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SubheadMATHEMATICS

Elementary & Popular Mathematics

SPEED MATHEMATICS SIMPLIFIED , Edward Stoddard. Entertaining, easy-to-

follow suggestions for developing greater

speed and accuracy in doing mathematical

calculations. Surefi re methods for multiply-

ing without carrying, mastering fractions,

working quickly with decimals, handling

percentages, and much more. 284pp. 5 3/8 x 8 1/2. 0-486-27887-5 $ 9.95

CHALLENGING PROBLEMS IN ALGEBRA , Alfred S. Posamentier and Charles T. Salkind. Over 300 unusual problems,

ranging from easy to diffi cult, involving

equations and inequalities, Diophantine

equations, number theory, quadratic equa-

tions, logarithms, more. Detailed solutions,

as well as brief answers, for all problems

are provided. 272pp. 5 3/8 x 8 1/2. 0-486-69148-9 $ 14.95

THE CURVES OF LIFE , Theodore A. Cook. Classic examination of the function

of the spiral, or helix, in nature and art examines shells, leaves, human body,

drawings of Leonardo, Leaning Tower of Pisa. 1914 edition. 426 illustrations. 512pp. 5 3/8 x 8 1/2. 0-486-23701-X $ 16.95

INTRODUCTION TO ARTIFICIAL INTELLIGENCE : Second, Enlarged Edition, Philip C. Jackson, Jr. Comprehensive survey of artifi cial intelligence — the

study of how computers can be made to act intelligently. Includes introductory

and advanced material. Extensive notes updating the main text. 132 illustra-

tions. 512pp. 5 3/8 x 8 1/2. 0-486-24864-X $ 17.95

MATHEMATICS AND THE PHYSICAL WORLD , Morris Kline. Stimulating

account of development of mathematics from arithmetic, algebra, geometry

and trigonometry, to calculus, differential equations, and non-Euclidean geom-

etries. Also describes how math is used in optics, astronomy, and other phe-

nomena. 496pp. 5 5/8 x 8 1/4. 0-486-24104-1 $ 18.95

WHAT IS MATHEMATICAL LOGIC? , J. N. Crossley and Frances A. Davis. This

concise, lively treatment is accessible to

nonmathematicians. Topics include model

theory, Godel’s theorems, computability and

recursive functions, set theory, and more.

Diagrams appear throughout the text. 82pp. 5 3/8 x 8 1/2. 0-486-26404-1 $ 6.95

ELEMENTARY MATHEMATICS FROM AN ADVANCED STANDPOINT : Arithmetic, Algebra, Analysis, Felix Klein. Graphical

and geometrically perceptive methods

enliven a distinguished mathematician’s

treatment of arithmetic, algebra, and

analysis. Topics include calculating with

natural numbers, complex numbers,

goniometric functions, and infi nitesimal

calculus. 1932 edition. Includes 125 fi g-

ures. 288pp. 5 3/8 x 8 1/2. 0-486-43480-X $ 15.95

MATHOGRAPHICS , Robert Dixon. Stimu-

lating, unique book explores mathematical

drawing through compass constructions

and computer graphics. Over 100 full-

page drawings: fi ve-point egg, golden

ratio, plughole vortex, blancmange curve,

more. Exercises. 1987 edition. 224pp. 8 3/8 x 11. 0-486-26639-7 $ 16.95

LADY LUCK : The Theory of Probability, Warren Weaver. This witty, non-

technical introduction to probability elucidates such concepts as per-

mutations, independent events, mathematical expectation, the law of

averages, and more. No advanced math required. 49 drawings. 384pp. 5 3/8 x 8 1/2. 0-486-24342-7 $ 12.95

THE RED BOOK OF MATHEMATICAL PROBLEMS , Kenneth S. Williams and Kenneth Hardy. Handy compilation of 100 practice problems, hints, and solu-

tions indispensable for students preparing for the William Lowell Putnam and

other mathematical competitions. Preface to the First Edition. Sources. 1988

edition. 192pp. 5 3/8 x 8 1/2. 0-486-69415-1 $ 8.95

ARITHMETIC REFRESHER , A. A. Klaf. These 937 most-asked questions deal

with tax problems, interest and discount, time-payment, etc. Features 809 prob-

lems and answers. “More than just a refresher . . . contains a great number of

items that are not just reminders but entirely new ideas. — Bookmarks . 438pp. 5 3/8 x 8 1/2. 0-486-21241-6 $ 12.95

THE WORLD OF MATHEMATICSEdited by James Newman

Monumental survey includes historical and biological infor-mation on prominent mathematicians; mathematics and the physical world; numbers and the art of counting; mathematics of music and art; statistics; mathematics and social science; laws of chance; mathematics of space and motion; and much more. Essays by Galileo, Mathus, Euler, Poincaré, Bertrand Russell, George Bernard Shaw, Aldous Huxley, Alfred North Whitehead, Sir James Jeans, and many others. Numerous figures. Total of 2,576pp. All books 5 3/8 x 8 1/2. Volume 1: 768pp. 0-486-41153-2 $19.95 Volume 2: 720pp. 0-486-41150-8 $17.95 Volume 3: 624pp. 0-486-41151-6 $17.95 Volume 4: 464pp. 0-486-41152-4 $17.95

Subhead

11

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Elementary & Popular MathematicsMATHEMATICS

