The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject.This text is part of the Walter Rudin Student Series in Advanced Mathematics.

    These noteworthy accounts of the lives of David Hilbert and Richard Courant are closely related: Courant's story is, in many ways, seen as the sequel to the story of Hilbert. Originally published to great acclaim, both books explore the dramatic scientific history expressed in the lives of these two great scientists and described in the lively, nontechnical writing style of Contance Reid.

    It is only as a result of pursuing the details of each example that students experience a significant increment in topological understanding. With that in mind, Professors Steen and Seebach have assembled 143 examples in this book, providing innumerable concrete illustrations of definitions, theorems, and general methods of proof. Far from presenting all relevant examples, however, the book instead provides a fruitful context in which to ask new questions and seek new answers.Ranging from the familiar to the obscure, the examples are preceded by a succinct exposition of general topology and basic terminology and theory. Each example is treated as a whole, with a highly geometric exposition that helps readers comprehend the material. Over 25 Venn diagrams and reference charts summarize the properties of the examples and allow students to scan quickly for examples with prescribed properties. In addition, discussions of general methods of constructing and changing examples acquaint readers with the art of constructing counterexamples. The authors have included an extensive collection of problems and exercises, all correlated with various examples, and a bibliography of 140 sources, tracing each uncommon example to its origin.This revised and expanded second edition will be especially useful as a course supplement and reference work for students of general topology. Moreover, it gives the instructor the flexibility to design his own course while providing students with a wealth of historically and mathematically significant examples. 1978 edition.

    Model of clear, scholarly exposition at graduate level with coverage of basic concepts, calculus of variations, principle of virtual work, equations of motion, relativistic mechanics, much more. First inexpensive paperbound edition. Index. Bibliography.

    Will take 25-35 days

    

    Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions. This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading.--back cover

    Many of them will, however, teach mathematics at the high school or junior college level, and this book is intended for those students learning to teach, in addition to a careful presentation of the standard material usually taught in a first course in elementary number theory, this book includes a chapter on quadratic fields which the author has designed to make students think about some of the obvious concepts they have taken for granted earlier. The book also includes a large number of exercises, many of which are nonstandard.

    This work includes differential forms and the elegant forms of Maxwell's equations, and a chapter on probability and statistics. It also illustrates and proves mathematical relations.

    It represents the most extensive revision since the book first appeared in 1948 and provides clear explanations of the methods of rankcorrelation widely used by statisticians, educators, psychologists, and others involved in analyzing qualitative material. Among the many topics covered are the Goodman-Kruskal coefficient, partial rank correlation, trend tests, and regression techniques. Real numerical examples and problems aretaken from interesting research in the social sciences. Expanded tables have also been added that include larger sample sizes and a table of distribution of Kendall's partial law. Reflecting the vast amount of research published in recent years, this edition updates the references and offers over300 new bibliographic entries. The valuable appendix tables have been revised and expanded.

    Included are articles on the nature of physical symmetry, invariance and conservation principles, the structure of solid bodies and of the compound nucleus, the theory of nuclear fission, the effects of radiation on solids, and epistemological problems of quantum mechanics. Other articles deal with the story of the first man-made nuclear chain reaction, the long-term prospects of nuclear energy, the problems of Big Science, and the role of mathematics in the natural sciences. In addition, the book contains statements of Wigner's convictions and beliefs, as well as memoirs of his friends, Enrico Fermi and John von Neumann.

    Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

    A primary source for the history and philosophy of mathematics, Proclus' treatise contains much priceless information about the mathematics and mathematicians of the previous seven or eight centuries that has not been preserved elsewhere. This is virtually the only work surviving from antiquity that deals with what we today would call the philosophy of mathematics.To all the students interested in the logic and history of mathematics and in the relations between philosophy and mathematics in antiquity, this volume will be an invaluable resource. In his new forward, Ian Muller discusses new scholarship on the commentary and places the work in historical and cultural context.

    

    

    The clear presentation of the subject and extensive applications supported with real data helped establish the book as a standard for the field. To date, it has been published into more that ten languages and has gone through five editions. The sixth edition is a major revision over the fifth. It contains new material and results on the Local Limit Theorem, the Integral Law of Large Numbers, and Characteristic Functions. The new edition retains the feature of developing the subject from intuitive concepts and demonstrating techniques and theory through large numbers of examples. The author has, for the first time, included a brief history of probability and its development. Exercise problems and examples have been revised and new ones added.

    It is based on the Markov process as a system model, and uses and iterative technique like dynamic programming as its optimization method.

    

    With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists.

    Both books became instant classics that were used as textbooks for many years and eventually became the basis for our contemporary digital computer systems. The book discusses direct theories of finite differences and integration, linear equations, variations of a constant, and equations of partial and mixed differences. Boole also includes exercises for daring students to ponder, and also supplies answers. Long a proponent of positioning logic firmly in the camp of mathematics rather than philosophy, Boole was instrumental in developing a notational system that allowed logical statements to be symbolically represented by algebraic equations. One of history's most insightful mathematicians, Boole is compelling reading for today's student of logic and Boolean thinking.

    The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook.

    Acton deals with a commonsense approach to numerical algorithms for the solution of equations: algebraic, transcendental, and differential. He assumes that a computer is available for performing the bulk of the arithmetic. The book is divided into two parts, either of which could form the basis of a one-semester course in numerical methods. Part I discusses most of the standard techniques: roots of transcendental equations, roots of polynomials, eigenvalues of symmetric matrices, and so on. Part II cuts across the basic tools, stressing such commonplace problems as extrapolation, removal of singularities, and loss of significant figures. The book is written with clarity and precision, intended for practical rather than theoretical use. This book will interest mathematicians, both pure and applied, as well as any scientist or engineer working with numerical problems.

    Its sole prerequisites are advanced calculus, theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, it discusses numerous practical applications as well. 1970 edition.

    Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

    Drawing on over thirty years of classroom experience, Jacobs shows students how to make observations, discover relationships, and solve problems in the context of ordinary experience. (WorldCat) Subjects: • The path of billiard ball• More billiard-ball mathematics • Inductive reasoning: Finding and extending patterns• The limitations of inductive reasoning • Deductive reasoning: Mathematical proof • Number tricks and deductive reasoning • Arithmetic sequences: Growth at a constant rate • Geometric sequences: Growth at an increasing rate • The binary sequence • The sequence of squares • The sequence of cubes• The Fibonacci sequence• The idea of a function• Descartes and the coordinate graph• Graphing linear functions• Functions with parabolic graphs• More functions with curved graphs• Interpolation and extrapolation: Guessing between and beyond• Large numbers• Scientific notation • An introduction to logarithms• Logarithms and scientific notation• Computing with Logarithms• Logarithmic scales• Symmetry• Regular polygons• Mathematical mosaics• Regular polyhedra: The platonic solids• Semiregular polyhedra• Pyramids and prisms• The circle and the ellipse• The parabola• They hyperbola• The sine curve• Spirals• The cycloid• The fundamental counting principle• Permutations• More on permutations• Combinations• Probability:The measure of chance• Binomial probability• Pascal's triangle• Dice games and probability• Independent and dependent events• The birthday problem: Complementary events• Organizing data: Frequency distributions• The breaking of ciphers and codes: An application of statistics• Measures of location• Measures of variability• Displaying data: Statistical graphs• Collecting data: Sampling• The mathematics of distortion• The seven bridges of Königsberg: An introduction to networks• Euler paths • Trees• The Möbius strip and other surfaces.(WorldCat)