It is based around an in-depth examination of what is meant by game theory optimal play (GTO) and how it can be applied at the table. Understanding GTO is fundamental to being able to make accurate poker decisions and being able to exploit players who don’t. Modern Poker Theory uses modern poker tools to develop a systematic approach to the analysis of GTO. It organizes the ideas and concepts in an intuitive manner that is totally focused to practical applications. Next time you are at a table some of the players will have studied Modern Poker Theory and some won’t. The players who have studied Modern Poker Theory will, without doubt, have a better theoretical and practical understanding of No-Limit Hold’em. They will be the favourites in the game. Make sure you are one of them. Michael Acevedo, one of the world’s leading poker theorists, is a game theory expert who is renowned for creating cutting-edge content for the world’s leading players. The production of Modern Poker Theory is the culmination of many thousands of hours of his research work with the most advanced poker software tools available. It is poker theory for the 21st century.

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    These noteworthy accounts of the lives of David Hilbert and Richard Courant are closely related: Courant's story is, in many ways, seen as the sequel to the story of Hilbert. Originally published to great acclaim, both books explore the dramatic scientific history expressed in the lives of these two great scientists and described in the lively, nontechnical writing style of Contance Reid.

    Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic--for example, emotion--is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.

    The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    

    With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction--and whether the universe truly has a future.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.

     According to MSNBC, having a child makes you stupid. You actually lose IQ points. Good Morning America has announced that natural blondes will be extinct within two hundred years. Pundits estimated that there were more than a million demonstrators at a tea party rally in Washington, D.C., even though roughly sixty thousand were there. Numbers have peculiar powers-they can disarm skeptics, befuddle journalists, and hoodwink the public into believing almost anything. "Proofiness," as Charles Seife explains in this eye-opening book, is the art of using pure mathematics for impure ends, and he reminds readers that bad mathematics has a dark side. It is used to bring down beloved government officials and to appoint undeserving ones (both Democratic and Republican), to convict the innocent and acquit the guilty, to ruin our economy, and to fix the outcomes of future elections. This penetrating look at the intersection of math and society will appeal to readers of Freakonomics and the books of Malcolm Gladwell.

    Hungarian-born Erdős believed that the meaning of life was to prove and conjecture. His work in the United States and all over the world has earned him the titles of the century's leading number theorist and the most prolific mathematician who ever lived. Erdős's important work has proved pivotal to the development of computer science, and his unique personality makes him an unforgettable character in the world of mathematics. Incapable of the smallest of household tasks and having no permanent home or job, he was sustained by the generosity of colleagues and by his own belief in the beauty of numbers. Witty and filled with the sort of mathematical puzzles that intrigued Erdős and continue to fascinate mathematicians today, My Brain Is Open is the story of this strange genius and a journey in his footsteps through the world of mathematics, where universal truths await discovery like hidden treasures and where brilliant proofs are poetry.

    Many of these students are extremely intelligent and hardworking, but even the best will, at some point, struggle with the demands of making the transition to advanced mathematics. Some have difficulty adjusting to independent study and to learning from lectures. Other struggles, however, are more fundamental: the mathematics shifts in focus from calculation to proof, so students are expected to interact with it in different ways. These changes need not be mysterious - mathematics education research has revealed many insights into the adjustments that are necessary - but they are not obvious and they do need explaining.This no-nonsense book translates these research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics degree, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time. Part 1 provides an in-depth discussion of advanced mathematical thinking, and explains how a student will need to adapt and extend their existing skills in order to develop a good understanding of undergraduate mathematics. Part 2 covers study skills as these relate to the demands of a mathematics degree. It suggests practical approaches to learning from lectures and to studying for examinations while also allowing time for a fulfilling all-round university experience.The first subject-specific guide for students, this friendly, practical text will be essential reading for anyone studying mathematics at university.

    For all ages and all levels of difficulty, these puzzles range from those that can be solved in minutes to those that will beguile for hours.

    Calculus is not a prerequisite, although examples and exercises using very basic calculus are included (labeled Calculus Required.) The most technology-friendly text on the market, Introductory Linear Algebra is also the most flexible. By omitting certain sections, instructors can cover the essentials of linear algebra (including eigenvalues and eigenvectors), to show how the computer is used, and to introduce applications of linear algebra in a one-semester course.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.