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String, Straightedge, and Shadow: The Story of Geometry
by Julia E. DigginsThis book explains how the basic principles of elementary geometry were discovered over 2,000 years ago. Indicates the major roles played by the early civilizations of Mesopotamia, Egypt, and Greece.
Studies in Profit, Business Saving and Investment in the United Kingdom 1920-1962: Volume 1 (Routledge Revivals)
by P. E. HartThe results of the 1959 Glasgow University investigation into British industrial profit, business saving, and investment are the subject of this book, originally published in 1965. Part 1 presents original estimates of profits in British industries 1920-1938, which when linked with Government estimates of such profits since 1948, permit long runs studies of the fortunes of individual industries. In addition, the appropriation of profit between dividends and business saving is also estimated for manufacturing industry 1920-1938. Part 2 begins the analysis of the extensive financial data collected in the Glasgow enquiry and is concerned with the effects of the size of a firm on its financial performance. The financial performance of large companies quoted on the Stock Exchange with a sample of small unquoted private companies and unincorporated firms is compared.
Sundials: History, Theory, and Practice
by René R.J. Rohr"His lively pen, his direct and simple style, his expressive vocabulary, his avoidance of pedantry, his conciseness in the exposition of his thoughts make his book a pleasure to read." -- Henri Michel, International Academy of the History of ScienceThe story of man's efforts to measure time is a long one -- reaching back thousands of years to the dawn of civilization. Among the earliest instruments developed for telling time was the sundial. In this expert study, a noted sundial expert offers a fascinating and informative account of these ancient devices, presented in simple, lively language.Over the centuries, many different varieties of sundials have been constructed, and Mr. Rohr provides detailed, accurate descriptions of them all: classical sundials, inclined dials, solar calendars, analemmatic dials, moon dials, and many more. There is even a chapter devoted to especially remarkable dials past and present, and a listing of the most popular sundial mottoes. In this profusely illustrated volume, you will not only learn about the long and colorful history of the sundial, you will learn a practical method of building one yourself. No special knowledge is required, other than an understanding of the basic principles of cosmography and of the relative movements of the sun and the planets. (These are recalled in an elementary way in a special chapter.) For mathematically inclined readers, more complex formulae and calculations have been included, some of which have never been printed in a book of gnomonics.
Tangrams: 330 Puzzles (Dover Recreational Math)
by Ronald C. ReadThis collection gathers together nearly 330 tangrams, the best creations of both Chinese and Occidental puzzle devisers. Included are puzzles carefully selected from rare 19th-century books and some of the most inventive and imaginative inventions of Loyd and Dudeney. Tangrams range from the relatively easy to the difficult.
Theory of Approximation (Dover Books on Mathematics)
by N. I. AchieserA pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of problems and applications (elementary extremal problems, Szego's theorem, the Carathéodory-Fejér problem, and more).
A Vector Space Approach to Geometry (Dover Books on Mathematics)
by Melvin HausnerThe effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.
About Vectors (Dover Books on Mathematics)
by Banesh HoffmannFrom his unusual beginning in "Defining a vector" to his final comments on "What then is a vector?" author Banesh Hoffmann has written a book that is provocative and unconventional. In his emphasis on the unresolved issue of defining a vector, Hoffmann mixes pure and applied mathematics without using calculus. The result is a treatment that can serve as a supplement and corrective to textbooks, as well as collateral reading in all courses that deal with vectors. Major topics include vectors and the parallelogram law; algebraic notation and basic ideas; vector algebra; scalars and scalar products; vector products and quotients of vectors; and tensors. The author writes with a fresh, challenging style, making all complex concepts readily understandable. Nearly 400 exercises appear throughout the text. Professor of Mathematics at Queens College at the City University of New York, Banesh Hoffmann is also the author of The Strange Story of the Quantum and other important books. This volume provides much that is new for both students and their instructors, and it will certainly generate debate and discussion in the classroom.
