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A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science - including physics, analysis, and group theory - as well as its value in understanding probability, determinant theory, and...
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This volume became the standard text in the field almost immediately upon its original publication. Renowned for its lucid yet meticulous exposition, it can be appreciated by anyone familiar with high school algebra and geometry. Its arrangement follows the traditional pattern of plane and solid geometry, in which theorems are deduced from axioms and postulates. In this manner, students can follow the development of non-Euclidean geometry in strictly...
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This self-contained treatment offers a systematic development of the theory of iterative methods. Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. The text explores the convergence properties of the SOR method and related techniques in terms of the spectral radii of the associated matrices as well as in terms of certain...
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Designed for students just beginning their study of the discipline, this concise introductory history of mathematics is supplemented by brief but in-depth sketches of the more important individual topics. Covering such subjects as algebra symbols, negative numbers, the metric system, quadratic equations, and much more, this widely adopted work invites and encourages further study of mathematics.
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Intended to facilitate the use and calculation of spheroidal wave functions, this applications-oriented text features a detailed and unified account of the properties of these functions. Addressed to applied mathematicians, mathematical physicists, and mathematical engineers, it presents tables that provide a convenient means for handling wave problems in spheroidal coordinates. Topics include separation of the scalar wave equation in spheroidal coordinates,...
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This highly regarded text presents a self-contained introduction to some important aspects of modern qualitative theory for ordinary differential equations. It is accessible to any student of physical sciences, mathematics or engineering who has a good knowledge of calculus and of the elements of linear algebra. In addition, algebraic results are stated as needed; the less familiar ones are proved either in the text or in appendixes. The topics covered...
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This influential treatise presents upper-level undergraduates and graduate students with a mathematical analysis of choice behavior. It begins with the statement of a general axiom upon which the rest of the book rests; the following three chapters, which may be read independently of each other, are devoted to applications of the theory to substantive problems: psychophysics, utility, and learning. Applications to psychophysics include considerations...
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Both a challenge to mathematically inclined readers and a useful supplementary text for high school and college courses, One Hundred Problems in Elementary Mathematics presents an instructive, stimulating collection of problems. Many problems address such matters as numbers, equations, inequalities, points, polygons, circles, ellipses, space, polyhedra, and spheres. An equal number deal with more amusing or more practical subjects, such as a picnic...
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This captivating book explains some of the most fascinating ideas of mathematics to nonspecialists. It focuses on three main areas: non-Euclidean geometry, a basis for relativity theory; number theory, a major component of cryptography; and fractals, the key elements of computer-generated art. Numerous illustrations. 1993 edition.
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This famous little book was first published in German in 1933 and in Russian a few years later, setting forth the axiomatic foundations of modern probability theory and cementing the author's reputation as a leading authority in the field. The distinguished Russian mathematician A. N. Kolmogorov wrote this foundational text, and it remains important both to students beginning a serious study of the topic and to historians of modern mathematics. Suitable...
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Engaging introduction to that curious feature of mathematics which provides framework for so many structures in biology, chemistry, and the arts. Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much more.
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This concise and widely referenced monograph has served as a text for generations of advanced undergraduate math majors and graduate students. Prepared with an eye toward the needs of applied mathematicians, engineers, and physicists, the treatment is equally valuable as a reference for professionals. After discussing some mathematical preliminaries, author Raimond A. Struble presents detailed treatments of the existence and the uniqueness of a solution...
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This introduction to algebraic geometry makes particular reference to the operation of inversion and is suitable for advanced undergraduates and graduate students of mathematics. One of the major contributions to the relatively small literature on inversive geometry, the text illustrates the field's applications to comparatively elementary and practical questions and offers a solid foundation for more advanced courses. The two-part treatment begins...
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This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras. A short introduction to geometric shape explains specifics of the construction of the shape...
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This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and...
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The manuscripts and correspondence of Leibniz possess a special interest: they are invaluable as aids to the study of their author's part in the invention and development of the infinitesimal calculus. In addition, the main ideas behind Leibniz's philosophical theories lay here, in his mathematical work. This volume consists of two sections. The first part features Leibniz's own accounts of his work, and the second section comprises critical and historical...
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Brief, clear, and well written, this introduction to abstract algebra bridges the gap between the solid ground of traditional algebra and the abstract territory of modern algebra. The only prerequisite is high school–level algebra. Author W. W. Sawyer begins with a very basic viewpoint of abstract algebra, using simple arithmetic and elementary algebra. He then proceeds to arithmetic and polynomials, slowly progressing to more complex matters: finite...
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This book has been widely acclaimed for its clear, cogent presentation of the theory of partial differential equations, and the incisive application of its principal topics to commonly encountered problems in the physical sciences and engineering. It was developed and tested at Purdue University over a period of five years in classes for advanced undergraduate and beginning graduate students in mathematics, engineering and the physical sciences. The...
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As the author notes in the preface, "The purpose of this book is to acquaint a broad spectrum of students with what is today known as 'abstract algebra.'" Written for a one-semester course, this self-contained text includes numerous examples designed to base the definitions and theorems on experience, to illustrate the theory with concrete examples in familiar contexts, and to give the student extensive computational practice. The first three chapters...
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Students progressing to advanced calculus are frequently confounded by the dramatic shift from mechanical to theoretical and from concrete to abstract. This text bridges the gap, offering a systematic development of the real number system and careful treatment of mappings, sequences, limits, continuity, and metric spaces. The first five chapters consist of a systematic development of many of the important properties of the real number system, plus...
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