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Complex Analysis
Lars V. Ahlfors
0070006571
Jan 1979
Hardcover
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Book Description
A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short...


Meta Math!: The Quest for Omega
Gregory Chaitin
0375423133
October 2005
Hardcover
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From Booklist
Note the exclamation point: Chaitin is on fire about math and is unable to restrain his enthusiasm. No mere number cruncher, he is renowned for finding another proof of Kurt Godel's incompleteness theorem and another for Alan Turing's "halting problem" in computation. Chaitin explains these two achievements here, in prose that is difficult for general readers to follow, but the spirit he brings to his subject will be apparent to all. Chaitin radiates his zeal like a preacher seeking converts. His asides often directly speak to students who might want to become professional mathematicians, stoking their fire, for example, with the vulnerability of even ancient theorems to new analysis (he sketches two ways, in addition to Euclid's, to prove the infinity of prime numbers). Chaitin's freewheeling expressions of mathematical...


Understanding Pure Mathematics

0199142432


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A History of Pi
Petr Beckmann
0880294183
September 1989
Hardcover
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Review
"A pure delight . . . Entirely offbeat, which gives it its charm." --The Denver Post "A very readable account." --Science "A cheerful work." --Scientific American --This text refers to the Paperback edition.

Book Description
The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.


Functional Analysis
Walter Rudin
0070542368
Jan 1991
Hardcover
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Book Description
This classic text is written for graduate courses in functional analysis. This text is used in modern investigations in analysis and applied mathematics. This new edition includes up-to-date presentations of topics as well as more examples and exercises. New topics include Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem.

This text is part of the Walter Rudin Student Series in Advanced Mathematics.



The Shape of Space (Pure and Applied Mathematics (Marcel Dekker))
Jeffrey R. Weeks
0824707095
December 15, 2001
Hardcover
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Book Description
Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.


Men of Mathematics
Eric Temple Bell
0671628186
August 1986
Paperback
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Review
Bertrand RussellProfessor Bell has done his work well....Any [one] engaged in learning mathematics will profit by reading him, since he humanizes the subject and helps to a realization of the historical environment.
The New York TimesExtremely harmonious...a first text in the philosophy of mathematics....Bell's style is very enjoyable.
NatureProfessor E.T. Bell has written a fascinating book. The amount of biographical details and of mathematics that he has compressed into a volume of 600 pages is extraordinary...he carries the reader along; he whets the appetite.

Review
Nature Professor E.T. Bell has written a fascinating book. The amount of biographical details and of mathematics that he has compressed into a volume of 600 pages is extraordinary...he carries the reader...


The Joy of Sets: Fundamentals of Contemporary Set Theory (Undergraduate Texts in Mathematics Series)
Keith Devlin
0387940944
January 1993
Textbook Hardcover
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Book Description
This book provides an account of those parts of contemporary set theory that are relevant to other areas of pure mathematics. Intended for advanced undergraduates and beginning graduate students, the text is written in an easy-going style, with a minimum of formalism. The book begins with a review of "naive" set theory; it then develops the Zermelo-Fraenkel axioms of the theory, showing how they arise naturally from a rigorous answer to the question, "what is a set?" After discussing the ordinal and cardinal numbers, the book then delves into contemporary set theory, covering such topics as: the Borel hierarchy, stationary sets and regressive functions, and Lebesgue measure. Two chapters present an extension of the Zermelo-Fraenkel theory, discussing the axiom of constructibility and the question of provability in set...


Linear Systems, Fourier Transforms, and Optics (Wiley Series in Pure and Applied Optics)
Jack D. Gaskill
0471292885
June 1978
Hardcover
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Book Description
A complete and balanced account of communication theory, providing an understanding of both Fourier analysis (and the concepts associated with linear systems) and the characterization of such systems by mathematical operators. Presents applications of the theories to the diffraction of optical wave-fields and the analysis of image-forming systems. Emphasizes a strong mathematical foundation and includes an in-depth consideration of the phenomena of diffraction. Combines all theories to describe the image-forming process in terms of a linear filtering operation for both coherent and incoherent imaging. Chapters provide carefully designed sets of problems. Also includes extensive tables of properties and pairs of Fourier transforms and Hankle Transforms.

The publisher, John Wiley &...


Interpolation of Operators
Colin Bennett
0120887304
Feb 1988
Hardcover
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Book Description
This book presents interpolation theory from its classical roots beginning with Banach function spaces and equimeasurable rearrangements of functions, providing a thorough introduction to the theory of rearrangement-invariant Banach function spaces. At the same time, however, it clearly shows how the theory should be generalized in order to accommodate the more recent and powerful applications. Lebesgue, Lorentz, Zygmund, and Orlicz spaces receive detailed treatment, as do the classical interpolation theorems and their applications in harmonic analysis.
The text includes a wide range of techniques and applications, and will serve as an amenable introduction and useful reference to the modern theory of interpolation of operators.