Analysis of Numerical Methods (Dover Books on Mathematics)
by Herbert Bishop Keller Eugene IsaacsonIn this age of omnipresent digital computers and their capacity for implementing numerical methods, no applied mathematician, physical scientist, or engineer can be considered properly trained without some understanding of those methods. This text, suitable for advanced undergraduate and graduate-level courses, supplies the required knowledge — not just by listing and describing methods, but by analyzing them carefully and stressing techniques for developing new methods.Based on each author's more than 40 years of experience in teaching university courses, this book offers lucid, carefully presented coverage of norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation, numerical solution of differential equations, and more. No mathematical preparation beyond advanced calculus and elementary linear algebra (or matrix theory) is assumed. Examples and problems are given that extend or amplify the analysis in many cases.
The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy
by J. D. WilliamsWhen J. D. Williams wrote this entertaining, witty introduction for the nonscientist, game theory was still a somewhat mysterious subject familiar to very few scientists beyond those researchers, like himself, working for the military. Now, over thirty years after its original publication as a Rand Corporation research study, his light-hearted though thoroughly effective primer is the recognized classic introduction to an increasingly applicable discipline. Used by amateurs, professionals, and students throughout the world in the classroom, on the job, and for personal amusement, the book has been through ten printings, and has been translated into at least five languages (including Russian and Japanese).Revised, updated, and available for the first time in an inexpensive paperback edition, The Compleat Strategyst is a highly entertaining text essential for anyone interested in this provocative and engaging area of modern mathematics. In fully illustrated chapters complete with everyday examples and word problems, Williams offers readers a working understanding of the possible methods for selecting strategies in a variety of situations, simple to complex. With just a basic understanding of arithmetic, anyone can grasp all necessary aspects of two-, three-, four-, and larger strategy games with two or more sets of inimical interests and a limitless array of zero-sum payoffs.As research and study continues not only in this new discipline but in the related areas of statistics, probability and behavioral science, understanding of games, decision making, and the development of strategies will be increasingly important. In the areas of economics, sociology, politics, and the military, game theory is sure to have an even wider impact. For students and amateurs fascinated by game theory's implications there is no better, immediately applicable, or more entertaining introduction to the subject than this engaging text by the late J. D. Williams, Professor of Mathematics at Princeton University and a member of the Research Council of The Rand Corporation.
Elementary Matrix Theory (Dover Books on Mathematics)
by Howard EvesThe usefulness of matrix theory as a tool in disciplines ranging from quantum mechanics to psychometrics is widely recognized, and courses in matrix theory are increasingly a standard part of the undergraduate curriculum.This outstanding text offers an unusual introduction to matrix theory at the undergraduate level. Unlike most texts dealing with the topic, which tend to remain on an abstract level, Dr. Eves' book employs a concrete elementary approach, avoiding abstraction until the final chapter. This practical method renders the text especially accessible to students of physics, engineering, business and the social sciences, as well as math majors. Although the treatment is fundamental -- no previous courses in abstract algebra are required -- it is also flexible: each chapter includes special material for advanced students interested in deeper study or application of the theory.The book begins with preliminary remarks that set the stage for the author's concrete approach to matrix theory and the consideration of matrices as hypercomplex numbers. Dr. Eves then goes on to cover fundamental concepts and operations, equivalence, determinants, matrices with polynomial elements, similarity and congruence. A final optional chapter considers matrix theory from a generalized or abstract viewpoint, extending it to arbitrary number rings and fields, vector spaces and linear transformations of vector spaces. The author's concluding remarks direct the interested student to possible avenues of further study in matrix theory, while an extensive bibliography rounds out the book.Students of matrix theory will especially appreciate the many excellent problems (solutions not provided) included in each chapter, which are not just routine calculation exercises, but involve proof and extension of the concepts and material of the text. Scientists, engineers, economists and others whose work involves this important area of mathematics, will welcome the variety of special types of matrices and determinants discussed, which make the book not only a comprehensive introduction to the field, but a valuable resource and reference work.
Geography of South East Asia: தென்கிழக்கு ஆசியா
by G. Krishnamoorthyஇந்த தென்கிழக்கு ஆசிய புவியியல் புத்தகத்தில் தென்கிழக்கு ஆசியாவில் உள்ள மண்வளங்கள். கனிமங்கள், ஆறுகள், இயற்கை போன்றவற்றை பற்றி நாம் தெரிந்து கொள்வதற்கு நமக்கு பேரூதவியாக இருக்கிறது.
