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To Order Contact Your Local Dover Rep or Tel 800-223-3130 Fax 516-742-5049 www.doverdirect.com 83

Table of Contents

Aurora: Dover Modern Math Originals . . page 84Mathematics . . . . . . . . . . . . . . . . . . . . . . . page 86Science . . . . . . . . . . . . . . . . . . . . . . . . . . . page 88

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Category Theory in ContextEmily RiehlDerived from courses the author taught at Harvard and Johns Hopkins, this original book introduces the concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctive, monads — and other topics, revisiting a broad range of mathematical examples from the categori-cal perspective. Basic set theory and logic are the only prerequisites. 272pp. 6 x 9.

Calculus: A Rigorous First CourseDaniel J. VellemanDesigned for undergraduate math majors, this rigorous and reward-ing treatment covers the usual topics of first-year calculus: limits, derivatives, integrals, and infinite series. Prerequisites are a solid background in algebra and trigonometry. This original text is printed in two colors and provides substantial problems and complete proofs. Solutions will be available to instructors. 672pp. 6.14 x 9.21.

An Interactive Introduction to Knot TheoryAllison K. Henrich and Inga JohnsonThis well-written and engaging volume introduces knot theory, an area of growing interest in contemporary math teaching. The hands-on approach features many exercises to be completed by readers and requires only a basic familiarity with algebra. Topics include knot definition and equivalence, families of links and braids, knot notation, virtual knots, and related subjects. 128pp. 6 x 9.

Aurora: Dover Modern Math Originals

November 2016

$29.95 US0-486-80903-X978-0-486-80903-8

December 2016

$69.95 US0-486-80936-6978-0-486-80936-6

Concise text on category theory, the foundation for many of the 20th century’s greatest advances in pure mathematics

Immensely rewarding one-volume treatment for advanced undergraduates in mathematics

Original introduction to a fascinating topic that’s generating a great deal of interest in contemporary math teaching

Since 1941, Dover has reissued some of the most influential works in all areas of mathematics. Now, we are proud to present this important new series of all-original texts by some of today’s most prominent scholars. Each edition is presented in an affordable paperback format designed to withstand years of classroom use.

January 2017

$19.95 US0-486-80463-1978-0-486-80463-7

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To Order Contact Your Local Dover Rep or Tel 800-223-3130 Fax 516-742-5049 www.doverdirect.com 85

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Aurora: Dover Modern Math Originals

February 2017

$34.95 US0-486-81015-1978-0-486-81015-7

Clear, precise, self-contained treatment includes detailed proofs and complete solutions to the exercises

NEW & RECENT RELEASES

Algebra: Polynomials, Galois Theory, and ApplicationsFrédéric ButinA precise, self-contained treatment of Galois theory, this Dover Aurora original features detailed proofs and complete solutions to exercises. The approach advances from introductory material to extensions that contribute to a comprehensive understanding of the Galois group of a polynomial. Final chapters offer excellent discus-sions of several real-world applications. 336pp. 6 x 9.

Elementary Point-Set Topology: A Transition to Advanced Mathematics, André L. Yandl and Adam Bowers. This versatile, original approach, which focuses on learning to read and write proofs, serves as both an introductory treatment and a bridge between elementary calculus and more advanced courses. 2016 edition. 256pp. 6 x 9. 978-0-486-80349-4 $24.95

An Introductory Course on Differentiable Manifolds, Siavash Shahshahani. Rigorous course for advanced undergraduates and gradu-ate students requires a strong back-ground in undergraduate mathemat-ics. Complete, detailed treatment, enhanced with philosophical and historical asides and more than 200 exercises. 2016 edition. 368pp. 6 x 9. August 2016 978-0-486-80706-5 $29.95

Numbers: Histories, Mysteries, Theories, Albrecht Beutelspacher. Translated by Andrea Bruder, Andrea Easterday, and John J. Watkins. A writer of popular mathematics books presents this accessible charac-terization of the wealth of experiences that numbers have to offer, the many things described by numbers, and numbers that possess special fascinations. 2015 edition. 112pp. 6 x 9. 978-0-486-80348-7 $12.95

Optimization in Function Spaces, Amol Sasane. Classroom-tested at the London School of Economics, this origi-nal, highly readable text offers numer-ous examples and exercises as well as detailed solutions. Prerequisites are multivariable calculus and basic linear algebra. 2015 edition. 256pp. 6 x 9. 978-0-486-78945-3 $34.95

