What's New
- Jan 15: First day of class. This web-page will be your main source of information about this class. Plan to check this page regularly.
Course Details
Textbook
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Luck, Logic and White Lies: The Mathematics of Games by Jorg Bewersdorff, Translated by David Kramer, 2004 ISBN: 978-1568812106 Find this book at Amazon |
You will also need to purchase:
- One standard deck of playing cards
- Five standard six-sided dice (can be found in a game of Yahtzee)
- An account for playing games at Yahoo Games
Overview
A study of the relations and properties of countable sets within mathematics. Topics include elementary set theory, probability, combinations, permutations and propositional logic, with a focus on practical applications. Advanced topics are selected from matrices, linear programming, markov chains and game theory.In particular, in this course we will investigate the mathematics behind well-known board, card and dice games and puzzles, using logic, probability, combinatorics and game theory.
Course Outcomes
- Represent real-life problems through the use of mathematical formulas
You will use set theory, probability and game theory to represent odds of winning and real-life situations.
- Solve problems using symbolic manipulation
You will use rules of symbolic logic and probability to solve mathematical equations.
- Interpret the meaning of mathematical representations (such as calculations,
graphs and equations)
You will present interpretations of mathematics through homework, discussion, exams and an individual project.
- Verify the validity of a mathematical argument
You will assess the mathematical properties of a particular game in your term project.
Prerequisites
None.Quizzes and Participation
You are encouraged to attend class and participate in discussions. Active participation in class discussions will comprise 5% of your final grade.Extra Credit
Extra credit for this course can be earned by participating in the Centenary Math Problem of the Week (POTW), many of which are related to topics in finite mathematics. Each reasonable submission will be worth an additional 0.2% toward your final grade, and correct answers will earn 0.5%. Be sure to CC me with your submission for this extra credit.Disabilities
Centenary assures students with disabilities equal opportunity to reach the same level of achievement as other students. Strict confidentiality will be maintained on students with disabilities. Services for students with disabilities are available through the Counseling Center, located on the ground floor of Rotary Residence Hall, phone (318) 869-5424.Honor Code
All students are bound by the Honor System. The Honor System is applicable to all academic work. See the Centenary College Handbook for the complete Honor Code.Extensions
Extensions and rescheduling for homeworks and exams are only given when circumstances beyond your control (e.g. being sick, choir or sports travel) prevent you from completing a project on time. You must notify me either by email or phone of your circumstances well in advance of the due date. No extensions are given for requests made within two days of the due date.Syllabus
We will be covering pieces of the textbook from each of the three sections. We will also be using additional supplemental material such as relevant web-pages and background material. Readings will be assigned before material will be covered in class. You are expected to review the material and come to class prepared. As readings are assigned, they will be posted here.- Week of January 15th
- Preface
- Week of January 22th
- Chapter 1, 2, 8
- Week of Feb 7th, 12th
- Chapter 3, 4, 6
- Week of Feb 19th
- Chapter 9, 10
Homework
You will have between 10 and 12 Homeworks in this course, one about every week, for a total of 30% of your final grade. These homeworks will cover concepts we have discussed in class, and will always be due at the beginning of class on Tuesday.Your homework must be your own work and in your own words. You may discuss concepts and ideas with your classmates, tutors, and others as long as you credit them in your work, but the work you turn in must be your own.
You must show your work on all problems. If you only turn in solutions without work, you will not receive full credit for the assignment, and may receive a zero if this happens frequently.
Each homework will be worth a variable number of points depending on the number of problems assigned. Your score for the Homework section of your final grade will be calculated by dividing the total points you earned by the total points possible.
Links to homework problems will be posted here as they are made available
- Homework 1 Games, Puzzles and Logic
- Homework 2 Set Theory, Venn Diagrams
- Homework 3 Counting Sets, Probability
- Homework 4 Combinatorics and Recalibration
- Homework 5 Conditional Probability and Bayes' Rule
- Homework 6 Odds, Expected Value and Standard Deviation
- Homework 7 Nim and Combinatorial Games
- Homework 8 Natural Deduction
Project
The purpose of this project, worth 15% of your final grade, is to improve your research, writing and communication skills as well as give you an opportunity to explore in-depth a particular area of finite mathematics. This project will involve investigating the mathematical nature of a game of your choosing in consultation with me.
More details can be found on the Project page.
Exams
There will be three exams, each worth 16.6% of your final grade. The final exam will
be cumulative, and is scheduled by the registrar.
- Exam 1: Feb 28th
- Study Guide for Exam 1
- Study Problems for Exam 1
- Exam 2: April 3rd
- Study Guide for Exam 2
- Study Problems for Exam 2
- Final: Wednesday, May 7th, 12pm
- Study Guide and Problems for Exam 3
- Remember this is a cumulative final. Study also from the previous study guides.
Grading
Your final grade for this course will be based on the Homework, Project, Exams and Participation described above.
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© Mark Goadrich, Centenary College of Louisiana