Fat Chance: Probability from 0 to 1 is an introductory undergraduate-level textbook on probability theory, centered on the metaphor of games of chance. [1] It was written by Benedict Gross, Joe Harris, and Emily Riehl, based on a course for non-mathematicians taught to Harvard University undergraduates, and published by the Cambridge University Press in 2019. An associated online course has been offered to the public by Harvard. [2]
Unusually for a probability theory book, this book does not use the phrase "random variable", instead referring to random processes as games. [3] The first five chapters of the book concern counting problems, and include material on the exponential function, binomial coefficients, factorials, games of cards, dice, and coins, and the birthday paradox. [1] [2] [4] After an interlude involving the binomial theorem, Pascal's triangle, and the Catalan numbers, the second part of the book concerns probability more directly. Its chapters concern the expected value, conditional probability and Bayes' theorem, events with unequal probabilities (biased coins and loaded dice), geometric probability, the law of large numbers, and normal distributions. [1] [2] The third part moves from probability to statistics, with topics including the central limit theorem and the meaning of false positives and false negatives in medical testing. [4]
Although the main purpose of the book is to be a textbook for college courses aimed at non-mathematicians, it can also be read independently by those interested in the topic. [4] Reviewer Ludwig Paditz recommends the book to "readers without deeper knowledge in elementary statistics and probability". [3] Reviewer Massimo Nespolo recommends as well that its readers take advantage of the associated online course offering. [2]
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes . Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability theory describing such behaviour are the law of large numbers and the central limit theorem.
Joseph Daniel Harris is a mathematician at Harvard University working in the field of algebraic geometry. After earning an AB from Harvard College, he continued at Harvard to study for a PhD under Phillip Griffiths.
Ars Conjectandi is a book on combinatorics and mathematical probability written by Jacob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.
James Laurie Snell, often cited as J. Laurie Snell, was an American mathematician.
The Princeton Lectures in Analysis is a series of four mathematics textbooks, each covering a different area of mathematical analysis. They were written by Elias M. Stein and Rami Shakarchi and published by Princeton University Press between 2003 and 2011. They are, in order, Fourier Analysis: An Introduction; Complex Analysis; Real Analysis: Measure Theory, Integration, and Hilbert Spaces; and Functional Analysis: Introduction to Further Topics in Analysis.
Analytic Combinatorics is a book on the mathematics of combinatorial enumeration, using generating functions and complex analysis to understand the growth rates of the numbers of combinatorial objects. It was written by Philippe Flajolet and Robert Sedgewick, and published by the Cambridge University Press in 2009. It won the Leroy P. Steele Prize in 2019.
Emily Riehl is an American mathematician who has contributed to higher category theory and homotopy theory. Much of her work, including her PhD thesis, concerns model structures and more recently the foundations of infinity-categories. She is the author of two textbooks and serves on the editorial boards of three journals.
An Introduction to the Philosophy of Mathematics is a 2012 textbook on the philosophy of mathematics by Mark Colyvan. It has a focus on issues in contemporary philosophy, such as the mathematical realism–anti-realism debate and the philosophical significance of mathematical practice, and largely skips over historical debates. It covers a range of topics in contemporary philosophy of mathematics including various forms of mathematical realism, the Quine–Putnam indispensability argument, mathematical fictionalism, mathematical explanation, the "unreasonable effectiveness of mathematics", paraconsistent mathematics, and the role of mathematical notation in the progress of mathematics. The book was praised as accessible and well-written and the reaction to its contemporary focus was largely positive, although some academic reviewers felt that it should have covered the historical debates over logicism, formalism and intuitionism in more detail. Other aspects of the book that received praise were its coverage of mathematical explanation, its appeal to mathematicians and other non-philosophers, and its discussion questions and further readings, whilst its epilogue and short length received a more mixed reception.
