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Numbers have fascinated people for centuries. They are familiar to everyone, forming a central pillar of our understanding of the world, yet the number system was not presented to us "gift-wrapped" but, rather, was developed over millennia. Today, despite all this development, it remains true that a child may ask a question about numbers that no one can answer. Many unsolved problems surrounding number matters appear as quirky oddities of little account while others are holding up fundamental progress in mainstream mathematics. Peter Higgins distills centuries of work into one delightful narrative that celebrates the mystery of numbers and explains how different kinds of numbers arose and why they are useful. Full of historical snippets and interesting examples, the book ranges from simple number puzzles and magic tricks, to showing how ideas about numbers relate to real-world problems, such as: How are our bank account details kept secure when shopping over the internet? What are the chances of winning at Russian roulette; or of being dealt a flush in a poker hand? This fascinating book will inspire and entertain readers across a range of abilities. Easy material is blended with more challenging ideas about infinity and complex numbers, and a final chapter "For Connoisseurs" works through some of the particular claims and examples in the book in mathematical language for those who appreciate a complete explanation. As our understanding of numbers continues to evolve, this book invites us to rediscover the mystery and beauty of numbers and reminds us that the story of numbers is a tale with a long way to run...

Number theory. --- Number study --- Numbers, Theory of --- Algebra --- Science (General). --- Mathematics. --- Popular Science, general. --- Mathematics, general. --- Number Theory. --- Math --- Science --- Popular works.

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This revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory. The new edition also presents further improvements and surprises, among them a new proof for "Hilbert's Third Problem". From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately, and the proofs are brilliant. Moreover, the exposition makes them transparent. ..." LMS Newsletter, January 1999

Mathematics. --- Mathematics, general. --- Number Theory. --- Geometry. --- Combinatorics. --- Analysis. --- Computer Science, general. --- Mathematics. --- Computer science. --- Global analysis (Mathematics). --- Combinatorics. --- Geometry. --- Number theory. --- Mathématiques --- Informatique --- Analyse globale (Mathématiques) --- Géométrie --- Théorie des nombres

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Full-worked solutions to all exercises available at www.springer.com Written by students for students, Bridging the Gap to University Mathematics is a refreshing, new approach to making the transition into undergraduate-level mathematics or a similar numerate degree. Suitable for students of all backgrounds, whether A-level, Scottish Higher, International Baccalaureate or similar, the book helps readers to shape their existing knowledge and build upon current strengths in order to get the most out of their undergraduate studies. The book can be used as a source of private study before embarking on a degree or as a textbook for an introductory course. Clear descriptions and a vast assortment of exercises – complete with solutions – enable the reader to develop and then practice new skills. Topics are delivered as twenty self-contained, manageable chapters, allowing students to dip in and out as they require, easily identifying those areas on which they need practice, whilst skimming over more familiar material. Important concepts are introduced in an easy-to-read manner with a sustained emphasis on worked examples and applications rather than abstract theory. Each chapter also includes an insight into where the reader’s new skills will be employed during the course of their studies, providing a springboard to further research where desired. .

Mathematics. --- Mathematics, general. --- Engineering, general. --- Physics, general. --- Computer Science, general. --- Science, general. --- Computational Science and Engineering. --- Science (General). --- Computer science. --- Physics. --- Engineering. --- Mathématiques --- Informatique --- Physique --- Ingénierie --- Mathematics --- Electronic books. -- local. --- Mathematics -- Study and teaching (Secondary). --- Mathematics -- Study and teaching. --- Mathematics - General --- Physical Sciences & Mathematics --- Study and teaching. --- Study and teaching (Secondary) --- Science. --- Computer mathematics. --- Science, Humanities and Social Sciences, multidisciplinary. --- Informatics --- Science --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Construction --- Industrial arts --- Technology --- Math --- Computer mathematics --- Electronic data processing --- Mathematics - Problems, exercises, etc.

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This book follows Felix Klein’s proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective and hyperbolic. For simplicity the focus is on the two-dimensional case, which is already rich enough, though some aspects of the 3- or n-dimensional geometries are included. Once plane geometry is well understood, it is much easier to go into higher dimensions. The fundamental ideas of the classical geometries are presented in a clear and elementary way, making them accessible to a wide audience, and relating them to more advanced topics in modern geometry, such as manifolds, Lie groups, the Gaussian curvature, group actions, and foliations. The book appeals to, and develops, the geometric intuition of the reader. The only prerequisites are calculus, linear algebra and basic analytic geometry. After studying the material, the reader will have a good understanding of basic geometry as well as a clear picture of the relations of this beautiful subject to other branches of mathematics. This is supported by more than 100 carefully chosen illustrations and a large number of exercises. While mainly addressed to students at advanced undergraduate level, the text can be of interest to anyone wanting to learn classical geometry.

Geometry --- geometrie --- 514.11 --- 514.12 --- 514.12 Euclidean and pseudo-Euclidean geometries. Analytic geometry --- Euclidean and pseudo-Euclidean geometries. Analytic geometry --- 514.11 Elementary geometry, trigonometry, polygonometry --- Elementary geometry, trigonometry, polygonometry --- Mathematics --- Euclid's Elements --- Geometry. --- Mathematics. --- Math --- Science --- Mathematics, general.

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Why should mathematics, the purest of sciences, have a history? Medieval mathematicians took little interest in the history of their discipline. Yet in the Renaissance the history of mathematics flourished. This book explores how Renaissance scholars recovered and reconstructed the origins of mathematics by tracing its invention in prehistoric Antiquity, its development by the Greeks, and its transmission to modern Europe via the works of Euclid, Theon and Proclus. The principal architects of this story -- the French philosopher and University of Paris reformer Peter Ramus, and his critic, the young Oxford astronomy lecturer Henry Savile - worked out diametrically opposed models for the development of the mathematical arts, models of historical progress and decline which mirrored each scholar's larger convictions about the nature of mathematical thinking, the purpose of the modern university, and the potential of the human mind. In their hands, the obscure story of mathematical history became a site of contention over some of the most pressing philosophical and pedagogical debates of the sixteenth century.

Philosophy. --- Philosophy of Science. --- Mathematics, general. --- Classical Studies. --- Philosophy (General). --- Science --- Mathematics. --- Humanities. --- Sciences --- Mathématiques --- Sciences humaines --- Philosophie --- Mathematics --- Math --- History&delete& --- Historiography --- Ramus, Petrus, --- Savile, Henry, --- De La Ramée, Pierre, --- La Ramée, Pierre de, --- Ramée, Pierre de La, --- Ramo, Pedro, --- Ramo, Pietro, --- Ramus, P. --- Ramus, Pʹer, --- Ramus, Peter, --- ראאמוס, --- Savilius, Henricus, --- History