# MATH 1701: Discrete Mathematics

This course is an introduction to the foundation of modern mathematics including basic set theory; solution to recurrence relations; logic and quantifiers; properties of integers; mathematical induction; introduction to graphs and trees; Boolean algebra and finite state machines. Students will apply the critical thinking skills developed in Mathematics to derive meaning from complex problems.

## Learning outcomes

• Construct a truth table, determine the truth values of quantified statements, and apply logical operators and arguments.
• Prove/Disprove number theory facts, construct a proof by induction, and find a closed form for recursively defined sequences.
• Apply set operations and be able to use them to establish set equality.
• Define a function and its inverse and determine whether it is one-to-one/onto.
• Define a relation using words, symbols, or an arrow diagram and determine whether it is an equivalence relation.
• Define basic terms from graph theory and prove statements about trees.
• Describe the languages defined by regular expressions and finite-state automata.
• Write mathematical proofs using clear and logical reasoning.

## Course topics

• The Logic of Compound and Quantified Statements
• Elementary Number Theory and Methods of Proof
• Mathematical Induction and Recurrence Relations
• Set Theory and Functions
• Relations
• Counting Techniques
• Elementary Graph Theory and Algorithms
• Analysis of Algorithm Efficiency and Finite-State Automata

## Required text and materials

The following textbook is required for this course:

1. Epp, S. S. (2020). Discrete Mathematics with Applications (5th edition). Boston: Brooks/Cole Cengage Learning.
Type: Textbook. ISBN-13: 978-1-337-69419-3

## Assessments

Please be aware that should your course have a final exam, you are responsible for the fee to the online proctoring service, ProctorU, or to the in-person approved Testing Centre. Please contact exams@tru.ca with any questions about this.

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 mandatory final examination.

Note: The final exam for this course is only available as a paper exam and must be taken in person at an approved Testing Centre. Please email exams@tru.ca with any questions.

 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% 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 1 5% Quiz 2 5% Mandatory Final Exam 50% Total 100%

## Open Learning Faculty Member Information

An Open Learning Faculty Member is available to assist students. Students will receive the necessary contact information at the start of the course.

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