Using the Borsuk–Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry is a graduate-level mathematics textbook in topological combinatorics. It describes the use of results in topology, and in particular the Borsuk–Ulam theorem, to prove theorems in combinatorics and discrete geometry. It was written by Czech mathematician Jiří Matoušek, and published in 2003 by Springer-Verlag in their Universitext series (ISBN 978-3-540-00362-5).
Treks into Intuitive Geometry: The World of Polygons and Polyhedra is a book on geometry, written as a discussion between a teacher and a student in the style of a Socratic dialogue. It was written by Japanese mathematician Jin Akiyama and science writer Kiyoko Matsunaga, and published by Springer-Verlag in 2015 (ISBN 978-4-431-55841-5).
A Guide to the Classification Theorem for Compact Surfaces is a textbook in topology, on the classification of two-dimensional surfaces. It was written by Jean Gallier and Dianna Xu, and published in 2013 by Springer-Verlag as volume 9 of their Geometry and Computing series. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries.
Pearls in Graph Theory: A Comprehensive Introduction is an undergraduate-level textbook on graph theory, by Nora Hartsfield and Gerhard Ringel. It was published in 1990 by Academic Press, Inc., with a revised edition in 1994 and a paperback reprint of the revised edition by Dover Books in 2003. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.
The Mathematics of Games and Gambling is a book on probability theory and its application to games of chance. It was written by Edward Packel, and published in 1981 by the Mathematical Association of America as volume 28 of their New Mathematical Library series, with a second edition in 2006.
Introduction to Circle Packing: The Theory of Discrete Analytic Functions is a mathematical monograph concerning systems of tangent circles and the circle packing theorem. It was written by Kenneth Stephenson and published in 2005 by the Cambridge University Press.
Extensions of First Order Logic is a book on mathematical logic. It was written by María Manzano, and published in 1996 by the Cambridge University Press as volume 19 of their book series Cambridge Tracts in Theoretical Computer Science.
The Geometry of Numbers is a book on the geometry of numbers, an area of mathematics in which the geometry of lattices, repeating sets of points in the plane or higher dimensions, is used to derive results in number theory. It was written by Carl D. Olds, Anneli Cahn Lax, and Giuliana Davidoff, and published by the Mathematical Association of America in 2000 as volume 41 of their Anneli Lax New Mathematical Library book series.
Primality Testing for Beginners is an undergraduate-level mathematics book on primality tests, methods for testing whether a given number is a prime number, centered on the AKS primality test, the first method to solve this problem in polynomial time. It was written by Lasse Rempe-Gillen and Rebecca Waldecker, and originally published in German as Primzahltests für Einsteiger: Zahlentheorie, Algorithmik, Kryptographie. It was translated into English as Primality Testing for Beginners and published in 2014 by the American Mathematical Society, as volume 70 of their Student Mathematical Library book series. A second German-language edition was publisher by Springer in 2016.
Combinatorics: The Rota Way is a mathematics textbook on algebraic combinatorics, based on the lectures and lecture notes of Gian-Carlo Rota in his courses at the Massachusetts Institute of Technology. It was put into book form by Joseph P. S. Kung and Catherine Yan, two of Rota's students, and published in 2009 by the Cambridge University Press in their Cambridge Mathematical Library book series, listing Kung, Rota, and Yan as its authors. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.
Convergence of Probability Measures is a graduate textbook in the field of mathematical probability theory. It was written by Patrick Billingsley and published by Wiley in 1968. A second edition in 1999 both simplified its treatment of previous topics and updated the book for more recent developments. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries. Readers are expected to already be familiar with both the fundamentals of probability theory and the topology of metric spaces.
Introduction to Lattices and Order is a mathematical textbook on order theory by Brian A. Davey and Hilary Priestley. It was published by the Cambridge University Press in their Cambridge Mathematical Textbooks series in 1990, with a second edition in 2002. The second edition is significantly different in its topics and organization, and was revised to incorporate recent developments in the area, especially in its applications to computer science. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.