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Vision in Elementary Mathematics PDF

482 Pages·2011·3.591 MB·English
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DOVER BOOKS ON MATHEMATICS HANDBOOK OF MATHEMATICAL FUNCTIONS: WITH FORMULAS, GRAPHS, AND MATHEMATICAL TABLES, EDITED BY MILTON ABRAMOWITZ AND IRENE A. STEGUN. (0-486-61272-4) ABSTRACT AND CONCRETE CATEGORIES: THE JOY OF CATS, JIRI ADAMEK, HORST HERRLICH, GEORGE E. STRECKER. (0-486-46934-4) NONSTANDARD METHODS IN STOCHASTIC ANALYSIS AND MATHEMATICAL PHYSICS, SERGIO ALBEVERIO, JENS ERIK FENSTAD, RAPHAEL HØEGH-KROHN AND TOM LINDSTRØM. (0-486-46899-2) MATHEMATICS: ITS CONTENT, METHODS AND MEANING, A. D. ALEKSANDROV, A. N. KOLMOGOROV, AND M. A. LAVRENT’EV. (0-486-40916-3) COLLEGE GEOMETRY: AN INTRODUCTION TO THE MODERN GEOMETRY OF THE TRIANGLE AND THE CIRCLE, NATHAN ALTSHILLER-COURT. (0-486-45805-9) 2 THE WORKS OF ARCHIMEDES, ARCHIMEDES. TRANSLATED BY SIR THOMAS HEATH. (0-486-42084-1) REAL VARIABLES WITH BASIC METRIC SPACE TOPOLOGY, ROBERT B. ASH. (0-486-47220-5) INTRODUCTION TO DIFFERENTIABLE MANIFOLDS, LOUIS AUSLANDER AND ROBERT E. MACKENZIE. (0-486-47172-1) PROBLEM SOLVING THROUGH RECREATIONAL MATHEMATICS, BONNIE AVERBACH AND ORIN CHEIN. (0-486-40917-1) THEORY OF LINEAR OPERATIONS, STEFAN BANACH. TRANSLATED BY F. JELLETT. (0-486-46983-2) VECTOR CALCULUS, PETER BAXANDALL AND HANS LIEBECK. (0-486-46620-5) INTRODUCTION TO VECTORS AND TENSORS: SECOND EDITION--TWO VOLUMES BOUND AS ONE, RAY M. BOWEN AND C.-C. WANG. (0-486-46914-X) ADVANCED TRIGONOMETRY, C. V. DURELL AND A. ROBSON. (0-486-43229-7) FOURIER ANALYSIS IN SEVERAL COMPLEX VARIABLES, LEON EHRENPREIS. (0-486-44975-0) THE THIRTEEN BOOKS OF THE ELEMENTS, VOL. 1, EUCLID. EDITED BY THOMAS L. HEATH. (0-486-60088-2) 3 BASIC ALGEBRA I : SECOND EDITION, NATHAN JACOBSON. (0-486-47189-6) BASIC ALGEBRA II: SECOND EDITION, NATHAN JACOBSON. (0-486-47187-X) NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS BY THE FINITE ELEMENT METHOD, CLAES JOHNSON. (0-486-46900-X) ADVANCED EUCLIDEAN GEOMETRY, ROGER A. ,IOHNSON. (0-486-46237-4) GEOMETRY AND CONVEXITY: A STUDY IN MATHEMATICAL METHODS, PAUL J. KELLY AND MAX L. WEISS. (0-486-46980-8) TRIGONOMETRY REFRESHER, A. ALBERT KLAF. (0-486-44227-6) CALCULUS: AN INTUITIVE AND PHYSICAL APPROACH (SECOND EDITION), MORRIS KLINE. (0-486-40453-6) THE PHILOSOPHY OF MATHEMATICS: AN INTRODUCTORY ESSAY, STEPHAN KÖRNER. (0-486-47185-3) COMPANION TO CONCRETE MATHEMATICS: MATHEMATICAL TECHNIQUES AND VARIOUS APPLICATIONS, Z. A. MELZAK. (0-486-45781-8) NUMBER SYSTEMS AND THE FOUNDATIONS OF ANALYSIS, ELLIOTT MENDELSON. (0-486-45792-3) EXPERIMENTAL STATISTICS, MARY GIBBONS NATRELLA. (0-486-43937-2) 5 