Mathematics of Games

Course Number:
MTH 140
Transcript Title:
Mathematics of Games
Created:
Feb 22, 2025
Updated:
Feb 24, 2025
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
Repeats available for credit:
0
Prerequisites

MTH 65 or MTH 98 or equivalent placement
WR 115 or equivalent placement

Course Description

Explores the mathematics of games by analyzing strategies, probabilities, and decision trees. Utilizes concepts from game theory, combinatorics, and probability theory to understand optimal moves, equilibrium points, and expected payoffs, enhancing strategic thinking and problem-solving skills. Prerequisites: MTH 65 or MTH 98, WR 115, or equivalent placement. Audit available.

Course Outcomes

Upon successful completion of this course, students will be able to:
  1. Develop problem-solving skills through the analysis of strategies and decision-making processes.
  2. Apply understanding of probability theory and applications in real-world scenarios.
  3. Develop critical thinking abilities by evaluating and optimizing game outcomes.
  4. Develop mathematical reasoning skills by exploring the combinatorial aspects of games.

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.

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: Develop problem-solving skills through the analysis of strategies and decision-making processes.

  • Construct and analyze decision trees

    • Classification

    • Regression

    • Binary

    • Probability

    • Multi-way

  • Apply decision-making strategies to practical scenarios in economics, business, and other fields

Outcome #2: Apply understanding of probability theory and applications in real-world scenarios.

  • Identify the key concepts of probability theory

  • Analyze risks 

  • Identify the risk

  • Assess the risk

  • Strategize to reduce the risk

  • Supply and Demand

  • Gerrymandering

  • Tactical game

Outcome #3: Develop critical thinking abilities by evaluating and optimizing game outcomes.

  • Identify patterns

  • Assess decisions

  • Anticipate consequences

  • Ethical and moral implications of games

Outcome #4: Develop mathematical reasoning skills by exploring the combinatorial aspects of games.

  • Calculate the number of possible arrangements of game elements

  • Calculate probabilities of specific events

  • Create algorithms to solve specific game scenarios

Suggested Texts and Materials

Suggested texts for the instructor:

  • The Mathematics of Games (Dover Books on Mathematics)

  • Game Theory 101: The complete Textbook by William Spaniel

  • Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life by Avinash K. Dixit and Barry Nalebuff

  • Game Theory: A Very Short Introduction by Ken Binmore

  • Game Theory: A Nontechnical Introduction by Morton d. Davis

  • Math Games with Bad Drawings by Ben Orlin

Suggested Games:

  • The Game of 21/15 (not the card game)

  • The Tower of Hanoi

  • Julia Robinson Math Festival Gerrymandering

  • Dots and Boxes

  • Fractal Structure

  • Rival Vines

  • Sim (combination)

  • Arpeggios (risk and reward)

  • Battleship

Department Notes

This should be a hands-on course where students play games first to try and learn strategy before they learn the theory of it.