galois theory pure and applied mathematics a wiley series of texts monographs and tracts

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Galois Theory

Author : David A. Cox
ISBN : 9781118072059
Genre : Mathematics
File Size : 34. 90 MB
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Praise for the First Edition ". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!" —Monatshefte fur Mathematik Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel's theory of Abelian equations, casus irreducibili, and the Galois theory of origami. In addition, this book features detailed treatments of several topics not covered in standard texts on Galois theory, including: The contributions of Lagrange, Galois, and Kronecker How to compute Galois groups Galois's results about irreducible polynomials of prime or prime-squared degree Abel's theorem about geometric constructions on the lemniscate Galois groups of quartic polynomials in all characteristics Throughout the book, intriguing Mathematical Notes and Historical Notes sections clarify the discussed ideas and the historical context; numerous exercises and examples use Maple and Mathematica to showcase the computations related to Galois theory; and extensive references have been added to provide readers with additional resources for further study. Galois Theory, Second Edition is an excellent book for courses on abstract algebra at the upper-undergraduate and graduate levels. The book also serves as an interesting reference for anyone with a general interest in Galois theory and its contributions to the field of mathematics.

Fibonacci And Lucas Numbers With Applications

Author : Thomas Koshy
ISBN : 9781118742174
Genre : Mathematics
File Size : 66. 32 MB
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Praise for the First Edition “ ...beautiful and well worth the reading ... with many exercises and a good bibliography, this book will fascinate both students and teachers.” Mathematics Teacher Fibonacci and Lucas Numbers with Applications, Volume I, Second Edition provides a user-friendly and historical approach to the many fascinating properties of Fibonacci and Lucas numbers, which have intrigued amateurs and professionals for centuries. Offering an in-depth study of the topic, this book includes exciting applications that provide many opportunities to explore and experiment. In addition, the book includes a historical survey of the development of Fibonacci and Lucas numbers, with biographical sketches of important figures in the field. Each chapter features a wealth of examples, as well as numeric and theoretical exercises that avoid using extensive and time-consuming proofs of theorems. The Second Edition offers new opportunities to illustrate and expand on various problem-solving skills and techniques. In addition, the book features: • A clear, comprehensive introduction to one of the most fascinating topics in mathematics, including links to graph theory, matrices, geometry, the stock market, and the Golden Ratio • Abundant examples, exercises, and properties throughout, with a wide range of difficulty and sophistication • Numeric puzzles based on Fibonacci numbers, as well as popular geometric paradoxes, and a glossary of symbols and fundamental properties from the theory of numbers • A wide range of applications in many disciplines, including architecture, biology, chemistry, electrical engineering, physics, physiology, and neurophysiology The Second Edition is appropriate for upper-undergraduate and graduate-level courses on the history of mathematics, combinatorics, and number theory. The book is also a valuable resource for undergraduate research courses, independent study projects, and senior/graduate theses, as well as a useful resource for computer scientists, physicists, biologists, and electrical engineers. Thomas Koshy, PhD, is Professor Emeritus of Mathematics at Framingham State University in Massachusetts and author of several books and numerous articles on mathematics. His work has been recognized by the Association of American Publishers, and he has received many awards, including the Distinguished Faculty of the Year. Dr. Koshy received his PhD in Algebraic Coding Theory from Boston University. “Anyone who loves mathematical puzzles, number theory, and Fibonacci numbers will treasure this book. Dr. Koshy has compiled Fibonacci lore from diverse sources into one understandable and intriguing volume, [interweaving] a historical flavor into an array of applications.” Marjorie Bicknell-Johnson

Topology And Its Applications

Author : William F. Basener
ISBN : 9781118626221
Genre : Mathematics
File Size : 25. 15 MB
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Discover a unique and modern treatment of topology employing a cross-disciplinary approach Implemented recently to understand diverse topics, such as cell biology, superconductors, and robot motion, topology has been transformed from a theoretical field that highlights mathematical theory to a subject that plays a growing role in nearly all fields of scientific investigation. Moving from the concrete to the abstract, Topology and Its Applications displays both the beauty and utility of topology, first presenting the essentials of topology followed by its emerging role within the new frontiers in research. Filling a gap between the teaching of topology and its modern uses in real-world phenomena, Topology and Its Applications is organized around the mathematical theory of topology, a framework of rigorous theorems, and clear, elegant proofs. This book is the first of its kind to present applications in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, and population modeling, as well as other areas of science and engineering. Many of these applications are presented in optional sections, allowing an instructor to customize the presentation. The author presents a diversity of topological areas, including point-set topology, geometric topology, differential topology, and algebraic/combinatorial topology. Topics within these areas include: Open sets Compactness Homotopy Surface classification Index theory on surfaces Manifolds and complexes Topological groups The fundamental group and homology Special "core intuition" segments throughout the book briefly explain the basic intuition essential to understanding several topics. A generous number of figures and examples, many of which come from applications such as liquid crystals, space probe data, and computer graphics, are all available from the publisher's Web site.