The Beginner's Guide to Construction: The Mathematical Archetypes of Nature, Art, and Science
Michael S. Schneider
0060926716
November 1995
Paperback
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From Booklist
In the spiral of the nautilus shell, in the veins of a maple leaf, in the bonds of the benzene ring--everywhere he looks, Schneider sees a cosmic geometry. Of course, the lines of this geometry have long attracted the attention of probing minds, including Pythagoras, Plato, the Psalmist, Demetrius, and Plotinus. The author weaves the insights of these thinkers and many more together in a tapestry of reflections (richly illustrated) on celestial harmonies. Once initiated into the ancient mysteries, the reader will recognize profound meanings--not merely scientific utility--in squares, triangles, and other common shapes. The reader needs no extraordinary expertise in mathematics to explore these pages, just a relish for intellectual adventure. Schneider helps us discover just how much mental energy can fit within the circle...


Eigenvalues in Riemannian Geometry
Isaac Chavel
0121706400
Nov 1984
Hardcover
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Book Description
The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and results, currently used in the subject, to those working in it, and (iii) to present some of the results that are attractive in their own right, and which lend themselves to a presentation not overburdened with technical machinery.


Functional Analysis (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
Peter D. Lax
0471556041
April 4, 2002
Hardcover
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Review
“…an excellent source of facts for anyone working in functional analysis or operator theory.” (Journal of Operator Theory, Vol.53, No.1, 2005)

"For years Lax has been counted among the world's very top people in PDEs, so no serious student can afford to ignore his view of the foundations leading up to that subject." (Choice, Vol. 40, No. 4, December 2002)

"...attractive...well suited for graduate courses...and useful for research mathematicians." (Mathematical Reviews, 2003a)

"...The book is highly recommended to all students of analysis". (Zentralblatt MATH, Vol.1009, No.9, 2003)

"A lot of good material, doled out in short chapters." (American Mathematical Monthly, August/September 2003)

Book...



Real Productive Groups I
Nolan R. Wallach
0127329609
Feb 1988
Hardcover
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A Course of Pure Mathematics (Cambridge Mathematical Library)
G.H. Hardy
0521092272
March 4, 1993
Paperback
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Book Description
There can be few textbooks of mathematics as well-known as Hardy's Pure Mathematics. Since its publication in 1908, it has been a classic work to which successive generations of budding mathematicians have turned at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of a missionary with the rigor of a purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.


Schaum's A-Z Mathematics
John Berry
0071419365
July 2003
Paperback
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Book Description
From the bestselling name in study guides comes an indispensable new resource for serious students Schaum's A-Z handbooks make excellent complements to course textbooks and test preparation guides. Ideal for ambitious high school seniors--especially AP students--and college freshmen, they feature concise, thoroughly cross-referenced definitions of hundreds of key terms and phrases that help students quickly break through the jargon barrier. Clear explanations of key concepts, supplemented with lucid illustrations, help build mastery of theory and provide a ready reference to supplement class work. Each entry begins with a clear, one-sentence definition and is followed by an explanation and examples. A-to-Z format for ready reference Clear definitions and explanations, cross-referenced and enhanced with...


Semi-Riemannian Geometry: With Applications to Relativity
Barrett O'Neill
0125267401
June 1983
Textbook Hardcover
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Book Description
This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.

About the Author
Barrett O'Neill is currently a Professor in the...


The Provenance of Pure Reason
William W. Tait
019514192X
May 2004
Hardcover
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Book Description
William Tait is one of the most distinguished philosophers of mathematics of the last fifty years. This volume collects his most important published philosophical papers from the 1980's to the present. The articles cover a wide range of issues in the foundations and philosophy of mathematics,
including some on historical figures ranging from Plato to Godel.

Tait's main contributions were initially in proof theory and constructive mathematics, later moving on to more philosophical subjects including finitism and skepticism about mathematics. This collection, presented as a whole, reveals the underlying unity of Tait's work. The volume includes an
introduction in which Tait reflects more generally on the evolution of his point of view, as well as an appendix and added endnotes in which he gives some...


Optical Shop Testing (Wiley Series in Pure and Applied Optics)
Daniel Malacara (Editor)
0471522325
January 1992
Hardcover
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Book Description
Fringe scanning techniques, now renamed heterodyning or phase shift interferometry, are covered in a completely rewritten chapter. New chapters have been added to cover wavefront fitting and evaluation as well as holographic and Moire methods. The chapter on parameter measurements has been completely rewritten and an appendix added suggesting appropriate tests for typical optical surfaces.