EXPERIMENTS IN TOPOLOGY , Stephen Barr. Classic, lively explana-

tion of one of the byways of mathe-

matics. Klein bottles, Moebius strips,

projective planes, map coloring, prob-

lem of the Koenigsberg bridges, much

more, described with clarity and wit. 210pp. 5 3/8 x 8 1/2. 0-486-25933-1 $ 12.95

TRIGONOMETRY REFRESHER , A. Albert Klaf. Covers the most

important aspects of plane and spher-

ical trigonometry. Discusses special

problems in navigation, surveying,

elasticity, architecture, and various

fi elds of engineering. Includes 1,738

problems, many with solutions. 1946

edition. Features 494 fi gures. 640pp. 5 3/8 x 8 1/2. 0-486-44227-6 $ 24.95

MATHEMATICS AND THE IMAGINA-TION , Edward Kasner and James Newman. With wit and clarity, the

authors progress from simple arith-

metic to calculus and non-Euclidean

geometry. Their subjects: geometry,

plane and fancy; puzzles that made

mathematical history; tantalizing par-

adoxes; more. Includes 169 fi gures. 400pp. 5 3/8 x 8 1/2. 0-486-41703-4 $ 15.95

GEOMETRY

GEOMETRY, RELATIVITY AND THE FOURTH DIMENSION , Rudolf Rucker. Exposition of fourth dimen-

sion, concepts of relativity as Flat-

land characters continue adventures.

Topics include curved space time as

a higher dimension, special relativity,

and shape of space-time. Includes 141

illustrations. 133pp. 5 3/8 x 8 1/2. 0-486-23400-2 $ 7.95

EXCURSIONS IN GEOMETRY , C. Stanley Ogilvy. A straightedge,

compass, and a little thought are all

that’s needed to discover the intel-

lectual excitement of geometry. Har-

monic division and Apollonian circles,

inversive geometry, hexlet, Golden

Section, more. 132 illustrations. 192pp. 5 3/8 x 8 1/2. 0-486-26530-7 $ 9.95

TAXICAB GEOMETRY : An Adven-ture in Non-Euclidean Geometry, Eugene F. Krause. Fascinating, acces-

sible introduction to unusual math-

ematical system in which distance

is not measured by straight lines.

Illustrated topics include applica-

tions to urban geography and com-

parisons to Euclidean geometry.

Selected answers to problems. 88pp. 5 3/8 x 8 1/2. 0-486-25202-7 $ 5.95

A LONG WAY FROM EUCLID , Constance Reid. Lively guide by a

prominent historian focuses on the

role of Euclid’s Elements in subse-

quent mathematical developments.

Elementary algebra and plane geom-

etry are sole prerequisites. 80 draw-

ings. 1963 edition. 304pp. 5 3/8 x 8 1/2. 0-486-43613-6 $ 13.95

INTRIGUING MATHEMATICAL PROBLEMS , Oswald Jacoby and William H. Benson. 208pp. 5 3/8 x 8 1/2. 0-486-29261-4 $ 9.95

ADVANCED TRIGONOMETRY , C. V. Durell and A. Robson. 1930 edition. 352pp. 5 3/8 x 8 1/2. 0-486-43229-7 $ 19.95

EXCURSIONS IN MATHEMATICS , C. Stanley Ogilvy. This lively and

accessible exploration of the nature

of mathematics examines the role of

the mathematician as well as the four

major branches: number theory, alge-

bra, geometry, and analysis. 192pp. 5 3/8 x 8 1/2. 0-486-28283-X $ 5.95

AN ILLUSTRATED GUIDE TO LIN-EAR PROGRAMMING , Saul I. Gass. Entertaining, nontechnical introduc-

tion covers basic concepts of linear

programming and its relationship to

operations research; geometric inter-

pretation and problem solving, solu-

tion techniques, network problems,

much more. Only high-school algebra

needed. 173pp. 6 1/8 x 9 1/4. 0-486-26258-8 $ 12.95

MATHEMATICS FOR EVERYMAN : From Simple Numbers to the Cal-culus, Egmont Colerus. This witty

and engaging stylebook presents the

fundamentals of mathematical opera-

tions: number systems, fi rst steps

in algebra and algebraic notation,

common fractions and equations,

and much more. 1958 edition. 272pp. 5 3/8 x 8 1/2. 0-486-42545-2 $ 12.95

HOW TO SOLVE MATHEMATICAL PROBLEMS , Wayne A. Wickelgren. Seven problem-solving techniques

include inference, classifi cation of

action sequences, subgoals, contra-

diction, working backward, relations

between problems, and mathematical

representation. Also, problems from

mathematics, science, and engineer-

ing with complete solutions. 272pp. 5 3/8 x 8 1/2. 0-486-28433-6 $ 12.95

MATHEMATICS FOR THE NON-MATHEMATICIAN , Morris Kline. Erudite and entertaining overview

follows development of mathematics

from ancient Greeks to present. Top-

ics include logic and mathematics,

the fundamental concept, differential

calculus, probability theory, much

more. Exercises and problems. 641pp. 5 3/8 x 8 1/2. 0-486-24823-2 $ 14.95

JOURNEY INTO MATHEMATICS : An Introduction to Proofs, Joseph J. Rotman. This treatment covers the

