xii Preface As I have indicated above, this book will be quite challenging for an undergraduate student, and, to be honest, will possibly be too hard to understand completely in a few spots, especially the physics- related material near the end. But I encourage all undergraduate students to “go for it” and persist with the difficult parts. If you reach for the stars, you will at least get to the moon. That said, students would likely get more out of the book if they could consult a faculty member or graduate student when needed, as in a directed reading class. Acknowledgements During the more than four years that I have worked on this project, I have been helped in many ways by many people. First and fore- most, I would like to thank the students who attended my lectures. They helped with their questions and corrections to the original set of lecture notes, helping me to improve the presentation. More sig- nificantly, their energy and enthusiasm convinced me that it would be worthwhile to expand the lectures into a book. They will unfortu- nately have to remain nameless, as I did not take roll and so would probably miss at least a few dozen if I tried to reconstruct the com- plete list from PCMI records and my memory. You know who you are, and I want to express my thanks to you here. I also owe a debt of gratitude to Artur Elezi, who both served as a Teaching Assistant at PCMI and suggested many improvements to the original lecture notes. I would also like to give special thanks to Michael Mulligan and Michael Sommers. These two University of Illinois students read most of the manuscript at different points, reported numerous typos and mistakes, and offered suggestions for improvement. Michael Mulligan worked through Chapters 1–10 during 2004. Michael Sommers read a near-final draft during the summer of 2005 with particular attention to Chapters 10–14 and provided assistance with the bibliography and the index. The book is much better as a result of their efforts. I also owe a debt of gratitude to Arthur Greenspoon, who volun- teered his professional skills and proofread the entire book. Parts of the book were proofread by Daniel Morton, whom I thank as well.
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