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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
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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
14 To see all Math & Science titles in print, visit www.doverdirect.com
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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