MATH 576 COMBINATORIAL GAME THEORY
Spring 2017 course syllabus

Instructor:  Prof. Lincoln Lu

Office: LC 400I, email: lu@math.sc.edu

Office hours: TTh 12:00PM-- 1:00PM or by appointment.

Lecture time: TTh 1:15PM-2:30PM at LC 310

Credit Hours:  3

Lecture and homework

Prerequisite:  MATH 526, MATH 544 OR MATH 574

Textbook:   Winning ways for your mathematical plays (vol I), second edition,  by Berlekamp, Conway, and Guy   published by A K Peters, Wellesley, Massachusetts.

Learning outcomes:   Through this course, students learn the winning strategy in in certain combinatorial games such as Nim, Hackenbush, and Domineering. They will learn equalities and inequalities among games, Sprague-Grundy theory of impartial games, games which are numbers. We shall cover most parts of the textbook and some supplemental material.

Homework:   Homework will be assigned roughly every other week and should be completed and be collected by next Wednesday.

Reading:  Reading the sections of the textbook corresponding to the assigned homework exercises is considered part of the homework assignment.

Exams:  There will be two exams given during lecture time. Exam 1 is scheduled on Tuesday (March 14, 2017). It covers Chapter 1-3, or note1 and note2.

Final project:   There is no final exam for this class. Instead, you will have a final project. Please form a group of two and do only one of the following projects. Each group will write a report of at least 4 pages and make a presentation in the classes.

  1. Design a combinatorial game and analyze it. The game should have two players moving alternatively. Whoever gets stuck in his/her turn is the loser.
  2. Implement any games using any computer language and any interface at your choice. It can play against user.

Grading: The homework is 30%. The first exam is 20%. The second exam is 20%. The final project is 30%. Your final grade is based on the percentage as follows.

Grading Scale

Grading Scale:

90-100% A

76-79% C+

60-65% D

86-89%   B+

70-75% C

0-59%   F

80-85%   B

66-69% D+

 


Links:

Conway's Game of Life

Peg Solitaire

Rubik's Cube