Fat Chance: Probability from 0 to 1

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.

Table of Contents:
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.

About the Author :
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.

Review :
'Probability is a subject of fundamental importance that's often taught as a dry slog through ball-filled urns. Fat Chance, a snappy and example-rich text, is the perfect antidote and a great choice for a general-audience math course.' Jordan Ellenberg, University of Wisconsin-Madison 'Mathematics is a minority sport. Only very few understand, say, algebraic geometry or ergodic theory, and that's perfectly OK. Yet, probability theory is different. We are surrounded by chance and uncertainty. You cannot be a fully-fledged, functioning twenty-first-century human, whether at work, as a consumer or as an active citizen, without understanding the basic rules that govern chance. This is a book explaining chance and probability to non-mathematicians: accessible, not expecting any prior knowledge - but, there being no free lunch, assuming basic intelligence and an open mind. A small price for great enlightenment.' Arieh Iserles, University of Cambridge 'Fat Chance is a fun and friendly introduction to the big ideas of risk, probability, and uncertainty in our everyday lives and in the world around us. It's written by three of the greatest mathematicians - and teachers - anywhere on the planet. I loved it! And according to my calculations, there's a high probability you'll love it too.' Steven Strogatz, Cornell University, and author of Infinite Powers '… Fat Chance is an enjoyable small introductory book that, without the pretension of serving as a reference textbook, will certainly help undergraduate students to approach the fascinating world of probability but will also be appreciated by whoever desires to learn the basics through self-education.' Massimo Nespolo, Journal of Applied Crystallography 'The book is an excellent text for anyone looking for a very enjoyable introduction to probability. It can be read on its own or used as a textbook for a math course for non-math majors.' Thomas Hagedorn, MAA Reviews