mechanics of writing proofs, the area

and circumference of circles, and

complex numbers and their applica-

tion to real numbers. 1998 edition. 256pp. 5 3/8 x 8 1/2. 0-486-45306-5 $ 13.95

12 To see all Table of Contents, visit www.doverdirect.com

SubheadMATHEMATICS

Logic & the Foundations of Mathematics

LECTURES ON ELEMENTARY MATH-EMATICS , Joseph Louis Lagrange. One of the 18th century’s greatest

mathematicians delivered these lec-

tures at a training school for teach-

ers. An exemplar among elementary

expositions, they combine original

ideas and elegant expression. 1898

edition. 176pp. 5 3/8 x 8 1/2. 0-486-46281-1 $ 11.95

NATURAL DEDUCTION : A Proof-Theoretical Study, Dag Prawitz. The

author of this study formulated the

theories behind intuitionistic type

theory and modern proof-theoretic

semantics. He explains the principles

of his proof-theoretical system, and

he illustrates its applications to natu-

ral deduction. 1965 edition. 128pp. 5 3/8 x 8 1/2. 0-486-44655-7 $ 9.95

MODELS AND ULTRAPRODUCTS : An Introduction, J. L. Bell and A. B. Slomson. This fi rst-year graduate text

assumes only an acquaintance with

set theory to explore homogeneous

universal models, saturated struc-

ture, extensions of classical fi rst-

order logic, and other topics. 1974

edition. 336pp. 5 3/8 x 8 1/2. 0-486-44979-3 $ 18.95

INTRODUCTION TO LOGIC , Patrick Suppes. Part I of this coher-

ent, well-organized text deals with

formal principles of inference and

defi nition. Part II explores elemen-

tary intuitive set theory, with sepa-

rate chapters on sets, relations, and

functions. Ideal for undergraduates.

330pp. 5 3/8 x 8 1/2. 0-486-40687-3 $ 14.95

MATHEMATICAL LOGIC , Stephen Cole Kleene. Contents include an

elementary but thorough overview

of mathematical logic of 1st order;

formal number theory; surveys of the

work by Church, Turing, and others,

including Gödel’s completeness theo-

rem, Gentzen’s theorem, more. 416pp. 5 3/8 x 8 1/2. 0-486-42533-9 $ 24.95

FIRST-ORDER LOGIC , Raymond M. Smullyan. This self-contained study

is both an introduction to quantifi ca-

tion theory and an exposition of new

results and techniques in “analytic”

or “cut free” methods. The focus is

on the tableau point of view. Includes

144 illustrations. 176pp. 5 3/8 x 8 1/2. 0-486-68370-2 $ 9.95

THE ELEMENTS OF MATHEMATI-CAL LOGIC , Paul C. Rosenbloom. This excellent introduction to math-

ematical logic provides a sound

knowledge of the most important

approaches, stressing the use of logi-

cal methods. “Reliable.” — The Math-

ematical Gazette. 1950 edition. 224pp. 5 3/8 x 8 1/2. 0-486-44617-4 $ 12.95

MATHEMATICAL LOGIC : A First Course, Joel W. Robbin. This self-

contained text will appeal to read-

ers from diverse fi elds and varying

backgrounds. Topics include 1st-

order recursive arithmetic, 1st- and

2nd-order logic, and the arithmetiza-

tion of syntax. Numerous exercises;

some solutions. 1969 edition. 224pp. 5 3/8 x 8 1/2. 0-486-45018-X $ 13.95

FOUNDATIONS OF MEASUREMENT , David H. Krantz, R. Duncan Luce, Patrick Suppes and Amos Tversky. All of the sciences have a need for quantitative

measurement. This infl uential series established the formal foundations for

measurement, justifying the assignment of numbers to objects in terms of their

structural correspondence. 1971 edition. All volumes 5 3/8 x 8 1/2.

Vol I: 624pp. Additive and Polynomial Representations 0-486-45314-6 $32.95 Vol II: 512pp. Geometrical, Threshold, and Probabilistic Representations 0-486-45315-4 $27.95 Vol III: 384pp. Representation, Axiomatization, and Invariance 0-486-45316-2 $21.95

JUST OUT

Subhead

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MATHEMATICS

INTRODUCTION TO MATHEMATICAL PHI-LOSOPHY , Bertrand Russell. Seminal work

focuses on concepts of number, order, rela-

tions, limits and continuity, propositional

functions, descriptions and classes, more.

Clear, accessible excursion into realm where

mathematics and philosophy meet. 208pp. 5 3/8 x 8 1/2. 0-486-27724-0 $ 10.95

INTRODUCTION TO MATHEMATICAL THINKING : The Formation of Concepts in Modern Mathematics, Friedrich Waismann. Examinations of arithmetic, geometry, and

theory of integers; rational and natural num-

bers; complete induction; limit and point of

accumulation; remarkable curves; complex

and hypercomplex numbers; more. Includes

27 fi gures. 1959 edition. 272pp. 5 3/8 x 8 1/2. 0-486-42804-4 $ 14.95

TOPOI : The Categorial Analysis of Logic, Robert Goldblatt. A classic exposition of a branch of mathemati-

cal logic that uses category theory, this text is suitable

for advanced undergraduates and graduate students and

accessible to both philosophically and mathematically ori-

ented readers. 576pp. 5 3/8 x 8 1/2. 0-486-45026-0 $ 29.95

AN INVESTIGATION OF THE LAWS OF THOUGHT , George Boole. A timeless introduction to the fi eld and a