Measure Theory and Integration (Pure and Applied Mathematics (Marcel Dekker))
M.M. Rao
0824754018
January 2004
Hardcover
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Review
"Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types - providing a complete and detailed review of every aspect of measure and integration theory[,] offering valuable examples, exercises, and applications. This book examines the Henstock-Kurzweil integral with approaches not found in any other text." - L'Enseignement Mathematique, Vol. 50, 1-2, Jan-Jun 2004

Book Description


Principles of Mathematical Analysis
Walter Rudin
007054235X
January 1976
Textbook Hardcover
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Book Description
The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included.

This text is part of the Walter Rudin Student Series in Advanced Mathematics.



Collected Works of A.M. Turing Pure Mathematics
Alan Mathison Turing
0444880593
Jan 1992
Hardcover
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Harvey Cohn, Computing Reviews
This work... should be not only in the regular science libraries but also in special computer science reference collections. I hope Turing's works will be available to all students, as Turing's vision is perpetually relevant.

Review
Harvey Cohn
This work... should be not only in the regular science libraries but also in special computer science reference collections. I hope Turing's works will be available to all students, as Turing's vision is perpetually relevant.
Computing Reviews

See all Editorial Reviews


An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised (Pure and Applied Mathematics)
William M. Boothby
0121160513
August 5, 2002
Paperback
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Book Description
The second edition of this text has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject.

Line and surface integrals
Divergence and curl of vector fields

From the Back Cover
Differentiable manifolds abd the differential and integral calculus of their associated structures, such as vectors, tensors, and differential forms are of great importance...


Complex Variables and Applications
James Ward Brown
0072872527
February 2003
Textbook Hardcover
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Book Description
This text is part of the International Series in Pure and Applied Mathematics. It is designed for junior, senior, and first-year graduate students in mathematics and engineering. This edition preserves the basic content and style of earlier editions and includes many new and relevant applications which are introduced early in the text. --This text refers to an out of print or unavailable edition of this title.

Book Info
Offers an introductory treatment of Fourier series and their applications to boundary value problems in partial differential equations that arise in engineering and physics. IBM Version. 3 1/2 inch disk included. DLC: Functions of complex variables. --This text refers to an out of print or unavailable edition of this title.


The Hilbert Transform of Schwartz Distributions and Applications
J. N. Pandey
0471033731
Dec 1995
Hardcover
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Book Description
This book provides a modern and up-to-date treatment of the Hilbert transform of distributions and the space of periodic distributions. Taking a simple and effective approach to a complex subject, this volume is a first-rate textbook at the graduate level as well as an extremely useful reference for mathematicians, applied scientists, and engineers.

The author, a leading authority in the field, shares with the reader many new results from his exhaustive research on the Hilbert transform of Schwartz distributions. He describes in detail how to use the Hilbert transform to solve theoretical and physical problems in a wide range of disciplines; these include aerofoil problems, dispersion relations, high-energy physics, potential theory problems, and others.

Innovative at every step, J. N. Pandey provides a...



Pure Mathematics 1 (International) (Cambridge International Examinations)
Hugh Neill, Douglas Quadling
0521530113
September 19, 2002
Paperback
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Book Description
This book is part of a series of textbooks created for the new Cambridge International Examinations (CIE) mathematics syllabus. The authors have worked with CIE to assure that the content matches the syllabus and is pitched at a suitable level. Pure Mathematics 1 corresponds to syllabus unit P1. The syllabus content is arranged in chapters to provide a viable teaching course. Each chapter starts with a list of learning objectives. Mathematical concepts, terminology and notation are explained clearly and carefully. Key results and procedures appear in boxes for easy reference. Stimulating worked examples take a step-by-step approach to problem solving. There are plenty of exercises throughout, as well as revision exercises and practice exam papers all written by experienced examiners.


A Course in Pure Mathematics
Margaret M. Gow
0340052171
January 1974
Paperback
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Book Description
For students reading Mathematics, either as part of a general degree or as an ancilliary course for an Honours degree, the subject should be presented in as straightforward a manners as is consistent with a moderate standard of rigour. This course in algebra, co-ordinate geometry and calculus is designed to fulfil these requirements for students at Universities, Polytechnics and Colleges of Technology.
The book contains 350 worked examples and 1550 practice examples selected mainly from university examination papers. The practice examples have been carefully graded and some hints are given with the answers so that the book may be used for private study as well as for class work.

From the Back Cover
For students reading Mathematics, either as part of a general degree or as an...


Real Analysis : Modern Techniques and Their Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
Gerald B. Folland
0471317160
April 7, 1999
Hardcover
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Book Description
An in-depth look at real analysis and its applications-now expanded and revised.

This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory.

This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive...

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