Research area: Algorithmic Combinatorics
| Email: | gwilliamson@ucsd.edu |
Missing Geology: Torrey Pines State Natural Reserve Missing Geology
Fiction: The Observers
The Observers is the story of an alien microrobotic civilization dedicated to recording natural history on a galactic scale. Using virtual reality and habitat simulation, they have been recording and classifying life forms for two billion years -- over a hundred million years on earth. Detached and professional, the aliens rarely interfere with the objects of their studies. But the ultimate folly has been committed by a group of engineers in a secret lab in Arizona. It's time for introductions. Humans must confront their past and adjust to a future with the possibility of digital immortality. Social and family relationships are changed forever.
You can browse through parts of The Observers at the website of the publisher, iUniverse. The Barnes and Noble and Amazon websites also have The Observers listed. Note: The technological constraints of the story are described in the second paragraph of the Acknowledgments section.
Author's Notes: Reader's Questions and Comments
Recent Lower Division Undergraduate Texts:
Professor Ed Bender (Department of Mathematics, UCSD) and I have written two introductory textbooks which, together, cover the material in the lower division discrete mathematics sequence at UCSD. Hundreds of students have used these texts and given us their feedback. These texts were published (2005) by Dover Publications, Inc. The list price is $14.95 for each book.
Here are links to the Dover books:
A Short Course in Discrete Mathematics
Mathematics for Algorithm and System Analysis
A HELPFUL HINT FOR STUDYING THIS MATERIAL: For both of these books, at the end of each unit of study you will find a collection of multiple choice questions (Multiple Choice Questions for Review). Read these questions before reading the corresponding unit. Try to work the questions by (1) reading each question and (2) looking back through the material to dig up just what you need to answer that particular question. Make a game of it Just learn the minimum needed to understand and work each multiple choice question. When you learn to work all of the multiple choice questions (answers are given), then go through the corresponding unit systematically.
A Recent Upper Division Undergraduate/Graduate Text:
Foundations of Combinatorics with Applications
This book, written with my colleague Ed Bender, has been published (2006) by Dover Publications, Inc. The list price is $22.95. This book has four parts. Parts I and II are suitable for an upper division undergraduate course. Part III is slightly more advanced. Part IV is much more advanced. Parts I, II, and III (selections) have regularly been taught to advanced undergraduates in mathematics at UCSD.
An Unusual Graduate Text:
Combinatorics for Computer Science
The above link is to the version published (2002) by Dover Publications, Inc. (originally published in 1985 by Computer Science Press). The list price is $22.95.
The unusual thing about this book is that it is a record of student participation in a graduate mathematics course taught by me in algorithmic combinatorics from 1978 to 1985. The Table of Contents is replaced by a Study Guide for each of the ten chapters. Each item in the Study Guide that is in capital letters, for example CODING DOMINO COVERINGS, was a topic presented in class at the blackboard by a graduate student in the Department of Mathematics at UCSD (where I was a professor from 1965 to 1991). Both master's and doctoral students participated. Over the years, we developed an approach to explaining and presenting this material that was due to the students themselves.
Being student-developed, this book has a unique style -- rich in examples with the proofs closely tied to the examples. There are many useful ideas for anyone attempting to program problems of a combinatorial nature. The various chapters, after the first, are largely independent.
Data Structure Properties Not Provable With Math (ZFC)?