Industrialization and Under-developed Countries (Routledge Revivals)
by Alan B MountjoyFirst published in 1966, Industrialization and Under-Developed Countries traces the distribution, causes and problems of under-development and, from the point of view of the economic geographer, goes on to examine the difficulties and possibilities of industrialization as a remedy. Particular emphasis is laid upon the demographic factor both in the world situation and as affecting the way of life of individual countries. This book will be of interest to students of economics and geography.
Matrices and Transformations (Dover Books on Mathematics)
by Anthony J. PettofrezzoThis book presents an elementary and concrete approach to linear algebra that is both useful and essential for the beginning student and teacher of mathematics. Here are the fundamental concepts of matrix algebra, first in an intuitive framework and then in a more formal manner. A Variety of interpretations and applications of the elements and operations considered are included. In particular, the use of matrices in the study of transformations of the plane is stressed. The purpose of this book is to familiarize the reader with the role of matrices in abstract algebraic systems, and to illustrate its effective use as a mathematical tool in geometry. The first two chapters cover the basic concepts of matrix algebra that are important in the study of physics, statistics, economics, engineering, and mathematics. Matrices are considered as elements of an algebra. The concept of a linear transformation of the plane and the use of matrices in discussing such transformations are illustrated in Chapter #. Some aspects of the algebra of transformations and its relation to the algebra of matrices are included here. The last chapter on eigenvalues and eigenvectors contains material usually not found in an introductory treatment of matrix algebra, including an application of the properties of eigenvalues and eigenvectors to the study of the conics. Considerable attention has been paid throughout to the formulation of precise definitions and statements of theorems. The proofs of most of the theorems are included in detail in this book. Matrices and Transformations assumes only that the reader has some understanding of the basic fundamentals of vector algebra. Pettofrezzo gives numerous illustrative examples, practical applications, and intuitive analogies. There are many instructive exercises with answers to the odd-numbered questions at the back. The exercises range from routine computations to proofs of theorems that extend the theory of the subject. Originally written for a series concerned with the mathematical training of teachers, and tested with hundreds of college students, this book can be used as a class or supplementary text for enrichments programs at the high school level, a one-semester college course, individual study, or for in-service programs.
Prelude to Civil War: 1816-1836
by William W. FreehlingFrom the preface: "My reasons for presenting a re-examination of the Nullification Controversy go beyond a desire to clarify its causes. The crisis of 1832-3 is one of the more dramatic events in United States history, and has, I think, never been chronicled fully or accurately. Furthermore, the Nullification Crisis has usually been presented as an isolated event. Viewed in proper perspective, the confrontation between Andrew Jackson and the Carolina nullifiers was the central occurrence in the broader transition of South Carolina from the enthusiastic nationalism of 1816 to the extreme sectionalism of 1836. And I hope the following analysis of the acute anxieties surrounding the mere discussion of slavery during these years of transition will help to explain why South Carolina led the South in a suicidal assault on the federal Union a generation later."
A Short Course in Automorphic Functions (Dover Books on Mathematics)
by Joseph LehnerThis concise three-part treatment introduces undergraduate and graduate students to the theory of automorphic functions and discontinuous groups. Author Joseph Lehner begins by elaborating on the theory of discontinuous groups by the classical method of Poincaré, employing the model of the hyperbolic plane. The necessary hyperbolic geometry is developed in the text. Chapter two develops automorphic functions and forms via the Poincaré series. Formulas for divisors of a function and form are proved and their consequences analyzed. The final chapter is devoted to the connection between automorphic function theory and Riemann surface theory, concluding with some applications of Riemann-Roch theorem. <p> The book presupposes only the usual first courses in complex analysis, topology, and algebra. Exercises range from routine verifications to significant theorems. Notes at the end of each chapter describe further results and extensions, and a glossary offers definitions of terms.
