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 demonstrates how to encourage, develop, and foster the processes which seem to come naturally to mathematicians.

    Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. KEY TOPICS: Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permutations; Orbits, Cycles, and the Alternating Groups; Cosets and the Theorem of Lagrange; Direct Products and Finitely Generated Abelian Groups; Plane Isometries; HOMOMORPHISMS AND FACTOR GROUPS; Homomorphisms; Factor Groups; Factor-Group Computations and Simple Groups; Group Action on a Set; Applications of G-Sets to Counting; RINGS AND FIELDS; Rings and Fields; Integral Domains; Fermat's and Euler's Theorems; The Field of Quotients of an Integral Domain; Rings of Polynomials; Factorization of Polynomials over a Field; Noncommutative Examples; Ordered Rings and Fields; IDEALS AND FACTOR RINGS; Homomorphisms and Factor Rings; Prime and Maximal Ideas; Gr�bner Bases for Ideals; EXTENSION FIELDS; Introduction to Extension Fields; Vector Spaces; Algebraic Extensions; Geometric Constructions; Finite Fields; ADVANCED GROUP THEORY; Isomorphism Theorems; Series of Groups; Sylow Theorems; Applications of the Sylow Theory; Free Abelian Groups; Free Groups; Group Presentations; GROUPS IN TOPOLOGY; Simplicial Complexes and Homology Groups; Computations of Homology Groups; More Homology Computations and Applications; Homological Algebra; Factorization; Unique Factorization Domains; Euclidean Domains; Gaussian Integers and Multiplicative Norms; AUTOMORPHISMS AND GALOIS THEORY; Automorphisms of Fields; The Isomorphism Extension Theorem; Splitting Fields; Separable Extensions; Totally Inseparable Extensions; Galois Theory; Illustrations of Galois Theory; Cyclotomic Extensions; Insolvability of the Quintic; Matrix Algebra MARKET: For all readers interested in abstract algebra.

    This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.

    

    There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study.Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.)Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc. The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references.

    Emphasizes the applications of theory, and contains new material on particle physics, electron-positron annihilation in solids and the Mossbauer effect. Includes new appendices on such topics as crystallography, Fourier Integral Description of a Wave Group, and Time-Independent Perturbation Theory.

    Theory and practice in the design of data graphics, 250 illustrations of the best (and a few of the worst) statistical graphics, with detailed analysis of how to display data for precise, effective, quick analysis. Design of the high-resolution displays, small multiples. Editing and improving graphics. The data-ink ratio. Time-series, relational graphics, data maps, multivariate designs. Detection of graphical deception: design variation vs. data variation. Sources of deception. Aesthetics and data graphical displays. This is the second edition of The Visual Display of Quantitative Information. Recently published, this new edition provides excellent color reproductions of the many graphics of William Playfair, adds color to other images, and includes all the changes and corrections accumulated during 17 printings of the first edition.

    Myerson introduces, clarifies, and synthesizes the extraordinary advances made in the subject over the past fifteen years, presents an overview of decision theory, and comprehensively reviews the development of the fundamental models: games in extensive form and strategic form, and Bayesian games with incomplete information.Game Theory will be useful for students at the graduate level in economics, political science, operations research, and applied mathematics. Everyone who uses game theory in research will find this book essential.

    Daniel Liang teaches concepts of problem-solving and object-oriented programming using a fundamentals-first approach. Beginning programmers learn critical problem-solving techniques then move on to grasp the key concepts of object-oriented and GUI programming using Java 5. Students start with the essential problem-solving and programming concepts (control statements, methods, and arrays), are then introduced to object-oriented programming, graphical user interface (GUI), and applets, and finally to exception handling, I/O, data structures, and other advanced subjects. Liang uses small, simple, and stimulating examples to demonstrate concepts and techniques while longer examples are presented in case studies with overall discussions and thorough line-by-line explanations. Students can now write short, interesting, graphical game programs starting from Chapter 2! reinforcing key concepts with objectives lists, introduction and chapter overviews, easy to follow examples, chapter summaries, review questions, programming exercises, interactive self-test. Students receive solutions to even-numbered programming exercises, source code for the examples in the book, online self assessment (w/over 1000 multiple-choice questions) and ONLINE homework through GRADIANCE, the industries most advanced online homework application. Instructors are offered the most extensive library of support materials available including interactive and animated slides, TestGen (w/over 2000 multiple-choice questions), solutions to all programming exercises, sample exams and supplemental exercises. Available in two versions, the Fundamentals First edition (chapters 1-19) and the Comprehensive version (chapters 1-36).

