MATH 1701 - Discrete Mathematics

Course Description

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

Students are responsible for purchasing the required materials on their own.

• Epp, S. S. (2020). Discrete Mathematics with Applications (5th ed.). Brooks/Cole Cengage Learning.
  Type: Textbook. ISBN: 9781337694193   

Note: A print or fixed-layout version is strongly recommended to ensure alignment with the course materials. 

Assessments

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 in-person exam and must be taken at an approved Testing Centre. Please email exams@tru.ca with any questions.

Recommended requisite(s)

• Pre-calculus 12 (or equivalent) with a minimum grade of C+ within the last 2 years.
  or
• Foundations of Math 12 (or equivalent) with a minimum grade of C+ within the last 2 years. 
  MATH 0600 with a minimum grade of B
  or
• MATH 0610 with a minimum grade of C-
  or
• MATH 0630 with a minimum grade of C-
  or
• MATH 0633 with a minimum grade of C-
  or
• MATH 0650 with a minimum grade of C-