The Theory and Practice of Conformal Geometry, Steven G. Krantz. An expert on conformal geom-etry introduces some of the subject's modern developments. Topics include the Riemann mapping theorem, invari-ant metrics, automorphism groups, harmonic measure, extremal length, analytic capacity, invariant geometry, and more. 2016 edition. 304pp. 6 x 9. 978-0-486-79344-3 $29.95

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Solid Analytic GeometryAbraham Adrian AlbertThe first seven chapters of this concise text provide an exposition of the basic topics of solid analytic geometry and comprise the material for a one-semester course on the subject. The remaining two chapters on spherical coordinates and the elements of projective geometry contain additional material for longer courses or supplementary study. Reprint of the McGraw-HillBook Company, Inc., New York, 1949 edition. 176pp. 5 1/2 x 8 1/2.

Calculus of Variations with ApplicationsGeorge M. EwingSuitable for advanced undergraduates and graduate students of mathematics, this clearly written treatment is equally suited to use as a primary or supplementary text. Topics include necessary and sufficient conditions of an extremum; variations and Hamilton's prin-ciple; parametric problems; direction methods; measure, integrals, and derivatives; variation theory in terms of Lebesque; and other topics. Reprint of the W. W. Norton & Company, New York, 1969 edition. 352pp. 5 1/2 x 8 1/2.

Elements of the Theory of FunctionsKonrad Knopp Translated by Frederick BagemihlThis well-known little book provides a clear and concise review of general function theory via complex variables. Five main sections offer students valuable background in complex numbers and their geometric representation; linear functions and circular transforma-tions; sets, sequences, and power series; analytic functions and conformal mapping; and the elementary functions. Reprint of the Dover 1953 edition. 140pp. 5 1/2 x 8 1/2.

September 2016

$12.95 US0-486-81026-7978-0-486-81026-3

October 2016

$19.95 US0-486-64856-7978-0-486-64856-9

October 2016

$10.95 US0-486-60154-4978-0-486-60154-0

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To Order Contact Your Local Dover Rep or Tel 800-223-3130 Fax 516-742-5049 www.doverdirect.com 87

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Mathematics

Invertibility and Singularity for Bounded Linear OperatorsRobin HarteSuitable for advanced undergraduate and graduate courses in func-tional analysis, this volume is also a valuable resource for research-ers in Fredholm theory, Banach algebras, and multiparameter spectral theory. The introductory treatment is based on the open mapping theorem, Hahn-Banach theorem, dual space construction, enlargement of normed space, and Liouville's theorem. Includes new Prologue and Epilogue by the author. Reprint of the Marcel Dekker, Inc., New York, 1988 edition. 608pp. 6 x 9.

September 2016

$12.95 US0-486-81026-7978-0-486-81026-3

October 2016

$19.95 US0-486-64856-7978-0-486-64856-9

October 2016

$10.95 US0-486-60154-4978-0-486-60154-0

Lapses in Mathematical ReasoningV. M. Bradis, V. L. Minkovskii and A. K. KharchevaThis unique approach to teaching high school students mathemati-cal reasoning skills leads them deliberately toward false conclusions. Afterward, teachers and students review the problems to identify and correct mistakes. Introductory exercises in refuting erroneous mathematical arguments are followed by examples from arithmetic, algebra, geometry, trigonometry, and approximate computations. Reprint of the Pergamon Press, Oxford and London, and the Macmillan Company, New York, 1963 edition. 224pp. 5 x 8.

Lectures on Measure and IntegrationHarold WidomThese well-known and concise lecture notes present the fundamen-tals of the Lebesgue theory of integration and an introduction to some of the theory's applications. Suitable for advanced undergradu-ates and graduate students of mathematics, the topics include mea-sures, integration, theorems of Fubini, representations of measures, Lebesgue spaces, differentiation, and Fourier series. Reprint of the Van Nostrand Reinhold Co., New York, 1969 edition. 176pp. 5 1/2 x 8 1/2.

Lectures on Integral EquationsHarold WidomThis concise and classic volume presents the main results of inte-gral equation theory as consequences of the theory of operators on Banach and Hilbert spaces. In addition, it offers a brief account of Fredholm's original approach. Other material discusses applications to second order linear differential equations and Fourier integral techniques. Reprint of the Van Nostrand Reinhold Co., New York, 1969 edition. 128pp. 5 x 8.

