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See below for a selection of the latest books from Mathematics category. Presented with a red border are the Mathematics books that have been lovingly read and reviewed by the experts at Lovereading. With expert reading recommendations made by people with a passion for books and some unique features Lovereading will help you find great Mathematics books and those from many more genres to read that will keep you inspired and entertained. And it's all free!
Hamiltonian systems began as a mathematical approach to the study of mechanical systems. As the theory developed, it became clear that the systems that had a sufficient number of conserved quantities enjoyed certain remarkable properties. These are the completely integrable systems. In time, a rich interplay arose between integrable systems and other areas of mathematics, particularly topology, geometry, and group theory.This book presents some modern techniques in the theory of integrable systems viewed as variations on the theme of action-angle coordinates. These techniques include analytical methods coming from the Galois theory of differential equations, as well as more classical algebro-geometric methods related to Lax equations. Audin has included many examples and exercises. Most of the exercises build on the material in the text. None of the important proofs have been relegated to the exercises. Many of the examples are classical, rather than abstract. This book would be suitable for a graduate course in Hamiltonian systems.
This three-volume set addresses the interplay between topology, functions, geometry, and algebra. Bringing the beauty and fun of mathematics to the classroom, the authors offer serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts. It is suitable for advanced high-school students, graduate students, and researchers. The three-volume set includes A Mathematical Gift I, II, and III.
Since 1993, the AMS has been publishing What's Happening in the Mathematical Sciences , a series of lively and highly readable accounts of the latest developments in mathematics. This seventh volume describes some genuine surprises, such as the recent discovery that coin tosses are inherently unfair; a mathematical theory of invisibility that was soon followed by the creation of a prototype 'invisibility cloak'; and, an ultra-efficient approach to image sensing that led to the development of a single-pixel camera. The past few years have also seen deep results on some classical mathematics problems. For example, this volume describes a proof of the Sato-Tate Conjecture in number theory and a major advance in the Minimal Model Program of algebraic geometry. The computation of the character table of the exceptional Lie group $E_8$ brings 'the most beautiful structure in mathematics' to public attention, and proves that human persistence is just as important as gigabytes of RAM. The amazing story of the Archimedes Palimpsest shows how the modern tools of high-energy physics uncovered the centuries-old secrets of the mathematical writings of Archimedes. Dana Mackenzie, a science writer specializing in mathematics, makes each of these topics accessible to all readers, with a style that is friendly and at the same time attentive to the nuances that make mathematics fascinating. Anyone with an interest in mathematics, from high school teachers and college students to engineers and computer scientists, will find something of interest here. The stories are well told and the mathematics is compelling.
A successful mathematical career involves doing good mathematics, to be sure, but also requires a wide range of skills that are not normally taught in graduate school. The purpose of this book is to provide guidance to the professional mathematician in how to develop and survive in the profession. There is information on how to begin a research program, how to apply for a grant, how to get tenure, how to teach, and how to get along with one's colleagues. After tenure, there is information on how to direct a Ph.D. student, how to serve on committees, and how to serve in various posts in the math department. There is extensive information on how to serve as Chairman. There is also material on trouble areas: sexual harassment, legal matters, disputes with colleagues, dealing with the dean, and so forth.One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration. In short, this is a survival manual for the professional mathematician - both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide .
The AMS series What's Happening in the Mathematical Sciences distills the amazingly rich brew of current research in mathematics down to a few choice samples. This volume leads off with an update on the Poincare Conjecture, a hundred-year-old problem that has apparently been solved by Grigory Perelman of St. Petersburg, Russia. So what did topologists do when the oldest and most famous problem about closed manifolds was vanquished? As the second chapter describes, they confronted a suite of problems concerning the 'ends' of open manifolds...and solved those, too. Not to be outdone, number theorists accomplished several unexpected feats in the first five years of the new century, from computing a trillion digits of pi to finding arbitrarily long equally-spaced sequences of prime numbers.Undergraduates made key discoveries, as explained in the chapters on Venn diagrams and primality testing. In applied mathematics, the Navier-Stokes equations of fluid mechanics continued to stir up interest. One team proved new theorems about the long-term evolution of vortices, while others explored the surprising ways that insects use vortices to move around. The random jittering of Brownian motion became a little less mysterious. Finally, an old and trusted algorithm of computer science had its trustworthiness explained in a novel way. Barry Cipra explains these new developments in his wry and witty style, familiar to readers of Volumes 1-5, and is joined in this volume by Dana Mackenzie. Volume 6 of What's Happening will convey to all readers - from mathematical novices to experts - the beauty and wonder that is mathematics.
This monograph is a thorough introduction to the Atiyah-Singer index theorem for elliptic operators on compact manifolds without boundary. The main theme is only the classical index theorem and some of its applications, but not the subsequent developments and simplifications of the theory. The book is designed for a complete proof of the K-theoretic index theorem and its representation in terms of cohomological characteristic classes, with an effort to make the demands on the knowledge of background materials as modest as possible by supplying the proofs of all most every result. The applications include Hirzebruch signature theorem, Riemann-Roch-Hirzebruch theorem, Atiyah-Segal-Singer fixed point theorem, etc.
The policy analyses and proposals presented in this book focus on national programmes to foster universal broadband access and the debate on Internet neutrality. The study of the current trends highlights the progress of cloud computing and the new developments induced by the entrance of over-the-top operators in the Latin American and Caribbean region. This book underscores the need to expand regional and national Internet traffic exchange points (IXPs) and the relevance of the increasing demand gap, which poses new challenges beyond those related to access and connectivity.
Beautifully produced and marvelously written, What's Happening in the Mathematical Sciences, Volume 3 , contains 10 articles on recent developments in the field. In an engaging, reader-friendly style, Barry Cipra explores topics ranging from Fermat's Last Theorem to Computational Fluid Dynamics. The volumes in this series highlight the many roles mathematics plays in the modern world. This volume includes articles on: a new mathematical method that's taking Wall Street by storm 'Ultra-parallel' supercomputing with DNA, and how a mathematician found the famous flaw in the Pentium chip. Unique in kind, and lively in style, What's Happening in the Mathematical Sciences, Volume 3 is a delight to read and a valuable source of information.
Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial $x^k$ is replaced by an arbitrary polynomial of degree $k$. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject. This is a reprint of the 1965 original. (MMONO/13.2)
Mathematical Thinking: From Assessment Items to Challenging Tasks is a compilation of 36 problem-based lessons that encourage students to engage in productive struggle and deep thinking. Its 36 full-length lessons for grades 2-8 are each inspired by an actual test item from the National Assessment of Educational Progress (NAEP). Students will be exposed to the tasks used on assessments, become more confident in solving them, and see how their problem-solving ability stacks up against students nationwide. Mathematical Thinking includes chapters on these subjects: Number and Operations; Algebraic Thinking; Geometry and Measurement; and Data Analysis, Statistics, and Probability. Each chapter begins by explaining how its topic has been treated in the NAEP assessment and what skills its lessons are designed to build. Each activity includes the NAEP item that inspired it, sample student responses, and the percentage of students who completed it correctly. All activities include these elements: Learning and performance goals, and a list of relevant Common Core standards and mathematical practices A list of materials needed-with all activity sheets and templates available for download and printing at NCTM's More4U website A step-by-step lesson plan in Launch-Explore-Summarize format, with questions and prompts to pose to students and a range of possible responses they might give Gearing Up and Gearing Down sections to customize and extend the lessons With these assessment-based lessons, teachers can not only help students become more adept at reaching a correct answer on tests, but they can also help them do so by becoming better mathematical thinkers and problem solvers.