Résumé
Designed for the intellectually curious, this book provides a solid foundation in basic probability theory in a charming style, without technical jargon. This text will immerse the reader in a mathematical view of the world, and teach them techniques to solve real-world problems both inside and outside the casino.In a world where we are constantly being asked to make decisions based on incomplete information, facility with basic probability is an essential skill. This book provides a solid foundation in basic probability theory designed for intellectually curious readers and those new to the subject. Through its conversational tone and careful pacing of mathematical development, the book balances a charming style with informative discussion. This text will immerse the reader in a mathematical view of the world, giving them a glimpse into what attracts mathematicians to the subject in the first place. Rather than simply writing out and memorizing formulas, the reader will come out with an understanding of what those formulas mean, and how and when to use them. Readers will also encounter settings where probabilistic reasoning does not apply or where intuition can be misleading. This book establishes simple principles of counting collections and sequences of alternatives, and elaborates on these techniques to solve real world problems both inside and outside the casino. Pair this book with the HarvardX online course for great videos and interactive learning: https://harvardx.link/fat-chance.Part I. Counting: 1. Simple counting; 2. The multiplication principle; 3. The subtraction principle; 4. Collections; 5. Games of chance; Interlude; 6. The binomial theorem; 7. Advanced counting; Part II. Probability: 8. Expected value; 9. Conditional probability; 10. Unfair coins and loaded dice; 11. Geometric probability; Part III. Probability in the Large: 12. Games and their payoffs; 13. The normal distribution; 14. Don't try this at home.Benedict Gross is Leverett Professor of Mathematics, Emeritus at Harvard University, Massachusetts, and Professor of Mathematics at University of California, San Diego. He has taught mathematics at all levels at Princeton University, Brown University, Harvard University, and University of California, San Diego, and served as the Dean of Harvard College from 2003-2007. He is a member of the American Academy of Arts and Sciences and the National Academy of Science. Among his awards and honors are the Cole Prize from the American Mathematical Society and a MacArthur Fellowship. His research is primarily in number theory. Joe Harris is the Higgins Professor of Mathematics at Harvard University, Massachusetts. He has been at Harvard University since 1988 and was previously on the faculty at Massachusetts Institute of Technology and Brown University. He is a member of the American Academy of Arts and Sciences and the National Academy of Science. Throughout his career, he has been deeply committed to education at every level, which led to a partnership with Benedict Gross to develop the Harvard course Fat Chance, the inspiration for the book of the same title. He is author of several books including 3264 and All That (Cambridge, 2016), Algebraic Geometry (1995), and The Geometry of Schemes (2000). Emily Riehl is an Assistant Professor of Mathematics at The Johns Hopkins University, Maryland and previously was a Benjamin Peirce and NSF postdoctoral fellow at Harvard University, Massachusetts. She has published over twenty papers and written two books: Categorical Homotopy Theory (Cambridge, 2014) and Category Theory in Context (2016). She has been awarded an NSF grant and a CAREER award to support her work and has been recognized for excellence in teaching at both Johns Hopkins and at Harvard.
