Folsom Library Collection Highlights

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them.

With the born storyteller's command of narrative and imaginative approach, Leonard Mlodinow vividly demonstrates how our lives are profoundly informed by chance and randomness and how everything from wine ratings and corporate success to school grades and political polls are less reliable than we believe

Fermat's Last Theorem became the Holy Grail of mathematics. Whole and colorful lives were devoted, and even sacrificed, to finding a proof. Leonhard Euler, the greatest mathematician of the eighteenth century, had to admit defeat. Sophie Germain took on the identity of a man to do research in a field forbidden to females, and made the most significant breakthrough of the nineteenth century. The dashing Evariste Galois scribbled down the results of his research deep into the night before venturing out to die in a duel in 1832. Yutaka Taniyama, whose insights would ultimately lead to the solution, tragically killed himself in 1958. On the other hand, Paul Wolfskehl, a famous German industrialist, claimed Fermat had saved him from suicide, and established a rich prize for the first person to prove the theorem. And then came Princeton professor Andrew Wiles, who had dreamed of proving Fermat's Last Theorem ever since he first read of it as a boy of ten in his local library. In 1993, some 356 years after Fermat's challenge, and after seven years of working in isolation and secrecy - "a kind of private and very personal battle I was engaged in"--Wiles stunned the world by announcing a proof. Fermat's Enigma is the story of the epic quest to solve the greatest math problem of all time.

Before John Glenn orbited the earth or Neil Armstrong walked on the moon, a group of dedicated female mathematicians known as 'human computers' used pencils, slide rules and adding machines to calculate the numbers that would launch rockets, and astronauts, into space. Among these problem-solvers were a group of exceptionally talented African American women, some of the brightest minds of their generation. Originally relegated to teaching math in the South's segregated public schools, they were called into service during the labor shortages of World War II, when America's aeronautics industry was in dire need of anyone who had the right stuff. Suddenly, these overlooked math whizzes had a shot at jobs worthy of their skills, and they answered Uncle Sam's call, moving to Hampton, Virginia, and the fascinating, high-energy world of the Langley Memorial Aeronautical Laboratory. Even as Virginia's Jim Crow laws required them to be segregated from their white counterparts, the women of Langley's all-black 'West Computing' group helped America achieve one of the things it desired most: a decisive victory over the Soviet Union in the Cold War, and complete domination of the heavens.

The sixth edition of the classic undergraduate text in elementary number theory includes a new chapter on elliptic curves and their role in the proof of Fermat's Last Theorem, a foreword by Andrew Wiles and extensively revised and updated end-of-chapter notes.

To solve one of the great mathematical problems of his day, Alan Turing proposed an imaginary programmable calculating machine. But the idea of actually producing a "Turing machine" did not crystallize until he and his brilliant Bletchley Park colleagues built devices to crack the Nazis' Enigma code, thus ensuring the Allies' victory in World War II. In so doing, Turing became a champion of artificial intelligence, formulating the famous (and still unbeaten) Turing Test that challenges our ideas of human consciousness. But Turing's postwar computer-building was cut short when, as an openly gay man in a time when homosexuality was officially illegal in England, he was apprehended by the authorities and sentenced to a "treatment" that amounted to chemical castration, leading to his suicide. With a novelist's sensitivity, David Leavitt portrays Turing in all his humanity, his eccentricities, his brilliance, and his fatal candor, while elegantly explaining his work and its implications.

Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists.

This book is an introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications.

A new history of mathematics focusing on the marginalized voices who propelled the discipline, spanning the globe and thousands of years of untold stories. Mathematics shapes almost everything we do. But despite math's reputation as the study of fundamental truths, the stories we have been told about it are wrong -- warped like the sixteenth-century map that enlarged Europe at the expense of Africa, Asia, and the Americas. In The Secret Lives of Numbers, renowned math historian Kate Kitagawa and journalist Timothy Revell make the case that the history of math is infinitely deeper, broader, and richer than the narrative we think we know. Their story takes us from Hypatia, one of the first great female mathematicians, whose ideas revolutionized geometry and who was killed for them, to Karen Uhlenbeck, the first woman to win the Abel Prize, math's Nobel. Along the way we travel the globe to meet the brilliant Arabic scholars of the House of Wisdom, a math temple whose destruction in the siege of Baghdad in the thirteenth century was a loss arguably on par with that of the Library of Alexandria; Mādhava of Sangamagrama, the fourteenth-century Indian genius who uncovered the central tenets of calculus three hundred years before Isaac Newton was born; and the Black mathematicians of the Civil Rights era, who played a significant role in dismantling early data-based methods of racial discrimination. A thrilling tour through the richness of mathematics, The Secret Lives of Numbers is an immensely compelling narrative history.