. . Algebra's importance lies in the student's future. . . as essential preparation for the serious study of science, engineering, economics, or for more advanced types of mathematics. . . The primary importance of trigonometry is not in its applications to surveying and navigation, or in making computations about triangles, but rather in the mathematical description of vibrations, rotations, and periodic phenomena of all kinds, including light, sound, alternating currents, and the orbits of the planets around the sun. In this brief, clearly written book, the essentials of geometry, algebra, and trigonometry are pulled together into three complementary and convenient small packages, providing an excellent preview and review for anyone who wishes to prepare to master calculus with a minimum of misunderstanding and wasted time and effort. Students and other readers will find here all they need to pull them through.

    A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabic countries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years.

    Worked examples and exercises support the text. An ELBS/LPBB edition is available.

    

    Mad Minute is a 30- to 40-day sequence of speed drills on the basic number facts. It's perfect for teachers that need to supplement their regular instruction in mathematics with some systematic drill and practice on the number facts - all in as little as five minutes a day!The quantity of basic facts are varied so that a student at a given achievement level can reasonably be expected to recall them in one minute. Level A students never work with more than 30 basic facts at a time, and Level F students work with as many as 60 basic facts at a time.Mad Minute really encourages students to learn their basic facts and to know them as well as they know their own name!

    This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane's Online Encyclopedia of Integer Sequences, at the end of several of the sections.

    Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen. The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates.

    

    This popular book blends both theory and application to equip the reader with an understanding of the basic principles necessary to apply regression model-building techniques in a wide variety of application environments. It assumes a working knowledge of basic statistics and a familiarity with hypothesis testing and confidence intervals, as well as the normal, t, x2, and F distributions. Illustrating all of the major procedures employed by the contemporary software packages MINITAB(r), SAS(r), and S-PLUS(r), the Fourth Edition begins with a general introduction to regression modeling, including typical applications. A host of technical tools are outlined, such as basic inference procedures, introductory aspects of model adequacy checking, and polynomial regression models and their variations. The book discusses how transformations and weighted least squares can be used to resolve problems of model inadequacy and also how to deal with influential observations. Subsequent chapters discuss: * Indicator variables and the connection between regression and analysis-of-variance models * Variable selection and model-building techniques and strategies * The multicollinearity problem--its sources, effects, diagnostics, and remedial measures * Robust regression techniques such as M-estimators, and properties of robust estimators * The basics of nonlinear regression * Generalized linear models * Using SAS(r) for regression problems This book is a robust resource that offers solid methodology for statistical practitioners and professionals in the fields of engineering, physical and chemical sciences, economics, management, life and biological sciences, and the social sciences. Both the accompanying FTP site, which contains data sets, extensive problem solutions, software hints, and PowerPoint(r) slides, as well as the book's revised presentation of topics in increasing order of complexity, facilitate its use in a classroom setting. With its new exercises and structure, this book is highly recommended for upper-undergraduate and beginning graduate students in mathematics, engineering, and natural sciences. Scientists and engineers will find the book to be an excellent choice for reference and self-study.

    We emphasize a careful treatment of basic structures in stochastic processes in symbiosis with the analysis of natural classes of stochastic processes arising from the biological, physical, and social sciences.

    

    

    These intellectuals transformed the uses of calculus from problem-solving methods into a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. Beginning with a survey of the characteristic 19th-century view of analysis, the book proceeds to an examination of the 18th-century concept of calculus and focuses on the innovative methods of Cauchy and his contemporaries in refining existing methods into the basis of rigorous calculus. 1981 edition.

    It defines geometric structure by specifying the parallel transport in an appropriate fiber bundle, focusing on the simplest cases of linear parallel transport in a vector bundle.The treatment opens with an introductory chapter on fiber bundles that proceeds to examinations of connection theory for vector bundles and Riemannian vector bundles. Additional topics include the role of harmonic theory, geometric vector fields on Riemannian manifolds, Lie groups, symmetric spaces, and symplectic and Hermitian vector bundles. A consideration of other differential geometric structures concludes the text, including surveys of characteristic classes of principal bundles, Cartan connections, and spin structures.

    There follows a comprehensive account of the mathematical theory for parallel shear flows. A number of applications of the linear theory are discussed, including the effects of stratification and unsteadiness. The emphasis throughout is on the ideas involved, the physical mechanisms, the methods used, and the results obtained. Wherever possible, the theory is related to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems (for which hints and references are given) not only provide exercises for students but also provide many additional results in a concise form.

    It may be used separately, or with other volumes in the series, or with any other text on theory of functions. It is unusual in its field in being concise, easy to follow, yet complete and rigorous. Demonstrations are full, and proofs are given in detail. THEORY OF FUNCTIONS, PART I considers the general foundations of theory of functions. It provides the student with background for further books on a more advanced level. Stress is upon general foundations rather than upon specific functions.

    It describes the general structure of equilibrium states, the KMS-condition and stability, quantum spin systems and continuous systems.Major changes in the new edition relate to Bose--Einstein condensation, the dynamics of the X-Y model and questions on phase transitions. Notes and remarks have been considerably augmented.

    It may be used separately, or with other volumes in the series,m or with any other text on theory of functions. It is unusual in its field in being concise, easy to follow, yet complete and rigorous. Demonstrations are full, and proofs are given in detail.THEORY OF FUNCTIONS, PART II considers general foundations of theory of functions to a certain extent, but major emphasis is placed upon special functions and characteristic, important types of functions, which are selected from single-valued and multiple-valued classes. Presentation is full.

    It is suitable for advanced undergraduates and graduate students in physics; its sole prerequisite is a first course in quantum mechanics. For applications requiring specialized knowledge, the author supplies background material.The first part of the book develops the techniques of path integration. Topics include probability amplitudes for paths and the correspondence limit for the path integral; vector potentials; the Ito integral and gauge transformations; free particle and quadratic Lagrangians; properties of Green's functions and the Feynman-Kac formula; functional derivatives and commutation relations; Brownian motion and the Wiener integral; and perturbation theory and Feynman diagrams.The second part, dealing with applications, covers asymptotic analysis and the calculus of variations; the WKB approximation and near caustics; the phase of the semiclassical amplitude; scattering theory; and geometrical optics. Additional topics include the polaron; path integrals for multiply connected spaces; quantum mechanics on curved spaces; relativistic propagators and black holes; applications to statistical mechanics; systems with random impurities; instantons and metastability; renormalization and scaling for critical phenomena; and the phase space path integral.

    The emphasis is not on the individual problems, but on methods that solve large classes of problems. The many chapters of the book can be read independently, without references to what precedes or follows. Besides the many problems solved in the book, others are left to the reader to solve, with sketches of solutions given in the later pages.

    Michael Dummett here expands upon his interpretation of Frege, and answers criticisms and objections that have been raised.

    Technical work, 613 pages. Lots of formulas, tables, graphs, charts, etc. Note: because of the amount of material here, the type face is on the small side; just so you know. A standard work in its field.

    It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.

    His clear presentation of the mathematical theory of games of strategy encompasses applications to many fields, including economics, military, business, and operations research. No advanced algebra or non-elementary calculus occurs in most of the proofs.

    This book, first published in 1976, adopts a different approach, developing a language close to that of ordinary discourse. It is intended to encourage readers of varying backgrounds, but especially students, to think spatially. The text is well illustrated, with toned drawings creating three-dimensional effects where appropriate, and there are abundant exercises. Useful appendices accompany the text, providing hints and solutions to these exercises and also a sketch of how the treatment can be modelled within a conventional topology course for more advanced students. The book can be regarded as an example of the emerging discipline of mathematics education, as well as being about surfaces.