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Books
Geometry & Topology
A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library)
Lowest new price: $77.95
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List price: $98.00
Author: G. N. Watson
Brand: Cambridge University Press

The late Professor G.N. Watson wrote his monumental treatise on the theory of Bessel functions in 1922 with two objects in view. The first was the development of applications of the fundamental processes of the theory of complex variables, and the second was compiling a collection of results of value for mathematicians and physicists who encounter Bessel functions in the course of their researches. The completeness of the theoretical account, combined with the wide scope of the collection of practical examples have resulted in a book that will be indispensable for pure mathematicians, applied mathematicians, and physicists.
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Topology via Logic (Cambridge Tracts in Theoretical Computer Science)
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Author: Steven Vickers
Brand: Brand: Cambridge University Press

This advanced textbook on topology has three unusual features. First, the introduction is from the locale viewpoint, motivated by the logic of finite observations: this provides a more direct approach than the traditional one based on abstracting properties of open sets in the real line. Second, the author freely exploits the methods of locale theory. Third, there is substantial discussion of some computer science applications. As computer scientists become more aware of the mathematical foundations of their discipline, it is appropriate that such topics are presented in a form of direct relevance and applicability. This book goes some way towards bridging the gap for computer scientists.
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More Mathematical Quilts: No Sewing Required!, Grades 612
Lowest new price: $62.20
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Author: Diana Venters
Brand: Brand: Key Curriculum Press

Designed to help students improve visualization skills and understanding of geometric relationships, and to help them succeed at geometrybased deductive reasoning
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Analysis: An Introduction
Lowest new price: $65.90
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Author: Richard Beals
Brand: Brand: Cambridge University Press

This selfcontained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics.
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Mathematical Analysis: A Straightforward Approach, 2nd Edition
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Author: K.G. Binmore
Brand: Cambridge University Press

For the second edition of this very successful text, Professor Binmore has written two chapters on analysis in vector spaces. The discussion extends to the notion of the derivative of a vector function as a matrix and the use of second derivatives in classifying stationary points. Some necessary concepts from linear algebra are included where appropriate. The first edition contained numerous worked examples and an ample collection of exercises for all of which solutions were provided at the end of the book. The second edition retains this feature but in addition offers a set of problems for which no solutions are given. Teachers may find this a helpful innovation.
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Introduction to Topology
Lowest new price: $40.43
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Author: Crump W. Baker
Brand: Brand: Krieger Pub Co

The fundamental concepts of general topology are covered in this text whic can be used by students with only an elementary background in calculus. Chapters cover: sets; functions; topological spaces; subspaces; and homeomorphisms.
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SpaceFilling Curves (Universitext)
Lowest new price: $59.96
Lowest used price: $44.32
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Author: Hans Sagan
Brand: Hans Sagan

The subject of spacefilling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like skating on the edge of reason. Unfortunately, no comprehensive treatment has ever been attempted other than the gallant effort by W. Sierpiriski in 1912. At that time, the subject was still in its infancy and the most interesting and perplexing results were still to come. Besides, Sierpiriski's paper was written in Polish and published in a journal that is not readily accessible (Sierpiriski [2]). Most of the early literature on the subject is in French, German, and Polish, providing an additional raison d'etre for a comprehensive treatment in English. While there was, understandably, some intensive research activity on this subject around the turn of the century, contributions have, nevertheless, continued up to the present and there is no end in sight, indicating that the subject is still very much alive. The recent interest in fractals has refocused interest on space filling curves, and the study of fractals has thrown some new light on this small but venerable part of mathematics. This monograph is neither a textbook nor an encyclopedic treatment of the subject nor a historical account, but it is a little of each. While it may lend structure to a seminar or proseminar, or be useful as a supplement in a course on topology or mathematical analysis, it is primarily intended for selfstudy by the aficionados of classical analysis.
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Topology Problem Solver (Problem Solvers Solution Guides)
Lowest new price: $72.42
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List price: $30.95
Author: The Editors of REA
Brand: Brand: Research Education Association

Thorough coverage is given to the fundamental concepts of topology, axiomatic set theory, mappings, cardinal numbers, ordinal numbers, metric spaces, topological spaces, separation axioms, Cartesian products, the elements of homotopy theory, and other topics. A comprehensive study aid for the graduate student and beyond.
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The Geometry of FourManifolds (Oxford Mathematical Monographs)
Lowest new price: $358.80
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Author: S. K. Donaldson

The last ten years have seen rapid advances in the understanding of differentiable fourmanifolds, not least of which has been the discovery of new 'exotic' manifolds. These results have had farreaching consequences in geometry, topology, and mathematical physics, and have proven to be a mainspring of current mathematical research. This book provides a lucid and accessible account of the modern study of the geometry of fourmanifolds. Consequently, it will be required reading for all those mathematicians and theoretical physicists whose research touches on this topic. The authors present both a thorough treatment of the main lines of these developments in fourmanifold topologynotably the definition of new invariants of fourmanifoldsand also a wideranging treatment of relevant topics from geometry and global analysis. All of the main theorems about YangMills instantons on fourmanifolds are proven in detail. On the geometric side, the book contains a new proof of the classification of instantons on the foursphere, together with an extensive discussion of the differential geometry of holomorphic vector bundles. At the end of the book the different strands of the theory are brought together in the proofs of results which settle longstanding problems in fourmanifolds topology and which are close to the frontiers of current research. Coauthor Donaldson is the 1994 corecipient of the prestigious Crafoord Prize.
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Complex Analysis with MATHEMATICA®
Lowest new price: $91.93
Lowest used price: $57.93
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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