xn + yn = zn, where n represents 3, 4, 5, no solutionI have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain.With these words, the seventeenth century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for than 350 years. In Fermat's Enigma based on the author's award winning documentary film, which aired on PBS's Nova Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.
This well developed, accessible text details the historical development of the subject throughout. It also provides wide ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.
Written for the one semester undergraduate number theory course, this text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity. It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.
This book is the first volume of a two volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little than 300 pages. MATHEMATICAL REVIEWS
An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history.
Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers.
Data visualizations introduce the reader to open questions and cutting edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition.
Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.
Number theory is concerned with the properties of the natural numbers: 1,2,3,. During the seventeenth and eighteenth centuries, number theory became established through the work of Fermat, Euler and Gauss. With the hand calculators and computers of today, the results of extensive numerical work are instantly available and mathematicians may traverse the road leading to their discoveries with comparative ease. Now in its second edition, this book consists of a sequence of exercises that will lead readers from quite simple number work to the point where they can prove algebraically the classical results of elementary number theory for themselves. A modern high school course in mathematics is sufficient background for the whole book which, as a whole, is designed to be used as an undergraduate course in number theory to be pursued by independent study without supporting lectures
Number theory has a long and distinguished history and the concepts and problems relating to the subject have been instrumental in the foundation of much of mathematics. In this book, Professor Baker describes the rudiments of number theory in a concise, simple and direct manner. Though most of the text is classical in content, he includes many guides to further study which will stimulate the reader to delve into the great wealth of literature devoted to the subject. The book is based on Professor Baker's lectures given at the University of Cambridge and is intended for undergraduate students of mathematics.