A timeless introduction to the field and a landmark in symbolic logic, showing that classical logic can be treated algebraically.

    The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as the American university.Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 50s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others.Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come."Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric."--The Mathematical Intelligencer"Learned, thought-provoking, politically incorrect, delighting in paradox, and likely to offend but everywhere readable and entertaining."--The American Mathematical Monthly"It is about mathematicians, the way they think, and the world in which the live. It is 260 pages of Rota calling it like he sees it... Readers are bound to find his observations amusing if not insightful. Gian-Carlo Rota has written the sort of book that few mathematicians could write. What will appeal immediately to anyone with an interest in research mathematics are the stories he tells about the practice of modern mathematics."--MAA Reviews"

    But now, with the aid of high-speed computers, scientists have been able to penetrate a reality that is changing the way we perceive the universe. Their findings -- the basis for chaos theory -- represent one of the most exciting scientific pursuits of our time.No better introduction to this find could be found than John Briggs and F. David Peat's Turbulent Mirror. Together, they explore the many faces of chaos and reveal how its law direct most of the processes of everyday life and how it appears that everything in the universe is interconnected -- discovering an "emerging science of wholeness."Turbulent Mirror introduces us to the scientists involved in study this endlessly strange field; to the theories that are turning our perception of the world on its head; and to the discoveries in mathematics, biology, and physics that are heralding a revolution more profound than the one responsible for producing the atomic bomb. With practical applications ranging from the control of traffic flow and the development of artifical intelligence to the treatment of heart attacks and schizophrenia, chaos promises to be an increasingly rewarding area of inquiry -- of interest to everyone.

    - predicted the reappearance of a lost planet, - discovered basic properties of magnetic forces, - invented a surveying tool used by professionals until the invention of lasers. Based on extensive research of original and secondary sources, this historical narrative will inspire young readers and even curious adults with its touching story of personal achievement.

    Jerry King is no exception. His informal, nontechnical book, as its title implies, is organized around what Bertrand Russell called the 'supreme beauty' of mathematics--a beauty 'capable of a stern perfection such as only the greatest art can show.'NATUREIn this clear, concise, and superbly written volume, mathematics professor and poet Jerry P. King reveals the beauty that is at the heart of mathematics--and he makes that beauty accessible to all readers. Darting wittily from Euclid to Yeats, from Poincare to Rembrandt, from axioms to symphonies, THE ART OF MATHEMATICS explores the difference between real, rational, and complex numbers; analyzes the intellectual underpinnings of pure and applied mathematics; and reveals the fundamental connection between aesthetics and mathematics. King also sheds light on how mathematicians pursue their research and how our educational system perpetuates the damaging divisions between the two cultures.

    Naturalist. Warrior. President. There are so many sides to Theodore Roosevelt that it is easy to overlook one of his most enduring contributions to American public life: the use of fame to fuel his political career.In this concisely written, enlightening book, presidential historian Lewis L. Gould goes beyond the bully pulpit stereotypes to reveal how Roosevelt used his celebrity to change American politics. Based on research gleaned from the personal papers of Roosevelt and his contemporaries, TheodoreRoosevelt recaptures its subject's bold activism and irrepressible, larger-than-life personality. Beginning with his privileged childhood in New York City, the narrative traces his election to the New York Assembly, where he quickly rose through the ranks of the Republican Party. It is here that hefirst applied his shrewd ability to keep himself in the spotlight--a skill that served him well as commander of a volunteer regiment (dubbed Roosevelt's Rough Riders) in the Spanish-American War. Gould shows how Roosevelt rode a wave of popular acclaim at the war's end, assuming the governorshipof New York and serving as president from 1901 to 1909. While covering his major accomplishments as chief executive, including his successes as a trust-buster, labor mediator, and conservationist, Gould explains how fame both sustained and limited Roosevelt when he ran for president in 1912 andopposed Woodrow Wilson's policies during World War I.Theodore Roosevelt delivers the most insightful look yet at a pioneer of political theater--a man whose vigorous idealism as a champion of democracy serves as a counterpoint to the cynicism of today's political landscape. The book will coincide with the 100th anniversary of Roosevelt's third partyrun for the Progressive or Bull Moose Party.

    Book by Waring, Chris

    The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology.Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings.

    Linear Equations; Vector Spaces; Linear Transformations; Polynomials; Determinants; Elementary canonical Forms; Rational and Jordan Forms; Inner Product Spaces; Operators on Inner Product Spaces; Bilinear Forms For all readers interested in linear algebra.

    Shilov, Professor of Mathematics at the Moscow State University, covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional algebras and their representations, with an appendix on categories of finite-dimensional spaces.The author begins with elementary material and goes easily into the advanced areas, covering all the standard topics of an advanced undergraduate or beginning graduate course. The material is presented in a consistently clear style. Problems are included, with a full section of hints and answers in the back.Keeping in mind the unity of algebra, geometry and analysis in his approach, and writing practically for the student who needs to learn techniques, Professor Shilov has produced one of the best expositions on the subject. Because it contains an abundance of problems and examples, the book will be useful for self-study as well as for the classroom.

    Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises explaining how they relate to the preceding section, and how they foreshadow later topics.

    In the four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects of our universe. From their successes and failures, delusions, and even duels, the trajectories of their innovations—and their impact on society—are traced in this fascinating narrative. Quantum mechanics, space-time, chaos theory and the workings of complex systems, and the impossibility of a "perfect" democracy are all here. Stein's book is both mind-bending and practical, as he explains the best way for a salesman to plan a trip, examines why any thought you could have is imbedded in the number π , and—perhaps most importantly—answers one of the modern world's toughest questions: why the garage can never get your car repaired on time.Friendly, entertaining, and fun, How Math Explains the World is the first book by one of California's most popular math teachers, a veteran of both "math for poets" and Princeton's Institute for Advanced Studies. And it's perfect for any reader wanting to know how math makes both science and the world tick.

    Covering various the materials needed by students in engineering, science, and mathematics, this calculus text makes effective use of computing technology, graphics, and applications. It presents at least two technology projects in each chapter.

    Increasingly, the decisions that affect our lives--where we go to school, whether we can get a job or a loan, how much we pay for health insurance--are being made not by humans, but by machines. In theory, this should lead to greater fairness: Everyone is judged according to the same rules.But as mathematician and data scientist Cathy O'Neil reveals, the mathematical models being used today are unregulated and uncontestable, even when they're wrong. Most troubling, they reinforce discrimination--propping up the lucky, punishing the downtrodden, and undermining our democracy in the process.

    Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program"