landmark in symbolic logic, showing that classical logic

can be treated algebraically. 424pp. 5 3/8 x 8 1/2. 0-486-60028-9 $ 16.95

LAPSES IN MATHEMATICAL REASONING , V. M. Bradis, V. L. Minkovskii and A. K. Kharcheva. Unique, effective

system for teaching mathematical reasoning leads stu-

dents toward clearly false conclusions. Students then ana-

lyze the reasoning lapse to correct the problem. Covers

arithmetic, algebra, geometry, trigonometry, and approxi-

mate computations. 1963 edition. 224pp. 5 3/8 x 8 1/2. 0-486-40918-X $ 11.95

FIRST COURSE IN MATHEMATICAL LOGIC , Patrick Suppes and Shirley Hill. Rigorous intro-

duction is simple enough in presentation and

context for wide range of students. Symbolizing

sentences; logical inference; truth and validity;

truth tables; terms, predicates, universal quanti-

fi ers; universal specifi cation and laws of identity;

more. 288pp. 5 3/8 x 8 1/2. 0-486-42259-3 $ 12.95

BOOLEAN REASONING : The Logic of Boolean Equations, Frank Markham Brown. Concise text begins with an

overview of elementary mathematical

concepts and outlines theory of Bool-

ean algebras; defi nes operators for

elimination, division, and expansion;

covers syllogistic reasoning, solution

of Boolean equations, and functional

deduction. 304pp. 5 3/8 x 8 1/2. 0-486-42785-4 $ 16.95

THE UNDECIDABLE : Basic Papers on Undecidable Propositions, Unsolv-able Problems and Computable Functions, Edited by Martin Davis. An anthology of fundamental papers

on undecidability and unsolvability,

this classic opens with Gödel’s land-

mark 1931 paper demonstrating that

systems of logic cannot admit proofs

of all true assertions of arithmetic.

416pp. 6 1/8 x 9 1/4. 0-486-43228-9 $ 24.95

ON FORMALLY UNDECIDABLE PROPOSITIONS OF PRINCIPIA MATH-EMATICA AND RELATED SYSTEM , Kurt Gödel. First English translation

of revolutionary paper (1931) that established that even in elementary

parts of arithmetic, there are propositions which cannot be proved or

disproved within the system. Introduction by R. B. Braithwaite. 80pp. 5 3/8 x 8 1/2. 0-486-66980-7 $ 6.95

COMPUTABILITY AND UNSOLVABILITY , Martin Davis. Classic graduate-level

introduction to theory of computability. Discusses general theory of comput-

ability, computable functions, operations on computable functions, Turing

machines self-applied, unsolvable decision problems, applications of general

theory, mathematical logic, Kleene hierarchy, more. 288pp. 5 3/8 x 8 1/2. 0-486-61471-9 $ 15.95

FOUNDATIONS AND FUNDAMENTAL CONCEPTS OF MATHEMATICS , Howard Eves. Third edition of popular undergraduate-level text offers historic

overview, readable treatment of mathematics before Euclid, Euclid’s Elements,

non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more.

Problems, some with solutions. Bibliography. 362pp. 6 1/8 x 9 1/4. 0-486-69609-X $ 16.95

BASIC CONCEPTS OF MATHEMATICS AND LOGIC , Michael C. Gemignani. Intended as a fi rst look at mathematics at the college level, this text emphasizes

logic and set theory — counting, numbers, functions, ordering, probabilities,

and other components of higher mathematics. 288pp. 5 3/8 x 8 1/2. 0-486-43506-7 $ 15.95

A PROFILE OF MATHEMATICAL LOGIC , Howard DeLong. This introduction

to mathematical logic explores philosophical issues and Gödel’s Theorem.

Its widespread infl uence extends to the author of Gödel, Escher, Bach , whose

Pulitzer Prize-winning book was inspired by this work. 320pp. 5 3/8 x 8 1/2. 0-486-43475-3 $ 19.95

INTRODUCTION TO ELEMENTARY MATHEMATICAL LOGIC , A. A. Stolyar. Lucid, non-intimidating presentation of propositional logic, propositional calcu-

lus and predicate logic. Accessible to high school students; valuable review of

fundamentals for professionals. Exercises (no solutions). Preface. Three appen-

dices. Indices. Bibliogaphy. Includes 14 fi gures. 220pp. 5 3/8 x 8 1/2. 0-486-64561-4 $ 10.95

MATHEMATICAL LOGIC AND THE FOUNDATIONS OF MATHEMAT-ICS : An Introductory Survey, G. T. Kneebone. Ideal for students intend-

ing to specialize in the topic. Part I

discusses traditional and symbolic

logic. Part II explores the foundations

of mathematics. Part III focuses on the

philosophy of mathematics. 452pp. 5 3/8 x 8 1/2. 0-486-41712-3 $ 16.95

MATHEMATICAL THEORY OF COM-PUTATION , Zohar Manna. Attempt-

ing to make into a science the art of

verifying computer programs (debug-

ging), the author addresses both

practical and theoretical aspects.

