Elements of Discrete Mathematics

Course Number:
MTH 231
Transcript Title:
Elements of Discrete Mathematics
Created:
Jan 02, 2026
Updated:
Jan 02, 2026
Total Credits:
4
Lecture Hours:
44
Lecture / Lab Hours:
0
Lab Hours:
0
Satisfies Cultural Literacy requirement:
No
Satisfies General Education requirement:
No
Grading Options
A-F, P/NP, Audit
Default Grading Options
A-F
Repeats available for credit:
0
Prerequisites

MTH 111Z

Course Description

Explores foundational concepts in discrete mathematics. Includes basic set theory, functions, counting, sequences, logic and proofs, graph theory, and introductory number theory. Investigates both theoretical and applied aspects using symbolic, graphical, and numerical methods. Prerequisite: MTH 111Z. Audit available.

Course Outcomes

Upon successful completion of this course, students will be able to:

  1. Apply basic set operations and rules of counting in various contexts.

  2. Recognize, express and compute arithmetic and geometric sequences and series using recursive definitions and closed-form equations.

  3. Apply mathematical induction to prove statements involving integers or sequences.

  4. Construct direct and indirect proofs, including proof by contradiction.

  5. Utilize graph algorithms.

Suggested Outcome Assessment Strategies

The determination of assessment strategies is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: writings (journals, self-reflections, pre-writing exercises, essays), quizzes, tests, midterm and final exams, group projects, presentations (in person, videos, etc), self-assessments, experimentations, lab reports, peer critiques, responses (to texts, podcasts, videos, films, etc), student generated questions, Escape Room, interviews, and/or portfolios.

Department required assessment: Graded assessment must include at least one project.

Course Activities and Design

The determination of teaching strategies used in the delivery of outcomes is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: lecture, small group/forum discussion, flipped classroom, dyads, oral presentation, role play, simulation scenarios, group projects, service learning projects, hands-on lab, peer review/workshops, cooperative learning (jigsaw, fishbowl), inquiry based instruction, differentiated instruction (learning centers), graphic organizers, etc.

Course Content

Outcome #1: Apply basic set operations and counting rules in various contexts.

  • Sets and basic set theory.
    • power sets
    • cardinality
    • set operations
    • products
    • Venn diagrams
  • Counting
    • properties from arithmetic.
    • binomial coefficients.
    • combinations and permutations.
    • combinatorial proofs.
  • Functions
    • domain and codomain
    • injections, surjections, and bijections

Outcome #2: Recognize, express and compute arithmetic and geometric sequences and series using recursive definitions and closed-form equations.

  • Sequences
    • description
    • arithmetic and geometric sequences (and series)
    • solving recurrence relations

Outcome #3: Apply mathematical induction to prove statements involving integers or sequences.

  • Sequences
    • mathematical induction

Outcome #4: Construct direct and indirect proofs, including proof by contradiction.

  • Symbolic Logic and Proofs
    • propositional Logic
    • proofs
      • direct proofs
      • indirect proofs

Outcome #5: Utilize graph algorithms.

  • Graph Theory
    • definitions
    • trees
    • planar graphs
    • coloring, including the four-color theorem.
  • Introduction to Number Theory
    • divisibility
    • remainder classes
    • properties of congruence
    • solving congruencies
    • solving linear Diophantine Equations

Suggested Texts and Materials

Department Notes

All application problems will be answered with complete sentences and using correct units.