Games and Puzzles

Description

In this course, I present a variety of games and puzzles and discuss various mathematical strategies for playing and solving them. The course consists of five video lessons, each about a half an hour long, and each with 2 to 4 simple homework exercises at the end, which I would like my students to complete and turn in by the following week. Each lesson can be purchased separately or as part of the entire course. No lesson in the course is a prerequisite for any of the others. The grade level for this course is grades 7 to 12. Students who purchase the course should have a thorough knowledge of grade school arithmetic, but there are no other math requirements. However, this course, and others to follow, are meant for students with a keen desire to learn math and how it can be enjoyed and used in their lives.

In the first lesson, I describe the basics of binary search, both for numbers and for binary trees, and how these methods can be applied to the number guessing game Higher or Lower and the word guessing game Twenty Questions, respectively.

In the second lesson, I describe frequency analysis of English letters and letter combinations, and how this can be applied to the game of Hangman as well as decryption of substitution ciphers.

The third lesson is the first of a two-part series on game theory, in which I describe the basics of game theory and how it can be used in connection with various two-player zero-sum games, like tic-tac-toe and checkers, as well as with various social issues, such as economic and defense strategies.

The fourth lesson is the second part of this two-part series on game theory, in which I explain the basics of probability theory and how it can be applied to various games of chance, including gambling and investing.

The fifth lesson is devoted to No Limit Hold 'Em, a particular version of poker, in which I first explain all the rules of this game and then outline a good strategy for playing it.

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