Square Summable Power Series (Dover Books on Mathematics)
by James Rovnyak Louis De BrangesThis text for advanced undergraduate and graduate students introduces Hilbert space and analytic function theory, which is centered around the invariant subspace concept. The book's principal feature is the extensive use of formal power series methods to obtain and sometimes reformulate results of analytic function theory. The presentation is elementary in that it requires little previous knowledge of analysis, but it is designed to lead students to an advanced level of performance. This is achieved chiefly through the use of problems, many of which were proposed by former students. The book's tried-and-true approach was developed from the authors' lecture notes on courses taught at Lafayette College, Bryn Mawr College, and Purdue University.
The Theory of Spinors
by Élie CartanThe French mathematician Élie Cartan (1869-1951) was one of the founders of the modern theory of Lie groups, a subject of central importance in mathematics and also one with many applications. In this volume, he describes the orthogonal groups, either with real or complex parameters including reflections, and also the related groups with indefinite metrics. He develops the theory of spinors (he discovered the general mathematical form of spinors in 1913) systematically by giving a purely geometrical definition of these mathematical entities; this geometrical origin makes it very easy to introduce spinors into Riemannian geometry, and particularly to apply the idea of parallel transport to these geometrical entities.The book is divided into two parts. The first is devoted to generalities on the group of rotations in n-dimensional space and on the linear representations of groups, and to the theory of spinors in three-dimensional space. Finally, the linear representations of the group of rotations in that space (of particular importance to quantum mechanics) are also examined. The second part is devoted to the theory of spinors in spaces of any number of dimensions, and particularly in the space of special relativity (Minkowski space). While the basic orientation of the book as a whole is mathematical, physicists will be especially interested in the final chapters treating the applications of spinors in the rotation and Lorentz groups. In this connection, Cartan shows how to derive the "Dirac" equation for any group, and extends the equation to general relativity.One of the greatest mathematicians of the 20th century, Cartan made notable contributions in mathematical physics, differential geometry, and group theory. Although a profound theorist, he was able to explain difficult concepts with clarity and simplicity. In this detailed, explicit treatise, mathematicians specializing in quantum mechanics will find his lucid approach a great value.
Two-Person Game Theory
by Anatol Rapoport"Game theory is an intellectual X-ray. It reveals the skeletal structure of those systems where decisions interact, and it reveals, therefore, the essential structure of both conflict and cooperation." -- Kenneth BouldingThis fascinating and provocative book presents the fundamentals of two-person game theory, a mathematical approach to understanding human behavior and decision-making, Developed from analysis of games of strategy such as chess, checkers, and Go, game theory has dramatic applications to the entire realm of human events, from politics, economics, and war, to environmental issues, business, social relationships, and even "the game of love." Typically, game theory deals with decisions in conflict situations.Written by a noted expert in the field, this clear, non-technical volume introduces the theory of games in a way which brings the essentials into focus and keeps them there. In addition to lucid discussions of such standard topics as utilities, strategy, the game tree, and the game matrix, dominating strategy and minimax, negotiated and nonnegotiable games, and solving the two-person zero-sum game, the author includes a discussion of gaming theory, an important link between abstract game theory and an experimentally oriented behavioral science. Specific applications to social science have not been stressed, but the methodological relations between game theory, decision theory, and social science are emphasized throughout.Although game theory employs a mathematical approach to conflict resolution, the present volume avoids all but the minimum of mathematical notation. Moreover, the reader will find only the mathematics of high school algebra and of very elementary analytic geometry, except for an occasional derivative. The result is an accessible, easy-to-follow treatment that will be welcomed by mathematicians and non-mathematicians alike.
Variational Methods for Eigenvalue Problems: An Introduction to the Weinstein Method of Intermediate Problems (Second Edition) (Mathematical Expositions #10)
by S. H. GouldThe first edition of this book gave a systematic exposition of the Weinstein method of calculating lower bounds of eigenvalues by means of intermediate problems. From the reviews of this edition and from subsequent shorter expositions it has become clear that the method is of considerable interest to the mathematical world; this interest has increased greatly in recent years by the success of some mathematicians in simplifying and extending the numerical applications, particularly in quantum mechanics. Until now new developments have been available only in articles scattered throughout the literature: this second edition presents them systematically in the framework of the material contained in the first edition, which is retained in somewhat modified form.
Calculus, Volume 1
by Tom M. ApostolAn introduction to the Calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.
