Before the mid-seventeenth century, scholars generally agreed that it was impossible to predict something by calculating mathematical outcomes. One simply could not put a numerical value on the likelihood that a particular event would occur. Even the outcome of something as simple as a dice roll or the likelihood of showers instead of sunshine was thought to lie in the realm of pure, unknowable chance. The issue remained intractable until Blaise Pascal wrote to Pierre de Fermat in 1654, outlining a solution to the "unfinished game" problem: how do you divide the pot when players are forced to.

Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

Introduction to Logic is clear and concise, uses interesting examples (many philosophical in nature), and has easy-to-use proof methods. Its key features, retained in this Third Edition, include: simpler ways to test arguments, including an innovative proof method and the star test for syllogisms; a wide scope of materials, suiting it for introductory or intermediate courses; engaging examples, from philosophy and everyday life; useful for self-study and preparation for standardized tests, like the LSAT; a reasonable price (a third the cost of some competitors); and exercises that correspond to the free LogiCola instructional program. This Third Edition: improves explanations, especially on areas that students find difficult; has a fuller explanation of traditional Copi proofs and of truth trees; and updates the companion LogiCola software, which now is touch friendly (for use on Windows tablets and touch monitors), installs more easily on Windows and Macintosh, and adds exercises on Copi proofs and on truth trees. You can still install LogiCola for free (from http://www.harryhiker.com/lc or http://www.routledge.com/cw/gensler).

This well-respected introduction to statistics and statistical theory covers data processing, probability and random variables, utility and descriptive statistics, computation of Bayes strategies, models, testing hypotheses, and much more. 1959 edition.

Linear programming. Introduction to linear programming -- Linear programs and their duals -- How the dual indicates optimality -- Basic solutions -- The idea of the simplex methods -- Separating planes for convex sets -- Finite cones and the Farkas alternative -- The duality principle -- Perturbations and parametric programming -- The simplex tableau algorithm -- The revised simplex algorithm -- A simplex algorithm for degenerate problems -- Multiobjective linear programming -- Zero-sum, two-person games -- Integer programming: Gomory's method -- Network flows -- Assignment and shortest-route problems -- The transportation problem -- Nonlinear programming. Wolfe's method for quadratic programming -- Kuhn-Tucker theory -- Geometric programming -- Fixed-point theorems. Introduction to fixed points -- Contraction mappings -- Garsia's proof of the Brouwer fixed-point theorem -- Milnor's proof of the Brouwer fixed-point theorem -- Barycentric coordinates, Sperner's lemma, and an elementary proof of the Brouwer fixed-point theorem -- The Schauder fixed-point theorem -- Kakutani's fixed-point theorem and Nash's theorem for n-person games.