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In this Very Short Introduction Peter M. Higgins presents an overview of the number types featured in modern science and mathematics. Providing a non-technical account, he explores the evolution of the modern number system, examines the fascinating role of primes, and explains th...eir role in contemporary cryptography.
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The majority of students who take courses in number theory are mathematics majors who will not become number theorists. Many of them will, however, teach mathematics at the high school or junior college level, and this book is intended for those students learning to teach, In add...ition to a careful presentation of the standard material usually taught in a first course in elementary number theory, this book includes a chapter on quadratic fields which the author has designed to make students think about some of the obvious concepts they have taken for granted earlier. The book also includes a large number of exercises, many of which are nonstandard.
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From the Foreword: Dietmar Hildenbrand's new book, Introduction to Geometric Algebra Computing, in my view, fills an important gap in Clifford's geometric algebra literature...I can only congratulate the author for the daring simplicity of his novel educational approach taken in ...this book, consequently combined with hands on computer based exploration. Without noticing, the active reader will thus educate himself in elementary geometric algebra algorithm development, geometrically intuitive, highly comprehensible, and fully optimized. --Eckhard Hitzer, International Christian University, Tokyo, Japan Geometric Algebra is a very powerful mathematical system for an easy and intuitive treatment of geometry, but the community working with it is still very small. The main goal of this book is to close this gap with an introduction to Geometric Algebra from an engineering/computing perspective. This book is intended to give a rapid introduction to computing with Geometric Algebra and its power for geometric modeling. From the geometric objects point of view, it focuses on the most basic ones, namely points, lines and circles. This algebra is called Compass Ruler Algebra, since it is comparable to working with a compass and ruler. The book explores how to compute with these geometric objects, and their geometric operations and transformations, in a very intuitive way. The book follows a top-down approach, and while it focuses on 2D, it is also easily expandable to 3D computations. Algebra in engineering applications such as computer graphics, computer vision and robotics are also covered.
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This book provides a starting point for the understanding of Geometric Algebra in a 2D setting as a foundation for the understanding of 3D applications, especially those using the very popular Conformal Geometric Algebra. The focus is on an algebra, called Compass Ruler Algebra. ...This algebra offers the possibility to compute with circles, lines and point pairs in a very intuitive way. While focusing on 2D, it is easily expandable to 3D computations. The book is divided into three parts: Part I is an easy to understand tutorial with many figures; Part II presents the mathematical background; Part III is dedicated to applications.
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By Hida, Haruzo
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- RRP: $486.50
- $263.49
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Provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. This book includes the construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura - Taniyama con...jecture.
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This book gives a reasonably self-contained account of a number of algorithmic problems and their solutions for linear algebraic groups. The theory underpinning the algorithms is described as well. Topics include closed sets in affine space, lie algebras, linear algebraic groups ...basic constructions, algebraic groups and their lie algebras in characteristic zero, arithmetic groups, reductive algebraic groups, and -groups.
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Explores an important aspect of number theory - the theory of exponential sums over finite fields and their Mellin transforms - from a categorical point of view. This book presents fundamentally important results and a plethora of examples, opening up new directions in the subjec...t.
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Considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. This book considers algebraic subgroups that meet a given subvariety in a set of un...likely dimension.
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By Beiler, A. H.
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- RRP: $34.50
- $25.88
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Number theory proves to be a virtually inexhaustible source of intriguing puzzle problems. Includes divisors, perfect numbers, the congruences of Gauss, scales of notation, the Pell equation, more. Solutions to all problems.
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This book studies the interplay between the geometry and topology of locally symmetric spaces, and the arithmetic aspects of the special values of L-functions. The authors study the cohomology of locally symmetric spaces for GL(N) where the cohomology groups are with coefficients... in a local system attached to a finite-dimensional algebraic repre
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