    This guide also helps you understand the many data-mining techniques in use today.Based on an MBA course Provost has taught at New York University over the past ten years, Data Science for Business provides examples of real-world business problems to illustrate these principles. You’ll not only learn how to improve communication between business stakeholders and data scientists, but also how participate intelligently in your company’s data science projects. You’ll also discover how to think data-analytically, and fully appreciate how data science methods can support business decision-making.Understand how data science fits in your organization—and how you can use it for competitive advantageTreat data as a business asset that requires careful investment if you’re to gain real valueApproach business problems data-analytically, using the data-mining process to gather good data in the most appropriate wayLearn general concepts for actually extracting knowledge from dataApply data science principles when interviewing data science job candidates

    Nobel-Prize-winner Claude Cohen-Tannoudji and his colleagues have written this book to eliminate precisely these difficulties. Fourteen chapters provide a clarity of organization, careful attention to pedagogical details, and a wealth of topics and examples which make this work a textbook as well as a timeless reference, allowing to tailor courses to meet students' specific needs. Each chapter starts with a clear exposition of the problem which is then treated, and logically develops the physical and mathematical concept. These chapters emphasize the underlying principles of the material, undiluted by extensive references to applications and practical examples which are put into complementary sections. The book begins with a qualitative introduction to quantum mechanical ideas using simple optical analogies and continues with a systematic and thorough presentation of the mathematical tools and postulates of quantum mechanics as well as a discussion of their physical content. Applications follow, starting with the simplest ones like e.g. the harmonic oscillator, and becoming gradually more complicated (the hydrogen atom, approximation methods, etc.). The complementary sections each expand this basic knowledge, supplying a wide range of applications and related topics as well as detailed expositions of a large number of special problems and more advanced topics, integrated as an essential portion of the text.

    Air Force Academy and designed as a first course emphasizes the universal variable formulation. Develops the basic two-body and n-body equations of motion; orbit determination; classical orbital elements, coordinate transformations; differential correction; more. Includes specialized applications to lunar and interplanetary flight, example problems, exercises. 1971 edition.

    But for those of us who left math behind in high school, the numbers and figures hurled at us as we go about our days can sometimes leave us scratching our heads and feeling as if we’re fumbling through a mathematical minefield. In this eye-opening and extraordinarily accessible book, mathemati­cian Kit Yates illuminates hidden principles that can help us understand and navigate the chaotic and often opaque surfaces of our world. In The Math of Life and Death, Yates takes us on a fascinating tour of everyday situations and grand-scale applications of mathematical concepts, including exponential growth and decay, optimization, statistics and probability, and number systems. Along the way he reveals the mathematical undersides of controversies over DNA testing, medical screening results, and historical events such as the Chernobyl disaster and the Amanda Knox trial. Readers will finish this book with an enlightened perspective on the news, the law, medicine, and history, and will be better equipped to make personal decisions and solve problems with math in mind, whether it’s choosing the shortest checkout line at the grocery store or halting the spread of a deadly disease.

    Harmonograph is an introduction to the evolution of simple harmonic theory, from the discoveries of Pythagoras to diatonic tuning and equal temperament. Beautiful drawings show the octave as triangle, the fifth as pentagram; diagrams show the principles of harmonics, overtones, and the monochord. Anthony Ashton examines the phenomenon of resonance in Chladni patterns, describes how to build a harmonograph of your own, and provides tables of world tuning systems. This inspiring book will appeal to musicians, mathematicians, designers, and artists alike.