, McGraw Hall, 2007.

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_solutions.jpg

"Student's solutions guide", prepared by Jerrold Grossman, McGraw Hall, 2007.

Homework and exams

Homework assignments will be posted here (next to the syllabus) and on Blackboard each Wednesday. Of course you are free to work together on these problems, but please write out your own solutions (due the following Wednesday). 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 Wednesday 22nd September, Wednesday 20th October, and Wednesday 17th November. The final exam will be a two hour exam on Friday 10th December at 12noon.

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

Aug 25-27

Chapter 1 : Logic and proofs

  • 1.1 Propositional logic
  • 1.2 Propositional equivalences

1.1, exercises 4adf, 10ace, 28adf, 60ab.
1.2, exercises 8ab, 10bc, 20, 26, 40.
Due Wednesday 1st September.

Aug 30-Sep 3

  • 1.3 Predicates and quantifiers
  • 1.4 Nested quantifiers

1.3, exercises 10, 20, 34, 44, 48a.
1.4, exercises 10, 24, 32, 40, 46.
Due Wednesday 8th September.

Sep 6-10
No class Monday
Labour day

  • 1.5 Rules of inferences
  • 1.6 Introduction to proofs

1.5, exercises 10bef, 14acd, 16, 18, 26.
1.6, exercises 6, 8, 14, 22, 30, 38.
Due Wednesday 15th September.

Sep 13-17

  • 1.7 Proof methods and strategy
Chapter 2 : Sets and functions
  • 2.1 Sets
  • 2.2 Set operations

1.7, exercises 4, 22, 28.
Due Monday 20th September.
2.1, exercises 8, 22, 34.
2.2, exercises 12, 14, 18d, 24, 26c.
Due Friday 24th September.

Sep 20-24

  • 2.3 Functions
Midterm one : Wednesday 22nd September
  • 2.3 Functions

Practise problems for midterm:
1.1, exercises 27, 29, 31, 33.
1.2, exercises 19, 21, 23, 25, 27, 29.
1.3, exercises 33, 37.
1.4, exercises 27, 37.
1.5, exercises 15, 35.
1.6, exercises 11, 13, 15, 17.
1.7, exercise 21.
Chapter one supplementary exercises 3, 9, 15, 25, 27, 29.
Homework:
2.2, exercises 30, 48.
2.3, exercises 6abd, 12, 14, 16, 44.
Due Wednesday 29th September.

Sep 27-Oct 1

Chapter 3 : Number theory

  • 3.4 The integers and division
  • 3.5 Primes and greatest common divisors

3.4, exercises 6, 10def, 24, 32b.
3.5, exercises 4cde, 8, 10, 16, 20bd, 22bd, 26.
Due Wednesday 6th October.

Oct 4-8

  • 3.6 The Euclidean algorithm
  • 3.7 Applications

3.6, exercises 20, 22, 24cde, 28bc, 30.
3.7, exercises 8, 10, 12, 18, 28, 46.
Due Wednesday 13th October.

Oct 11-15

Chapter 4 : Induction

  • 4.1 Mathematical induction
  • 4.2 Strong induction

4.1, exercises 4, 10, 14, 18, 22, 34.
Due Monday 18th October.

Oct 18-22
No class Friday
Fall break

  • 4.2 Strong induction
Midterm two : Wednesday 20th October

Practise problems for midterm:
2.2, exercises 13, 15, 17, 19, 21, 23, 29, 31.
2.3, exercises 9, 13, 15, 17, 19, 43, 45, 47, 49, 69.
3.4, exercises 7, 13, 21, 25.
3.5, exercises 9, 11, 13, 21, 31.
3.6, exercises 1, 19, 21, 23, 25.
3.7, exercises 1, 3, 5, 7, 11, 15, 19, 23, 25, 27, 29.
4.1, exercises 3, 5, 7, 9, 11, 15.
Homework:
4.2, exercises 4, 8, 10, 12, 32.
Due Wednesday 27th October.

Oct 25-29

Chapter 8 : Relations

  • 8.1 Relations and their properties
  • 8.3 Representing relations

8.1, exercises 4, 6, 32abcdef, 34bdfh, 54.
8.3, exercises 2bc, 10ace, 14cd, 20, 32 (ignore irreflexive and asymmetric).
8.5, exercises 2, 16.
Due Wednesday 3rd November.

Nov 1-5

  • 8.5 Equivalence relations
Chapter 5 : Counting
  • 5.1 Basics of counting

8.5, exercises 24, 28ad, 40, 44.
5.1, exercises 8, 16, 20abcdef, 24, 30abfgh, 40, 46.
Due Wednesday 10th November.

Nov 8-12

  • 5.2 The pigeonhole principle
  • 5.3 Permutations and combinations

5.2, exercises 4, 10, 14, 24, 32.
5.3, exercises 8, 16, 18, 24, 30.
Due Monday 15th November.

Nov 15-19

  • 5.4 Binomial coefficients
Midterm three : Wednesday 17th November
  • 5.5 Generalized permutations and combinations

Practise problems for midterm:
4.2, exercises 3, 5, 7, 9, 11, 13.
8.1, exercises 3, 5, 7, 29, 31, 33, 35, 37, 39.
8.3, exercises 1, 3, 7, 9, 13c, 15, 19, 21, 23, 25, 27, 31.
8.5, exercises 1, 3, 7, 9, 15, 21, 23, 27, 35, 39, 45, 57.
5.1, exercises 3, 17, 21, 23, 25, 29, 31, 41, 47, 49, 53.
5.2, exercises 3, 11, 13, 15, 17, 19, 21, 25, 29, 31, 33.
5.3, exercises 7, 9, 15, 17, 19, 21, 25, 27, 29, 31, 33.
Homework:
5.4, exercises 8, 10, 20, 22, 28.
Due Monday 22nd November.

Nov 22-26
No classes Wed/Fri
Happy Thanksgiving!

  • 5.5 Generalized permutations and combinations

5.5, exercises 10acdf, 16, 30, 32, 38, 46, 54.
Due Wednesday 1st December.

Nov 29-Dec 3

Chapter 6 : Discrete probability

  • 6.1 An introduction to discrete probability
  • 6.2 Probability theory

6.1, exercises 8, 12, 14, 16, 24ab, 26ab, 36.
6.2, exercises 8, 12, 18, 24, 28, 38.
Due Wednesday 8th December.

Dec 6-10

Revision

Final exam 12noon Friday 10th

Practise problems for final:
Ch 1 supplementary exercises 1, 7, 17, 19, 23, 31, 33, 35.
Ch 2 supplementary exercises 1, 3, 5, 7, 9, 13, 19, 21, 23, 25.
Ch 3 supplementary exercises 19, 21, 23, 25, 27, 29, 31, 35.
Ch 4 supplementary exercises 1, 3, 5, 7, 9, 11, 13, 17, 23, 25, 27.
5.4, exercises 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25, 27, 29, 31.
5.5, exercises 7, 9, 11, 13, 15, 19, 21, 23, 27, 31, 35, 41, 51, 57.
Ch 5 supplementary exercises 1, 7, 11, 13, 15, 21, 27, 29, 33, 37, 43.
6.1, exercises 5, 9, 13, 15, 17, 21, 23, 25, 27, 29, 33, 35, 37, 41.
6.2, exercises 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 27, 29, 31, 33.
Ch 6 supplementary exercises 1, 3, 11ab, 15, 21, 23, 31.
Ch 8 supplementary exercises 1, 3, 5, 7, 9, 21.

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