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.
One of Pre-calculus 12 or Foundations of Math 12 (or equivalent) with a minimum grade of C+; within the last two years. Note: Students who already have credit for MATH 1380 and MATH 1390 may not take MATH 1701 for further credit. Cannot have credit for both Math 1700 and Math 1701.
Course duration30 weeks
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 [email protected] 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 [email protected] 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% |