This self-contained treatment includes

selected concepts of computability

theory and mathematical logic. 464pp. 5 3/8 x 8 1/2. 0-486-43238-6 $ 24.95

BESTSELLERBESTSELLER

Logic & the Foundations of Mathematics

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AlgebraMATHEMATICS

MODERN ALGEBRA , Seth Warner. Standard

text provides an exceptionally comprehen-

sive treatment of every aspect of modern

algebra. Explores algebraic structures, rings

and fi elds, vector spaces, polynomials, lin-

ear operators, much more. Over 1,300 exer-

cises. 1965 edition. 832pp. 5 3/8 x 8 1/2. 0-486-66341-8 $ 24.95

BASIC ABSTRACT ALGEBRA : For Graduate Students and Advanced Undergraduates, Robert B. Ash. Rela-

tions between groups and sets, results

and methods of abstract algebra in

terms of number theory and geometry,

and noncommutative and homological

algebra. Solutions. 2006 edition. 432pp. 6 1/2 x 9 1/4. 0-486-45356-1 $ 22.95

ELEMENTARY MATRIX ALGEBRA , Franz E. Hohn. This treatment starts with basics and

progresses to sweepout process for obtain-

ing complete solution of any given system

of linear equations and role of matrix alge-

bra in presentation of useful geometric

ideas, techniques, and terminology. 544pp. 5 3/8 x 8 1/2. 0-486-42534-7 $ 24.95 ABSTRACT ALGEBRA , W. E. Deskins. Excel-

lent textbook provides undergraduates with

an accessible introduction to the basic con-

cepts of abstract algebra and to the analysis

of abstract algebraic systems. Features many

examples and problems. 640pp. 5 3/8 x 8 1/2. 0-486-68888-7 $24.95

BOOLEAN ALGEBRA , R. L. Goodstein. This elementary treatment by a distin-

guished mathematician employs Boolean

algebra as a simple medium for introduc-

ing important concepts of modern algebra.

Numerous examples appear throughout

the text, plus full solutions. 160pp. 5 3/8 x 8 1/2. 0-486-45894-6 $ 10.95

LINEAR ALGEBRA AND PROJECTIVE GEOMETRY , Reinhold Baer. Geared

toward upper-level undergraduates and

graduate students, this text establishes

that projective geometry and linear alge-

bra are essentially identical. The support-

ing evidence consists of theorems offering

an algebraic demonstration of certain

geometric concepts. 1952 edition. 336pp. 5 3/8 x 8 1/2. 0-486-44565-8 $18.95

DIFFERENTIAL FORMS , Henri Cartan. The famous mathematician addresses

both pure and applied branches of mathematics in a book equally essential as a

text, reference, or a brilliant mathematical exercise. “Superb.” — Mathematical

Review. 1971 edition. 176pp. 6 1/2 x 9 1/4. 0-486-45010-4 $ 12.95

PROBABILITIES ON ALGEBRAIC STRUCTURES , Ulf Grenander. This

systematic approach covers semi-groups, groups, linear vector spaces,

and algebra. It states and studies fundamental probabilistic problems

for these spaces, focusing on concrete results. 1963 edition. 224pp. 5 3/8 x 8 1/2. 0-486-46287-0 $ 12.95

LINEAR ALGEBRA , Georgi E. Shilov. Covers determinants, linear spaces,

systems of linear equations, linear functions of a vector argument, coordinate

transformations, the canonical form of the matrix of a linear operator, bilinear

and quadratic forms, and more. 387pp. 5 3/8 x 8 1/2. 0-486-63518-X $16.95

ALGEBRA , Larry C. Grove. This graduate-level text is intended for

initial courses in algebra that proceed at a faster pace than undergraduate-level

courses. Subjects include groups, rings, fi elds and Galois theory. 1983 edition.

Includes 11 fi gures. Appendix. References. Index. 320pp. 5 3/8 x 8 1/2. 0-486-43947-X $ 19.95

LIE ALGEBRAS , Nathan Jacobson. Defi nitive treatment of important subject in

modern mathematics. Covers split semi-simple Lie algebras, universal envelop-

ing algebras, classifi cation of irreducible modules, automorphisms, simple Lie

algebras over an arbitrary fi eld, etc. Index. 331pp. 5 5/8 x 8 1/4. 0-486-63832-4 $15.95

MATRICES AND LINEAR ALGEBRA , Hans Schneider and George Phillip Barker. Basic textbook covers theory of matrices and its applications to sys-

tems of linear equations and related topics such as determinants, eigenvalues

and differential equations. Includes numerous exercises. 432pp. 5 3/8 x 8 1/2. 0-486-66014-1 $16.95

15

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TopologyMATHEMATICS

INTRODUCTION TO TOPOLOGY : Third Edition, Bert Mendelson. An undergraduate introduction

to the fundamentals of topology — engagingly writ-

ten, fi lled with helpful insights, complete with many

stimulating and imaginative exercises to help stu-

dents develop a solid grasp of the subject. 224pp. 5 3/8 x 8 1/2. 0-486-66352-3 $ 10.95

FROM GEOMETRY TO TOPOLOGY , H. Graham Flegg. Introductory text for fi rst-year math stu-

dents uses intuitive approach, bridges the gap from

familiar concepts of geometry to topology. Exer-

cises and Problems. Includes 101 black-and-white

illustrations. 1974 edition. 208pp. 5 3/8 x 8 1/2. 0-486-41961-4 $ 14.95

DIFFERENTIAL TOPOLOGY : An Introduction, David B. Gauld. This text covers topological spaces

and properties, some advanced calculus, differen-

tiable manifolds, orientability, submanifolds and an

embedding theorem, tangent spaces, vector fi elds

and integral curves, Whitney’s embedding theorem,

more. Includes 88 helpful illustrations. 1982 edition.