THE THIRTEEN BOOKS OF THE ELEMENTS, VOL. 2, EUCLID. (0-486-60089-0) THE THIRTEEN BOOKS OF THE ELEMENTS, VOL. 3, EUCLID. EDITED BY THOMAS L. HEATH. (0-486-60090-4) AN INTRODUCTION TO DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, STANLEY J. FARLOW. (0-486-44595-X) PARTIAL DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS, STANLEY J. FARLOW. (0-486-67620-X) STOCHASTIC DIFFERENTIAL EQUATIONS AND APPLICATIONS, AVNER FRIEDMAN. (0-486-45359-6) ADVANCED CALCULUS, AVNER FRIEDMAN. (0-486-45795-8) POINT SET TOPOLOGY, STEVEN A. GAAL. (0-486-47222-1) DISCOVERING MATHEMATICS: THE ART OF INVESTIGATION, A. GARDINER. (0-486-45299-9) LATTICE THEORY: FIRST CONCEPTS AND DISTRIBUTIVE LATTICES, GEORGE GRÄTZER. (0-486-47173-X) ORDINARY DIFFERENTIAL EQUATIONS, JACK K. HALE. (0-486-47211-6) METHODS OF APPLIED MATHEMATICS, FRANCIS B. HILDEBRAND. (0-486-67002-3) 4 AN INTRODUCTION TO IDENTIFICATION, J. P. NORTON. (0-486-46935-2) BEYOND GEOMETRY: CLASSIC PAPERS FROM RIEMANN TO EINSTEIN, EDITED WITH AN INTRODUCTION AND NOTES BY PETER PESIC. (0-486-45350-2) THE STANFORD MATHEMATICS PROBLEM BOOK: WITH HINTS AND SOLUTIONS, G. POLYA AND J. KILPATRICK. (0-486-46924-7) SPLINES AND VARIATIONAL METHODS, P. M. PRENTER. (0-486-46902-6) PROBABILITY THEORY, A. RENYI. (0-486-45867-9) LOGIC FOR MATHEMATICIANS, J. BARKLEY ROSSER. (0-486-46898-4) PARTIAL DIFFERENTIAL EQUATIONS: SOURCES AND SOLUTIONS, ARTHUR DAVID SNIDER. (0-486-45340-5) INTRODUCTION TO BIOSTATISTICS: SECOND EDITION, ROBERT R. SOKAL AND F. JAMES ROHLF. (0-486-46961-1) MATHEMATICAL PROGRAMMING, STEVEN VAJDA. (0-486-47213-2) THE LOGIC OF CHANCE, JOHN VENN. (0-486-45055-4) THE CONCEPT OF A RIEMANN SURFACE, HERMANN WEYL. (0-486-47004-0) INTRODUCTION TO PROJECTIVE GEOMETRY, C. R. WYLIE, JR. (0-486-46895-X) 6 FOUNDATIONS OF GEOMETRY, C. R. WYLIE, JR. (0-486-47214-0) SEE EVERY DOVER BOOK IN PRINT AT WWW.DOVERPUBLICATIONS.COM 7 8 Copyright Copyright © 1964 by W. W. Sawyer All rights reserved. Bibliographical Note This Dover edition, first published in 2003, is an unabridged reprint of the work originally published by Penguin Books Ltd., Hammondsworth, Middlesex, England, in 1964. Library of Congress Cataloging-in-Publication Data Sawyer, W. W. (Walter Warwick), 1911- Vision in elementary mathematics / W. W. Sawyer. p. cm. Originally published: Hammondsworth, Middlesex, England; Baltimore, Md. : Penguin Books, 1964, in series: Introducing mathematics; 1. 9780486143620 1. Mathematics—Study and teaching (Elementary) I. Title. QA135.6 .S39 2002 372.7—dc21 2002034825 9 Manufactured in the United States by Courier Corporation 42555X02 www.doverpublications.com 10

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