# MATH 1701: Discrete Mathematics

Students are introduced to the foundation of modern mathematics including basic set theory; counting; solutions to recurrence relations; logic and quantifiers; properties of integers; mathematical induction; asymptotic notation; introduction of graphs and trees; finite state machines and formal languages; Boolean algebra.

## Learning outcomes

After successfully completing this course, students will be able to:

• Determine truth value of statements to analyze a logical argument.
• Develop various proof techniques in elementary number theory
• Analyze properties of sequences and recurrence relations; apply the method of mathematical induction.
• Prove different properties of sets; identify and construct mathematical functions.
• Apply properties of relations to problems in modular arithmetic.
• Utilize various counting techniques and principles to solve problems.
• Prove elementary properties of graphs and utilize various algorithms in graph theory.
• Analyze the asymptotic behaviour of functions, the efficiency of algorithms, and use regular expressions and finite state automata to define regular languages.

## Course topics

1. The Logic of Compound and Quantified Statements
2. Elementary Number Theory and Methods of Proof
3. Mathematical Induction and Recurrence Relations
4. Set Theory and Functions
5. Relations
6. Counting Techniques
7. Elementary Graph Theory and Algorithms
8. Analysis of Algorithm Efficiency and Finite-State Automata

## Required text and materials

• Epp, S. S. (2011). Discrete Mathematics with Applications. 4th Edition, Boston: Brooks/Cole Cengage Learning.
Type: Textbook
ISBN: 978-0-495-39132-6

## Assessments

Please be aware that due to COVID-19 safety guidelines all in-person exams have been suspended. As such, all final exams are currently being delivered through ProctorU, which has an approximate fee of \$35 involved. There will be more information in your course shell, on how to apply, if your course has a final exam.

To successfully complete this course, students must achieve a passing grade of 50% or higher on the overall course, and 50% or higher on the final mandatory examination.

 Assignment 1: The Logic of Compound and Quantified Statements 5% Assignment 2: Elementary Number Theory and Methods of proof 5% Assignment 3: Mathematical Induction and Recurrence Relations 5% Quiz 1 (Online): 5% Assignment 4: Set Theory and Functions 5% Assignment 5: Relations 5% Assignment 6: Counting Techniques 5% Assignment 7: Elementary Graph Theory and Algorithms 5% Assignment 8: Analysis of Algorithm Efficiency and Finite-State Automata 5% Quiz 2 (Online): 5% Final Exam* 50% Total 100%

*Mandatory

## Open Learning Faculty Member

An Open Learning Faculty member is available to assist students throughout the course. Primary communication is through the Learning Environment's "Mail" tool or by phone. Students will receive the necessary contact information at the start of the course.

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