256pp. 6 1/8 x 9 1/4. 0-486-45021-X $ 15.95

SHAPE THEORY

Categorical Methods of Approximation

J.- M. Cordier and T. Porter

This in-depth treatment uses shape theory as a “case study” to illustrate situations common to many areas of mathematics, including the use of arche-typal models as a basis for systems of approximations. It offers a unifi ed, con-solidated presentation of research on category theory, shape theory, and the study of topological algebras. 1989 edi-tion. 208pp. 6 1/8 x 9 1/4. 0-486-46623-X $ 14.95

INVITATION TO COMBINATORIAL TOPOLOGY , Maurice Fréchet and Ky Fan. Translated by Howard W. Eves. Elementary text, accessible to

anyone with a background in high school geometry,

covers problems inherent to coloring maps, homeo-

morphism, applications of Descartes’ theorem,

topological polygons, more. Includes 108 fi gures.

1967 edition. 136pp. 5 3/8 x 8 1/2. 0-486-42786-2 $ 9.95

TOPOLOGY , John G. Hocking and Gail S. Young. 384pp. 5 3/8 x 8 1/4. 0-486-65676-4 $ 16.95

GENERAL TOPOLOGY , Waclaw Sierpinski. Translated and revised by C. Cecilia Krieger. Second edition. 304pp. 5 3/8 x 8 1/2. 0-486-41148-6 $ 12.95

TOPOLOGICAL METHODS IN EUCLIDEAN SPACES , Gregory L. Naber. 240pp. 5 3/8 x 8 1/2. 0-486-41452-3 $ 9.95

DIFFERENTIAL TOPOLOGY : First Steps, Andrew H. Wallace. 1968 edition. 144pp. 5 3/8 x 8 1/2. 0-486-45317-0 $ 9.95

ALGEBRAIC TOPOLOGY , C. R. F. Maunder. 1980

corrected edition. 384pp. 5 3/8 x 8 1/2. 0-486-69131-4 $ 16.95

TOPOLOGICAL UNIFORM STRUCTURES , Warren Page. 416pp. 5 3/8 x 8 1/2. 0-486-65808-2 $ 9.95

DIFFERENTIAL MANIFOLDS , Antoni A. Kosinski. 1993 edition. 288pp. 5 3/8 x 8 1/2. 0-486-46244-7 $ 15.95

SET TOPOLOGY , R. Vaidyanathaswamy. 320pp. 5 3/8 x 8 1/2. 0-486-40456-0 $ 14.95

ALGEBRAIC TOPOLOGY : Homology and Coho-mology, Andrew H. Wallace. 1970 edition. 288pp. 5 3/8 x 8 1/2. 0-486-46239-0 $ 15.95

GENERAL TOPOLOGY , Stephen Willard. 27 fi g-

ures. 1970 edition. 384pp. 6 1/8 x 9 1/4. 0-486-43479-6 $ 22.95

FORMAL KNOT THEORY , Louis H. Kauffman. 1983 edition. Includes 51 illustrations. 272pp. 5 3/8 x 8 1/2. 0-486-45052-X $ 14.95

INTRODUCTION TO TOPOLOGY : Second Edition, Theodore W. Gamelin and Robert Everist Greene. 51 illustrations. 1983 edition. 256pp. 5 3/8 x 8 1/2. 0-486-40680-6 $ 12.95

A COMBINATORIAL INTRODUCTION TO TOPOLOGY , Michael Henle. 1979 edition . 310pp. 5 3/8 x 8 1/2. 0-486-67966-7 $ 14.95

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GeometryMATHEMATICS

DIFFERENTIAL GEOMETRY

K. L. Wardle

This elementary account of the differential geometry of curves and surfaces in space deals with curva-ture and torsion, involutes and evo-lutes, curves on a surface, curvature of surfaces, and developable and ruled surfaces. The examples feature many special types of surfaces, and the numerous problems include com-plete solutions. 1965 edition. 112pp. 5 3/8 x 8 1/2. 0-486-46272-2 $ 8.95

INVITATION TO GEOMETRY

Z. A. Melzak

Intended for students of many dif-ferent backgrounds with only a modest knowledge of mathematics, this text features self-contained chap-ters that can be adapted to several types of geometry courses. The author emphasizes connections with calcu-lus and simple mechanics, focusing on developing students’ grasp of spatial relationships. 240pp. 5 3/8 x 8 1/2. 0-486-46626-4 $ 14.95

