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:
- 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.