October 2016

$39.95 US0-486-81030-5978-0-486-81030-0

November 2016

$14.95 US0-486-40918-X978-0-486-40918-4

November 2016

$14.95 US0-486-81028-3978-0-486-81028-7

December 2016

$12.95 US0-486-81027-5978-0-486-81027-0

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EScience

Mathematical Aspects of Subsonic and Transonic Gas DynamicsLipman BersThis concise treatment by a prominent mathematician offers a survey of mathematical aspects of the theory of compressible fluids. Topics include differential equations of a potential gas flow, mathematical background of subsonic flow theory, behavior of a flow at infinity, flows in channels and with a free boundary, and many other subjects. Reprint of the John Wiley & Sons, New York, 1958 edition. 176pp. 5 1/2 x 8 1/2.

Statistical PhysicsA Probabilistic ApproachBernard H. LavendaSuitable for graduate students in chemical physics, statistical phys-ics, and physical chemistry, this text develops an innovative, proba-bilistic approach to statistical mechanics. The treatment employs Gauss' principle and incorporates Bose-Einstein and Fermi-Dirac sta-tistics to provide a powerful tool for the statistical analysis of physi-cal phenomenon. Topics include Boltzmann's principle, black-body radiation, and quantum statistics. Reprint of the John Wiley & Sons, Inc., New York, 1991 edition. 384pp. 6.14 x 9.21.

The Theory of Linear ViscoelasticityD. R. BlandThis introduction to the concepts of viscoelasticity focuses on stress analysis. Three detailed sections present examples of stress-related problems, including sinusoidal oscillation problems, quasi-static problems, and dynamic problems. Concise and still universally ref-erenced, the text also explains procedures for model fitting to mea-sured values of complex modulus or compliance. Reprint of the Pergamon Press, Oxford, 1960 edition. 144pp. 5 x 8.

October 2016

$15.95 US0-486-81016-X978-0-486-81016-4

October 2016

$29.95 US0-486-81031-3978-0-486-81031-7

October 2016

$12.95 US0-486-46269-2978-0-486-46269-1

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To Order Contact Your Local Dover Rep or Tel 800-223-3130 Fax 516-742-5049 www.doverdirect.com 89

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Science

Energy Methods in Applied MechanicsHenry L. LanghaarThis comprehensive work presents an integrated and modern treat-ment of the energy principles of mechanics. Topics include applica-tions to dynamics of rigid bodies, analysis of elastic frames, general elastic theory, the theory of plates and shells, the theory of buck-ling, and the theory of vibrations. Includes a substantial section of answers to problems. Reprint of the the John Wiley & Sons, Inc., New York, 1962 edition. 352pp. 6 x 9.

Introduction to Renormalization Group Methods in PhysicsSecond EditionR. J. Creswick, H. A. Farach, and C. P. Poole, JrThis introduction to the renormalization group, an edited and cor-rected second edition, discusses examples from diverse areas of physics. Designed for a one-semester course for advanced graduate students, the treatment requires a solid background in classical mechanics, statistical mechanics, and quantum mechanics. Each chapter is augmented by problems and references. Revised and corrected second edition, John Wiley & Sons, New York, 1992. 448pp. 6 x 9.

Wave Propagation in a Turbulent MediumV.I. Tatarski Translated by Richard SilvermanThis monograph describes the phenomena associated with the propa-gation of electromagnetic and acoustic waves through atmospheric turbulence. Geared toward specialists in radiophysics and atmospheric acoustics and optics, it covers both theoretical and experimental aspects. The treatment stresses applications to phase and amplitude fluctuations, scintillation of stars, radio scattering, and other problems. Reprint of the McGraw-Hill, Inc., New York, 1961 edition. 288pp. 5 1/2 x 8 1/2.

November 2016

$24.95 US0-486-81113-1978-0-486-81113-0

October 2016

$15.95 US0-486-81016-X978-0-486-81016-4

October 2016

$29.95 US0-486-81031-3978-0-486-81031-7

October 2016

$12.95 US0-486-46269-2978-0-486-46269-1

December 2016

$44.95 US0-486-79345-1978-0-486-79345-0

December 2016

$16.95 US0-486-81029-1978-0-486-81029-4

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