ROTATIONS, QUATERNIONS, AND DOUBLE GROUPS , Simon L. Altmann. This self-contained

text presents a consistent description of the geo-

metric and quaternionic treatment of rotation

operators, employing methods that lead to a rigor-

ous formulation and offering complete solutions to

many illustrative problems. 336pp. 5 3/8 x 8 1/2. 0-486-44518-6 $ 19.95

PROOF IN GEOMETRY : With “Mistakes in Geomet-ric Proofs,” A. I. Fetisov and Ya. S. Dubnov. This

single-volume compilation of 2 books explores the

construction of geometric proofs. It offers useful

criteria for determining correctness and presents

examples of faulty proofs that illustrate common

errors. 1963 editions. 128pp. 5 3/8 x 8 1/2. 0-486-45354-5 $ 9.95

FAMOUS PROBLEMS OF GEOMETRY AND HOW TO SOLVE THEM , Benjamin Bold. Each chapter

devoted to single type of problem, with commen-

tary and practice problems. Amateur puzzlists and

students of mathematics will enjoy this rare oppor-

tunity to match wits with civilization’s great math-

ematicians. 128pp. 5 3/8 x 8 1/2. 0-486-24297-8 $ 6.95

COLLEGE GEOMETRY : An Introduction to the Modern Geometry of the Triangle and the Circle, Nathan Altshiller-Court. The standard university-

level text for decades, this volume offers exercises

in construction problems, harmonic division, circle

and triangle geometry, and other areas. 1952 edi-

tion, revised and enlarged by the author. 336pp. 5 3/8 x 8 1/2. 0-486-45805-9 $ 15.95

LINEAR ALGEBRA AND GEOMETRY : A Second Course, Irving Kaplansky. The author of this text

seeks to remedy a common failing in teaching alge-

bra: the neglect of related instruction in geometry.

This volume features examples, exercises, and

proofs. 1974 edition. 160pp. 5 3/8 x 8 1/2. 0-486-43233-5 $ 12.95

ADVANCED EUCLIDEAN GEOMETRY , Roger A. Johnson. This classic text explores the geometry of

the triangle and the circle, concentrating on exten-

sions of Euclidean theory, and examining in detail

many relatively recent theorems. 1929 edition. 336pp. 5 3/8 x 8 1/2. 0-486-46237-4 $ 17.95

CONVEX SURFACES , Herbert Busemann. This

exploration of convex surfaces focuses on extrinsic

geometry and applications of the Brunn-Minkowski

theory. It also examines intrinsic geometry and the

realization of intrinsic metrics. 1958 edition. 208pp. 5 3/8 x 8 1/2. 0-486-46243-9 $ 12.95

GENERAL INVESTIGATIONS OF CURVED SUR-FACES : Edited with an Introduction and Notes by Peter Pesic, Karl Friedrich Gauss. This infl uential

work defi nes the concept of surface curvature and

presents the important theorem stating that the

“Gauss curvature” is invariant under arbitrary iso-

metric deformation of a curved surface. 1902 edi-

tion. 144pp. 6 1/2 x 9 1/4. 0-486-44645-X $ 12.95

NON-EUCLIDEAN GEOMETRY , Stefan Kulczycki. This accessible approach features stereometric and

planimetric proofs, and elementary proofs employ-

ing only the simplest properties of the plane. A

short history of geometry precedes the systematic

exposition. 1961 edition. 208pp. 5 3/8 x 8 1/2. 0-486-46264-1 $ 13.95

SPACE AND GEOMETRY : In the Light of Physi-ological, Psychological and Physical Inquiry, Ernst Mach. Three essays by an eminent scientist

explore the nature, origin, and development of our

concepts of space, in a manner suitable for under-

graduate students and other readers. 1906 edition. 160pp. 5 3/8 x 8 1/2. 0-486-43909-7 $ 9.95

INTRODUCTORY NON-EUCLIDEAN GEOMETRY , Henry Parker Manning. This fi ne and versatile

introduction begins with the theorems common to

Euclidean and non-Euclidean geometry, and then it

addresses the specifi c differences that constitute

elliptic and hyperbolic geometry. 1901 edition. 112pp. 5 3/8 x 8 1/2. 0-486-44262-4 $ 8.95

LECTURES IN PROJECTIVE GEOMETRY , A. Seidenberg. An ideal text for undergraduate

courses, this volume takes an axiomatic approach

that covers relations between the basic theorems,

conics, coordinate systems and linear transforma-

tions, quadric surfaces, and the Jordan canonical

form. 1962 edition. 240pp. 5 3/8 x 8 1/2. 0-486-44618-2 $ 14.95

GEOMETRY : A Comprehensive Course, Dan Pedoe. Introduction to vector algebra in the plane; circles

and coaxal systems; mappings of the Euclidean

plane; similitudes, isometries, Moebius transfor-

mations, much more. Includes over 500 exercises.

464pp. 6 1/2 x 9 1/4. 0-486-65812-0 $ 21.95

THE ELEMENTS OF NON-EUCLIDEAN GEOMETRY , D. M. Y. Sommerville. Renowned for its lucid yet

meticulous exposition, this classic allows students

to follow the development of non-Euclidean geom-

etry from a fundamental analysis of the concept of

parallelism to more advanced topics. 1914 edition.

Includes 133 fi gures. 288pp. 5 3/8 x 8 1/2. 0-486-44222-5 $ 16.95

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MATHEMATICSGeometry

INTRODUCTION TO THE GEOMETRY OF COMPLEX NUMBERS , Roland Deaux. Geared toward readers unfa-

miliar with complex numbers, this

text explains how to solve problems

that frequently arise in the applied

sciences and emphasizes construc-

tions related to algebraic operations.

