While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.

    Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

    It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.

    Originally written to define the relation between the theories of transfinite numbers and mathematical games, the resulting work is a mathematically sophisticated but eminently enjoyable guide to game theory. By defining numbers as the strengths of positions in certain games, the author arrives at a new class, the surreal numbers, that includes both real numbers and ordinal numbers. These surreal numbers are applied in the author's mathematical analysis of game strategies. The additions to the Second Edition present recent developments in the area of mathematical game theory, with a concentration on surreal numbers and the additive theory of partizan games.

    Now in its fifth updated edition, it is easy to understand, and convenient to use. Inside you ll find the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes. For the 5th edition, the chapters "Computer Algebra Systems" and "Dynamical Systems and Chaos" have been revised, updated and expanded."

    As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the "Super," in their historical introduction to this behind-the-scenes look at the minds and ideas that ushered in the nuclear age. An epilogue by Françoise Ulam and Jan Mycielski sheds new light on Ulam's character and mathematical originality.

    For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."--MATHEMATICAL REVIEWS

    Over 100 problems at ends of chapters. Answers in back of book. 1962 edition.

    The book's careful account is a contemporary balance between theory, application, and historical development, providing it's readers with an insight into how mathematics progresses and is in turn influenced by the natural world.

    "...a story of great mathematicians and their achievements, of practical successes and failures, and of human perfidy and generosity...this is one of the still too rare occasions in which mathematicians are shown as frail, flesh-and-blood creatures...a very worthwhile book." -CHOICE

    This volume covers local as well as global differential geometry of curves and surfaces.

    

    The algebraic and order properties of the real number system are presented in a simpler fashion than in the previous edition.

    Buckminster Fuller introduced geodesic domes when literary critic Hugh Kenner published this fully-illustrated practical manual for their construction. Now, some twenty-five years later, Geodesic Math and How to Use It again presents a systematic method of design and provides a step-by-step method for producing mathematical specifications for orthodox geodesic domes, as well as for a variety of elliptical, super-elliptical, and other nonspherical contours. Out of print since 1990, Geodesic Math and How To Use It is California's most requested backlist title. This edition is fully illustrated with complete original appendices.

    A book that discusses the general problems of poll taking.

    Paperback with spiral binding, as pictured; name inside; mild shelf wear (mth)

    Covers the basic concepts of the finite element method and their application to the analysis of plane structures and two-dimensional continuum problems in heat transfer, irrotational fluid flow, and elasticity. This revised edition includes a reorganization of topics and an increase in the number of homework problems. The emphasis on numerical illustrations make topis clear without heavy use of sophisticated mathematics.

    Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topics. Each subject illustrates a significant idea and lends itself easily to experiments and problems. Useful appendices offer an overview of the basic ideas of arithmetic, the rudiments of algebra, suggestions on teaching mathematics, and much more, including answers and comments for selected exercises.

    After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom- etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol- ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note- worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.

    

    

    

    To do this I have had to exercise a certain amount of selectivity in choosing and in rejecting both authors and papers. I have rather arbitrarily chosen, in the main, the most famous mathematicians of the period in question and have concentrated on their major works in numerical analysis at the expense, perhaps, of other lesser known but capable analysts. This selectivity results from the need to choose from a large body of literature, and from my feeling that almost by definition the great masters of mathematics were the ones responsible for the most significant accomplishments. In any event I must accept full responsibility for the choices. I would particularly like to acknowledge my thanks to Professor Otto Neugebauer for his help and inspiration in the preparation of this book. This consisted of many friendly discussions that I will always value. I should also like to express my deep appreciation to the International Business Machines Corporation of which I have the honor of being a Fellow and in particular to Dr. Ralph E. Gomory, its Vice-President for Research, for permitting me to undertake the writing of this book and for helping make it possible by his continuing encouragement and support.

    Each of them has been carefully selected so that none will be too tough for anyone without a math background — but they're not too easy. Some are original, and all are clearly and accurately answered at the back of the book.

    It explains effective procedures for performing mathematical tasks that arise in many fields, including operations research, engineering, systems sciences, statistics, and economics.Readers will learn how to resolve linear independence and find null spaces and factors of matrices, determine existence of restricted solutions to linear equations and inequalities, and resolve definiteness of Hermitian and real symmetric matrices by Gaussian pivoting. Additional topics include how to diagonalize — or "nearly" diagonalize — square matrices, differentiate vectors and matrices by the chain rule, solve systems of differential and difference equations, and other subjects. Most of the examples and many of the 1,300 problems illustrate techniques, and nearly all of the tables display reference material for procedures. Differential and integral calculus are prerequisites.

    Dr Batty organises the book around the main theme of designing and using such models in practical situations and develops a family of static and dynamic models dealing with the location of land use and economic activities. He describes the models both as urban theories and as computer algorithms, and thoroughly explores the process of calibrating or 'tuning' the models to reflect reality. Problems concerning the definition of the spatial systems to which these models refer are examined, as are other practical difficulties such as data organisation. The quasi-experimental approach which characterises this style of computer model-building extends to using the models in conditional prediction and Dr Batty discusses their role in the planning process, with their use in testing the impact of public policies on existing conditions.