Conformal Mapping on Riemann Surfaces (Dover Books on Mathematics)
by Harvey CohnThe subject matter loosely called "Riemann surface theory" has been the starting point for the development of topology, functional analysis, modern algebra, and any one of a dozen recent branches of mathematics; it is one of the most valuable bodies of knowledge within mathematics for a student to learn.Professor Cohn's lucid and insightful book presents an ideal coverage of the subject in five parts. Part I is a review of complex analysis analytic behavior, the Riemann sphere, geometric constructions, and presents (as a review) a microcosm of the course. The Riemann manifold is introduced in Part II and is examined in terms of intuitive physical and topological technique in Part III. In Part IV the author shows how to define real functions on manifolds analogously with the algebraic and analytic points of view outlined here. The exposition returns in Part V to the use of a single complex variable z. As the text is richly endowed with problem material -- 344 exercises -- the book is perfect for self-study as well as classroom use.Harvey Cohn is well-known in the mathematics profession for his pedagogically superior texts, and the present book will be of great interest not only to pure and applied mathematicians, but also engineers and physicists. Dr. Cohn is currently Distinguished Professor of Mathematics at the City University of New York Graduate Center.
From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931
by Jean Van HeijenoortThe fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for the first time. Modern logic, heralded by Leibniz, may be said to have been initiated by Boole, De Morgan, and Jevons, but it was the publication in 1879 of Gottlob Frege’s Begriffsschrift that opened a great epoch in the history of logic by presenting, in full-fledged form, the propositional calculus and quantification theory. <p><p> Frege’s book, translated in its entirety, begins the present volume. The emergence of two new fields, set theory and foundations of mathematics, on the borders of logic, mathematics, and philosophy, is depicted by the texts that follow. Peano and Dedekind illustrate the trend that led to Principia Mathematica. Burali-Forti, Cantor, Russell, Richard, and König mark the appearance of the modern paradoxes. Hilbert, Russell, and Zermelo show various ways of overcoming these paradoxes and initiate, respectively, proof theory, the theory of types, and axiomatic set theory. Skolem generalizes Löwenheim’s theorem, and he and Fraenkel amend Zermelo’s axiomatization of set theory, while von Neumann offers a somewhat different system. The controversy between Hubert and Brouwer during the twenties is presented in papers of theirs and in others by Weyl, Bernays, Ackermann, and Kolmogorov. The volume concludes with papers by Herbrand and by Gödel, including the latter’s famous incompleteness paper. <p> Of the forty-five contributions here collected all but five are presented in extenso. Those not originally written in English have been translated with exemplary care and exactness; the translators are themselves mathematical logicians as well as skilled interpreters of sometimes obscure texts. Each paper is introduced by a note that sets it in perspective, explains its importance, and points out difficulties in interpretation. Editorial comments and footnotes are interpolated where needed, and an extensive bibliography is included.
Invitation to Combinatorial Topology (Dover Books on Mathematics)
by Ky Fan Maurice Fréchet Howard W. EvesAn elementary text that can be understood by anyone with a background in high school geometry, Invitation to Combinatorial Topology offers a stimulating initiation to important topological ideas. This translation from the original French does full justice to the text's coherent presentation as well as to its rich historical content. Subjects include the problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, and topological polygons. Considerations of the topological classification of closed surfaces cover elementary operations, use of normal forms of polyhedra, reduction to normal form, and application to the geometric theory of functions. 1967 edition. 108 figures. Bibliography. Index.
Mathematical Logic
by Stephen Cole KleeneUndergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text. It begins with an elementary but thorough overview of mathematical logic of first order. The treatment extends beyond a single method of formulating logic to offer instruction in a variety of techniques: model theory (truth tables), Hilbert-type proof theory, and proof theory handled through derived rules.The second part supplements the previously discussed material and introduces some of the newer ideas and the more profound results of twentieth-century logical research. Subsequent chapters explore the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Godel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Godel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. The author, Stephen Cole Kleene, was Cyrus C. MacDuffee Professor of Mathematics at the University of Wisconsin, Madison. Preface. Bibliography. Theorem and Lemma Numbers: Pages. List of Postulates. Symbols and Notations. Index.
Mathematics for the Nonmathematician
by Morris KlinePractical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these--the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.