1956 edition. 208pp. 5 3/8 x 8 1/2. 0-486-46629-9 $ 13.95

GEOMETRY OF CLASSICAL FIELDS , Ernest Binz, Jedrzej Sniatycki and Hans Fischer. A canonical quantiza-

tion approach to classical fi eld the-

ory, this text includes an introduction

to differential geometry, the theory

of Lie groups, and covariant Hamilto-

nian formulation of fi eld theory. 1988

edition. 480pp. 6 1/2 x 9 1/4. 0-486-45053-8 $ 24.95

THE GEOMETRY OF GEODESICS , Herbert Busemann. A comprehen-

sive approach to qualitative problems

in intrinsic differential geometry, this

text examines Desarguesian spaces,

perpendiculars and parallels, cover-

ing spaces, the infl uence of the sign

of the curvature on geodesics, more.

1955 edition. Includes 66 fi gures.

432pp. 5 3/8 x 8 1/2. 0-486-44237-3 $ 24.95

DIRICHLET’S PRINCIPLE, CON-FORMAL MAPPING, AND MINIMAL SURFACES , Richard Courant. An

examination of approaches to easy-

to-understand but diffi cult-to-solve

mathematical problems, this classic

text explores conformal mapping

on parallel-slit domains, Plateau’s

problem, the general problem of

Douglas, more. 1950 edtion. 352pp. 5 3/8 x 8 1/2. 0-486-44552-6 $ 19.95

NON-RIEMANNIAN GEOMETRY , Luther Pfahler Eisenhart. This con-

cise text by a prominent mathema-

tician deals chiefl y with manifolds

dominated by the geometry of paths.

Topics include asymmetric and sym-

metric connections, the projective

geometry of paths, and the geometry

of sub-spaces. 1927 edition. 192pp. 5 3/8 x 8 1/2. 0-486-44243-8 $ 12.95

COORDINATE GEOMETRY , Luther Pfahler Eisenhart. This volume

affords exceptional insights into coor-

dinate geometry. Covers invariants of

conic sections and quadric surfaces;

algebraic equations on the 1st degree

in 2 and 3 unknowns; and more. Over

500 exercises. 1939 edition. 320pp. 5 3/8 x 8 1/2. 0-486-44261-6 $ 19.95

DIFFERENTIAL GEOMETRY , William C. Graustein. This fi rst course in dif-

ferential geometry presents the fun-

damentals of the metric differential

geometry of curves and surfaces in

a Euclidean space of 3 dimensions,

using vector notation and technique.

Nearly 200 problems. 1935 edition.

240pp. 5 3/8 x 8 1/2. 0-486-45011-2 $ 14.95

ELEMENTARY VECTOR GEOMETRY , Seymour Schuster. Appropriate for

high school and college courses, this

elementary text addresses the devel-

opment of vector algebra as a mathe-

matical tool and features applications

to trigonometry and algebra. Exer-

cises, solutions. 1962 edition. 224pp. 5 3/8 x 8 1/2. 0-486-46672-8 $ 12.95

REGULAR POLYTOPES , H. S. M. Coxeter. Foremost book available

on polytopes, incorporating ancient

Greek and most modern work. Dis-

cusses polygons, polyhedrons, and

multi-dimensional polytopes. Defi ni-

tions of symbols. Includes 8 tables

plus many diagrams and examples.

1963 edition. 321pp. 5 3/8 x 8 1/2. 0-486-61480-8 $ 16.95

EUCLIDEAN GEOMETRY AND TRANSFORMATIONS , Clayton W. Dodge. This introduction to Euclid-

ean geometry emphasizes trans-

formations, particularly isometries

and similarities. Suitable for under-

graduate courses, it includes numer-

ous examples, many with detailed

answers. 1972 edition. 304pp. 6 1/8 x 9 1/4. 0-486-43476-1 $ 19.95

PROBLEMS IN EUCLIDEAN SPACE : Application of Convexity, H. G. Egg-leston. This study of convex sets in

real Euclidean spaces of 2 or 3 dimen-

sions illustrates the different ways in

which convexity can enter into the

formulation as the solution. 1957 edi-

tion. 176pp. 5 3/8 x 8 1/2. 0-486-45846-6 $ 11.95

LINEAR GEOMETRY , Rafael Artzy. This text stresses the relationship

between algebra and linear geometry,

examining transformations in the

Euclidean plane, affi ne and Euclidean

geometry, projective geometry and

non-Euclidean geometries, and axi-

omatic plane geometry. 1974 edition. 288pp. 6 1/2 x 9 1/4. 0-486-46627-2 $ 16.95

ANALYTICAL GEOMETRY OF THREE DIMENSIONS , William H. McCrea. Geared toward advanced undergrad-

uates and graduate students, this text

covers the coordinate system, planes

and lines, spheres, homogeneous

coordinates, general equations, quad-

ric in Cartesian coordinates, and

intersection of quadrics. 1947 edition.

160pp. 5 3/8 x 8 1/2. 0-486-45313-8 $ 11.95

DIFFERENTIAL GEOMETRIC STRUC-TURES , Walter A. Poor. This introduc-

tory text defi nes geometric structure

by specifying parallel transport in an

appropriate fi ber bundle and focus-

ing on simplest cases of linear paral-

lel transport in a vector bundle. 1981

edition. 352pp. 6 1/8 x 9 1/4. 0-486-45844-X $ 19.95

ANALYTICAL CONICS , Barry Spain. This concise text introduces ana-

lytical geometry, covering basic

ideas and methods. An invaluable

preparation for more advanced treat-

ments, it features solutions to many

of its problems. 1957 edition. 160pp. 5 3/8 x 8 1/2. 0-486-45773-7 $ 10.95

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