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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. Read more
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Random matrix theory is applied by physicists and mathematicians to understand phenomena in nature and deep mathematical structures. This book offers a comprehensive look at random matrix theory by leading researchers, including applications inside and outside of physics and math...ematics. Read more
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Number concepts are a human invention developed and refined over millennia. They allow us to grasp quantities precisely: recent research shows that most specific quantities are not perceived in the absence of a number system. Numbers are not innate or universal; yet without them,... the world as we know it would not exist. Read more
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The Rogers--Ramanujan identities are a pair of infinite series-infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and ...vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers-Ramanujan identities and will include related historical material that is unavailable elsewhere. Read more
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A remarkable interplay exists between the fields of elliptic functions and orthogonal polynomials. In the first monograph to explore their connections, Elliptic Polynomials combines these two areas of study, leading to an interesting development of some basic aspects of each. It ...presents new material about various classes of polynomials and about the odd Jacobi elliptic functions and their inverses. The term elliptic polynomials refers to the polynomials generated by odd elliptic integrals and elliptic functions. In studying these, the authors consider such things as orthogonality and the construction of weight functions and measures, finding structure constants and interesting inequalities, and deriving useful formulas and evaluations. Although some of the material may be familiar, it establishes a new mathematical field that intersects with classical subjects at many points. Its wealth of information on important properties of polynomials and clear, accessible presentation make Elliptic Polynomials valuable to those in real and complex analysis, number theory, and combinatorics, and will undoubtedly generate further research. Read more
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Addresses linear algebra from the basics to the spectral theorem and examines a range of topics in multivariable calculus. This title introduces the derivative as a linear transformation, presents linear algebra in a concrete context based on complementary ideas in calculus, and ...explains differential forms on Euclidean space. Read more
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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. Read more
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From Polynomials to Sums of Squares describes a journey through the foothills of algebra and number theory based around the central theme of factorization. The book begins by providing basic knowledge of rational polynomials, then gradually introduces other integral domains, and ...eventually arrives at sums of squares of integers. The text is complemented with illustrations that feature specific examples. Other than familiarity with complex numbers and some elementary number theory, very little mathematical prerequisites are needed. The accompanying disk enables readers to explore the subject further by removing the tedium of doing calculations by hand. Throughout the text there are practical activities involving the computer. Read more
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A revised and updated translation of a work originally published in Portuguese in 1997. It introduces the algorithmic aspects of number theory and its applications to the study of codes, and of code-breaking. The work ends with study of the Rivest, Shamir, and Aldeman (RSA) publi...c key cryptosystem, Read more
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Innovative study applies classical analytic number theory to nontraditional subjects. Covers arithmetical semigroups and algebraic enumeration problems, arithmetical semigroups with analytical properties of classical type, and analytical properties of other arithmetical systems. ...1975 edition. Read more
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