In the first edition of The Mathematical Tourist, renowned science journalist Ivars Peterson took readers on an unforgettable tour through the sometimes bizarre, but always fascinating, landscape of modern mathematics. Now the journey continues in a new, updated edition that includes all the latest information on mathematical proofs, fractals, prime numbers, and chaos, as well as new material on * the relationship between mathematical knots and DNA * how computers based on quantum logic can significantly speed up the factoring of large composite numbers * the relationship between four-dimensional geometry and physical theories of the nature of matter * the application of cellular automata models to social questions and the peregrinations of virtual ants * a novel mathematical model of quasicrystals based on decagon-shaped tiles Blazing a trail through rows of austere symbols and dense lines of formulae, Peterson explores the central ideas behind the work of professional mathematicians-- how and where their pieces of the mathematical puzzle fit in, the sources of their ideas, their fountains of inspiration, and the images that carry them from one discovery to another.

In the first edition of The Mathematical Tourist, renowned science journalist Ivars Peterson took readers on an unforgettable tour through the sometimes bizarre, but always fascinating, landscape of modern mathematics. Now the journey continues in a new, updated edition that includes all the latest information on mathematical proofs, fractals, prime numbers, and chaos, as well as new material on * the relationship between mathematical knots and DNA * how computers based on quantum logic can significantly speed up the factoring of large composite numbers * the relationship between four-dimensional geometry and physical theories of the nature of matter * the application of cellular automata models to social questions and the peregrinations of virtual ants * a novel mathematical model of quasicrystals based on decagon-shaped tiles Blazing a trail through rows of austere symbols and dense lines of formulae, Peterson explores the central ideas behind the work of professional mathematicians-- how and where their pieces of the mathematical puzzle fit in, the sources of their ideas, their fountains of inspiration, and the images that carry them from one discovery to another.

In this revised, updated edition of Peterson's classic work, the author blazes a trail into math's wilderness, a domain of unsettled truths full of unanswered questions, and shows us the wonderland beyond the thicket. He presents the latest information on mathematical proofs, fractals, prime numbers, and chaos, as well as new material on such intriguing topics as the relationship between mathematical knots and DNA; the application of cellular automata models to social questions; and the significant increase in the speed of factoring large composite numbers by means of computers based on quantum logic. Demystifying the major discoveries in mathematics, Peterson explores the work of key mathematicians along with the sources of their ideas and inspiration. He also shows how their discoveries fit into the mathematical puzzle and have spawned further developments. More than 100 lively line drawings and sixteen color plates of computer-generated images graphically illuminate the concepts.--From publisher description.

A revised, updated edition of Peterson's classic work. Presents the latest information on mathematical proofs, fractals, prime numbers, and chaos, as well as new material on such intriguing topics as the relationship between mathematical knots and DNA; the application of cellular automata models to social questions; and the significant increase in the speed of factoring large composite numbers by means of computers based on quantum logic.

Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam–Weinberg model of electromagnetic and weak interactions.

Ivars Peterson has come up with another itinerary of Mathland - where the habitat is mysterious and the inhabitants fascinating. He explores uncharted islands, introducing strange vibrations in the shadows of chaos, new twists in knot physics, and the straight side of circles. The tour is enjoyable to experienced travellers and first-time tourists alike. Peterson, a journalist with Science News, makes the arcane intelligible by interpreting mathematics into engaging prose.

With his critically acclaimed best-sellers The Mathematical Tourism and Islands of Truth, Ivars Peterson took readers to the frontiers of modern mathematics. His new book provides an up-to-date look at one of science's greatest detective stories: the search for order in the workings of the solar system. In the late 1600s, Sir Isaac Newton provided what astronomers had long sought: a seemingly reliable way of calculating planetary orbits and positions. Newton's laws of motion and his coherent, mathematical view of the universe dominated scientific discourse for centuries. At the same time, observers recorded subtle, unexpected movements of the planets and other bodies, suggesting that the solar system is not as placid and predictable as its venerable clock work image suggests. Today, scientists can go beyond the hand calculations, mathematical tables, and massive observational logs that limited the explorations of Newton, Copernicus, Galileo, Kepler, Tycho Brahe, and others. Using supercomputers to simulate the dynamics of the solar system, modern astronomers are learning more about the motions they observe and uncovering some astonishing examples of chaotic behavior in the heavens. Nonetheless, the long-term stability of the solar system remains a perplexing, unsolved issue, with each step toward its resolution exposing additional uncertainties and deeper mysteries. To show how our view of the solar system has changed from clocklike precision to chaos and complexity, Newton's Clock describes the development of celestial mechanics through the ages - from the star charts of ancient navigators to the seminal discoveries of the 17th century from the crucial work of Poincare to thestartling, sometimes controversial findings and theories made possible by modern mathematics and computer simulations. The result makes for entertaining and provocative reading, equal parts science, history and intellectual adventure.

"Peterson's knowledge of and affection for mathematics comes through with every word."--San Diego Union Tribune. "Peterson is, in short, the math teacher everyone wishes they had in high school."--Publishers Weekly. "Peterson has honed his explanatory skills finely. He is a readable guide through the tangles of probability and random chance. The Jungles of Randomness will give some insight into one of the most fruitful areas where math meets practical living."--Christian Science Monitor. The delightful trek through the exotic and powerful world of randomness. Popular math author Ivars Peterson leads readers on an exciting foray into the wilds of randomness, introducing exciting new discoveries--from hidden rules governing games of chance to how the first molecules of life formed and how random numbers can protect sensitive information on the Internet. Along the way, he charts the ambiguous boundary between order and chaos, revealing the astonishing patterns so often hidden in apparent randomness as well as the startling randomness often embedded in apparent order. Ivars Peterson (Washington, D.C.) is the mathematics and physics editor at Science News and the author of four previous trade books, including The Mathematical Tourist and Islands of Truth: A Mathematical Mystery Cruise.