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Books
Geometry & Topology
Complex Analysis with MATHEMATICA®
Lowest new price: $91.93
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List price: $118.00
Author: William T. Shaw
Brand: Brand: Cambridge University Press

Complex Analysis with Mathematica offers a new way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a stateoftheart computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for selfstudy and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos, and advanced conformal mapping. A CD is included which contains a live version of the book, and the Mathematica code enables the user to run computer experiments.
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 Used Book in Good Condition
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The SeibergWitten Equations and Applications to the Topology of Smooth FourManifolds (Mathematical Notes, Vol. 44)
Lowest new price: $33.31
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Author: John W. Morgan
Brand: John W Morgan

The recent introduction of the SeibergWitten invariants of smooth fourmanifolds has revolutionized the study of those manifolds. The invariants are gaugetheoretic in nature and are close cousins of the muchstudied SU(2)invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the SeibergWitten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the SeibergWitten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the SeibergWitten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)case, the SeibergWitten moduli spaces are shown to be compact. The SeibergWitten invariant is then essentially the homology class in the space of configurations represented by the SeibergWitten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.
Features:
 The Seiberg Witten equations and applications to the topology of smooth four manifolds
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Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets (Texts in Applied Mathematics)
Lowest new price: $76.30
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Author: Claude Gasquet

The object of this book is twofold  on the one hand it conveys to mathematical readers a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations. On the other hand, it presents physics readers with a body of theory in which the wellknown formulae find their justification. The basic study of fundamental notions, such as Lebesgue integration and theory of distribution, allow the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis timefrequency analysis (gabor transforms and wavelets). The whole is rounded off with a large number of exercises as well as selected workedout solutions.
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Numbers and Functions: Steps to Analysis
Lowest new price: $24.01
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List price: $35.00
Author: R. P. Burn
Brand: Brand: Cambridge University Press

The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this book, Dr Burn follows a route that proved successful with A Pathway to Number Theory and Groups: A Path to Geometry. He invites the student reader to tackle each of the key concepts in turn, progressing from experience (using computers for graph drawing where appropriate) through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, which all have solutions supplied, draws students into constructing definitions and theorems for themselves. This natural development is informed by historical insight and complemented by historical discussion. The sequence also takes into account recent research which has shown how intuitive ideas about numbers, limits, functions and infinity may be at odds with the standard definitions. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties. Teachers in sixth forms will find that questions at the beginning of every chapter provide ways of preparing those at school for university mathematics. Lecturers in universities will be challenged to rethink their conventions about the best way to introduce the central ideas of analysis to undergraduates.
Features:
 Used Book in Good Condition
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Understanding Geometry
Lowest new price: $15.00
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List price: $21.95
Author: Kathy Richardson

This valuable teachers resource provides teachers with classroom tested activities that help children develop indepth understandings about 2D and 3D geometry concepts and spatial awareness. Understanding Geometry is more than a book about geometry activities. Kathy provides the following resources for teachers:  Background information on what we need to know about geometry  Assessment and observation moments are highlighted  Geometry Terminology Glossary  Planning Guide for Grades K3  Task Cards
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Yet Another Introduction to Analysis
Lowest new price: $48.55
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Author: Victor Bryant
Brand: Brand: Cambridge University Press

Mathematics education in schools has seen a revolution in recent years. Students everywhere expect the subject to be wellmotivated, relevant and practical. When such students reach higher education, the traditional development of analysis, often divorced from the calculus they learned at school, seems highly inappropriate. Shouldn't every step in a first course in analysis arise naturally from the student's experience of functions and calculus in school? And shouldn't such a course take every opportunity to endorse and extend the student's basic knowledge of functions? In Yet Another Introduction to Analysis, the author steers a simple and wellmotivated path through the central ideas of real analysis. Each concept is introduced only after its need has become clear and after it has already been used informally. Wherever appropriate, new ideas are related to common topics in math curricula and are used to extend the reader's understanding of those topics. In this book the readers are led carefully through every step in such a way that they will soon be predicting the next step for themselves. In this way students will not only understand analysis, but also enjoy it.
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 Used Book in Good Condition
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A Hilbert Space Problem Book (Graduate Texts in Mathematics)
Lowest new price: $49.99
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List price: $79.99
Author: P.R. Halmos
Brand: P R Halmos

From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."
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 A Hilbert Space Problem Book
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The Science of Fractal Images
Lowest new price: $38.55
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List price: $99.00
Brand: Springer

This book is based on notes for the course Fractals:lntroduction, Basics and Perspectives given by MichaelF. Barnsley, RobertL. Devaney, HeinzOtto Peit gen, Dietmar Saupe and Richard F. Voss. The course was chaired by HeinzOtto Peitgen and was part of the SIGGRAPH '87 (Anaheim, California) course pro gram. Though the five chapters of this book have emerged from those courses we have tried to make this book a coherent and uniformly styled presentation as much as possible. It is the first book which discusses fractals solely from the point of view of computer graphics. Though fundamental concepts and algo rithms are not introduced and discussed in mathematical rigor we have made a serious attempt to justify and motivate wherever it appeared to be desirable. Ba sic algorithms are typically presented in pseudocode or a description so close to code that a reader who is familiar with elementary computer graphics should find no problem to get started. Mandelbrot's fractal geometry provides both a description and a mathemat ical model for many of the seemingly complex forms and patterns in nature and the sciences. Fractals have blossomed enormously in the past few years and have helped reconnect pure mathematics research with both natural sciences and computing. Computer graphics has played an essential role both in its de velopment and rapidly growing popularity. Conversely, fractal geometry now plays an important role in the rendering, modelling and animation of natural phenomena and fantastic shapes in computer graphics.
Features:
 Used Book in Good Condition
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Conjecture and Proof (Classroom Resource Materials)
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Author: Miklós Laczkovich

The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to Englishspeaking students. This book is an elaborate version of the course on 'Conjecture and Proof'. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of e, the BanachTarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps. Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.
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Several Complex Variables (Mathematical Sciences Research Institute Publications)
Lowest new price: $19.17
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List price: $144.00
Brand: Brand: Cambridge University Press

The contributions in this major work focus on a central area of mathematics with strong ties to partial differential equations, algebraic geometry, number theory, and differential geometry. The 199596 MSRI program on Several Complex Variables emphasized these interactions and concentrated on current developments and problems that capitalize on this interplay of ideas and techniques. This collection provides a remarkably complete picture of the status of research in these overlapping areas and a basis for significant continued contributions from researchers. Several of the articles are expository or have extensive expository sections, making this an excellent introduction for students on the use of techniques from these other areas in several complex variables. This volume comprises a representative sample of some of the best work recently done in Several Complex Variables.
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 Used Book in Good Condition
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