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
- 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
- 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:
- 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 final mandatory 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 (Online): | 5% |
| Quiz 2 (Online): | 5% |
| Final Exam (mandatory) | 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.
