SAVE THE DATE:
Splash Spring 2019 is May 4-5, 2019!

Sign in or create an account above for account-specific details and links

For Splash Students

For Splash Teachers and Volunteers


ESP Biography



THEODORE HWA, Stanford alum with a passion for math and games




Major: Mathematics

College/Employer: Learning Unlimited

Year of Graduation: 2003

Picture of Theodore Hwa

Brief Biographical Sketch:

I graduated from Stanford with a bachelor's degree in computer science in 1998, and a PhD in Mathematics in 2003. I have a keen interest in many games - chess, bridge, backgammon, and many others. For the upcoming Splash!, I will be teaching a course on retrograde analysis chess problems.



Past Classes

  (Clicking a class title will bring you to the course's section of the corresponding course catalog)

H4353: Chess Puzzles: Proof Games in Splash Spring 2015 (Apr. 11 - 12, 2015)
Given a chess position, can you find a game that leads to it? Can you find the shortest possible game? If you enjoy logic puzzles, and know the rules of chess, you should find this class fun! No particular skill level in chess is needed because we consider all possible games, not just "well-played" games. Many beautiful ideas and tricks will arise when we find a short (or shortest) game leading to a position.


M3680: Wallpaper Symmetries in Splash! Spring 2014 (Apr. 12 - 13, 2014)
In this class, we'll study wallpaper patterns. For two-dimensional wallpaper (the most common kind :) it turns out there are 17 distinct possible types of symmetries in a wallpaper pattern. We'll look at different patterns, see how to identify and classify their symmetries, how to construct patterns with particular symmetries, and briefly discuss why there are only 17 possible patterns.


H2686: Chess Puzzles: Proof Games in Splash! Spring 2013 (Apr. 13 - 14, 2013)
Given a chess position, can you find a game that leads to it? Can you find the shortest possible game? If you enjoy logic puzzles, and know the rules of chess, you should find this class fun! No particular skill level in chess is needed because we consider all possible games, not just "well-played" games. Many beautiful ideas and tricks will arise when we find a short (or shortest) game leading to a position.


M2338: Peg Solitaire in Splash! Fall 2012 (Nov. 03 - 04, 2012)
You've probably played it at some point: start with a board full of pegs except for one hole in the center, and remove pegs one by one by jumping over them. The object is to leave just a final peg in the center. But this "central" game is only one of numerous puzzles on a peg solitaire board. We can try to end the game in a hole other than the center, or to start the game with a different initial vacancy, or start the game with more than one vacancy, or end the game with some pretty pattern on the board... you get the point. Some of these puzzles are possible to solve, and others are unfortunately impossible. In this class, we'll look at some of the mathematics that help us either to solve peg solitaire puzzles, or to prove that certain puzzles are impossible.


M1960: Impartial Games in Splash! Spring 2012 (Apr. 21 - 22, 2012)
An impartial combinatorial game is a game where both players choose from the same set of moves (unlike most games such as chess or checkers, where the players can only move their own pieces). Furthermore, the winner is the player who makes the last move. Impartial games are different from other games because there is no concept of score; the players are fighting over who gets the last move. We'll begin by studying the game of nim, which is the most fundamental impartial game. We will present a complete strategy for playing nim. Then we'll look at other impartial games and see how understanding nim can help us play them too.


M1282: Retrograde Analysis Chess Problems in Splash! Spring 2011 (Apr. 16 - 17, 2011)
Retrograde analysis chess problems are a type of chess logic puzzle. You are given a position, and asked to deduce something about it, such as: What were the last several moves played? Is there a game leading to this position? What is the shortest game leading to this position? We only assume that games are legal, not well-played, so no chess skill is required. If you are a chess player of any skill level that likes logic puzzles, you should find these problems enjoyable.


M1116: The Mathematics of Card Shuffling in Splash! Fall 2010 (Nov. 13 - 14, 2010)
You've probably heard that it takes 7 shuffles to completely randomize a deck of cards. But did you know that 8 perfect shuffles will restore a (52-card) deck to its original state? In this class, we'll discuss the mathematics behind card shuffling, and take a look at some card tricks based on shuffling.


M690: The Mathematics of Symmetry in Splash! Spring 2010 (Apr. 17 - 18, 2010)
Symmetry is all around us, both in natural and man-made objects. A starfish has fivefold rotational symmetry, while a brick wall has translational symmetry. In this course, we'll discuss how mathematics helps us classify symmetries, and why there are 7 types of one-dimensional symmetries and 17 types of two-dimensional symmetries.


M455: Games and Surreal Numbers in Splash! Fall 2009 (Oct. 10 - 11, 2009)
Let's play a game! In this course, we'll explore how a number system called the Surreal Numbers can help us understand many different games. Games that, at first glance, look very different turn out to be equivalent because they correspond to the same surreal number. We'll study a variety of games such as Nim, Hackenbush, Domineering, Amazons, and possibly others!


M155: The Game of Dots and Boxes in Splash! Fall 2008 (Oct. 18, 2008)
Dots and Boxes is a deceptively simple game you've probably played before. Starting with a grid of dots, two players take turns connecting two adjacent dots. A player that completes a box scores a point (by placing his or her initials in the box) and immediately takes another turn. When there are no more moves left, the player with more boxes wins. However, despite its simple rules, the game turns out to be quite rich in strategy. After playing several games, we will uncover several levels of strategies for the game. We will later relate the strategy of Dots and Boxes to the game of nim.