## Mathematics 120

### Discrete Mathematics I

Length of course: 14 weeks

Classroom hours per week: 4

Number of Credits: 3

Prerequisite: Precalculus 12, Math 100, or Math 110

Text: Discrete and Combinatorial Mathematics by Ralph P. Grimaldi, 5th Edition

### Course Description:

This is an introductory course in discrete mathematics with introduction to logic and formal reasoning.

### Course Outline:

Length Description

Week 1

Fundamental Principles of Counting (The Rules of Sum and Product, Permutation, Combinations: The Binomial Theorem)

Week 2

Fundamental Principles of Counting (Combinations with Repetition: Distributions)

Fundamentals of Logic (Basic Connectives and Truth Tables)

Week 3

Fundamentals of Logic (Logical Equivalence: The Laws of Logic, Logical Implication: Rules of Inference)

Week 4

Fundamentals of Logic (The use of quantifiers, Quantifiers, Definitions, and the proofs of Theorems)

Week 5

Set Theory (Sets and Subsets, Set Operations and the Laws of Set Theory)

Week 6

Set Theory (Counting and Venn Diagrams)

Mathematical Induction (The Well-Ordering Principle: Mathematical Induction)

Week 7

Mathematical Induction (Recursive Definitions)

Properties of the Integers (The Division Algorithm: Prime Numbers)

Week 8

Properties of the Integers (The Greatest Common Divisor: The Euclidean Algorithm, The Fundamental Theorem of Arithmetic)

Week 9

Relations and Functions (Cartesian Product and Relations, Functions: Plain and One-to-one)

Week 10

Relations and Functions (Onto Functions: Stirling Numbers of the Second Kind, Special Functions)

Week 11

Relations and Functions (The Pigeonhole Principle, Function Composition and Inverse Functions)

Week 12

Relations and Functions (The Pigeonhole Principle, Function Composition and Inverse Functions)

Week 13

Review

Week 14

Final Exam

### Evaluation:

10-20% Quizzes and Homework Midterm Exam(s) Final Exam

### Instructors

Arman Ahmadieh B.Sc., M.Sc. (Sharif University of Technology)
Hayri Ardal, B.Sc.(Bogazici), Ph.D.(Simon Fraser)
Kim Peu Chew, B.Sc. (Nanjing), M.A., Ph.D. (British Columbia)