Introduction To Topology And Geometry

Author : Saul Stahl
ISBN : 9781118546147
Genre : Mathematics
File Size : 42. 11 MB
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An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition “. . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.” —CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the Second Edition: • Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being • Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods • Bridges seemingly disparate topics by creating thoughtful and logical connections • Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.

Principles Of Differential Equations

Author : Nelson G. Markley
ISBN : 9781118031537
Genre : Mathematics
File Size : 24. 9 MB
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An accessible, practical introduction to the principles of differential equations The field of differential equations is a keystone of scientific knowledge today, with broad applications in mathematics, engineering, physics, and other scientific fields. Encompassing both basic concepts and advanced results, Principles of Differential Equations is the definitive, hands-on introduction professionals and students need in order to gain a strong knowledge base applicable to the many different subfields of differential equations and dynamical systems. Nelson Markley includes essential background from analysis and linear algebra, in a unified approach to ordinary differential equations that underscores how key theoretical ingredients interconnect. Opening with basic existence and uniqueness results, Principles of Differential Equations systematically illuminates the theory, progressing through linear systems to stable manifolds and bifurcation theory. Other vital topics covered include: Basic dynamical systems concepts Constant coefficients Stability The Poincaré return map Smooth vector fields As a comprehensive resource with complete proofs and more than 200 exercises, Principles of Differential Equations is the ideal self-study reference for professionals, and an effective introduction and tutorial for students.

Primes Of The Form X2 Ny2

Author : David A. Cox
ISBN : 9781118031001
Genre : Mathematics
File Size : 64. 69 MB
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Logic Of Mathematics

Author : Zofia Adamowicz
ISBN : 9781118030790
Genre : Mathematics
File Size : 44. 85 MB
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A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems: * Gödel's theorems of completeness and incompleteness * The independence of Goodstein's theorem from Peano arithmetic * Tarski's theorem on real closed fields * Matiyasevich's theorem on diophantine formulas Logic of Mathematics also features: * Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types * Clear, concise explanations of all key concepts, from Boolean algebras to Skolem-Löwenheim constructions and other topics * Carefully chosen exercises for each chapter, plus helpful solution hints At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logic-requiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms. Part I contains a thorough introduction to mathematical logic and model theory-including a full discussion of terms, formulas, and other fundamentals, plus detailed coverage of relational structures and Boolean algebras, Gödel's completeness theorem, models of Peano arithmetic, and much more. Part II focuses on a number of advanced theorems that are central to the field, such as Gödel's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems. With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom use-the perfect textbook for advanced students of mathematics, computer science, and logic.

Linear Algebra And Its Applications

Author : Peter D. Lax
ISBN : 9781118626924
Genre : Mathematics
File Size : 45. 80 MB
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Praise for the First Edition ". . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician's bookshelf." -American Mathematical Monthly Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book's accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems. Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces. Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including: The QR algorithm for finding the eigenvalues of a self-adjoint matrix The Householder algorithm for turning self-adjoint matrices into tridiagonal form The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space Additionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy's elegant proof of Halmos' conjecture about the numerical range of matrices. Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals.

Principles Of Linear Algebra With Mathematica

Author : Kenneth M. Shiskowski
ISBN : 9781118627266
Genre : Mathematics
File Size : 21. 79 MB
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A hands-on introduction to the theoretical and computational aspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationally intensive, and computer algebra systems such as Mathematica® are essential not only for learning to apply the concepts to computationally challenging problems, but also for visualizing many of the geometric aspects within this field of study. Principles of Linear Algebra with Mathematica uniquely bridges the gap between beginning linear algebra and computational linear algebra that is often encountered in applied settings, and the commands required to solve complex and computationally challenging problems using Mathematica are provided. The book begins with an introduction to the commands and programming guidelines for working with Mathematica. Next, the authors explore linear systems of equations and matrices, applications of linear systems and matrices, determinants, inverses, and Cramer's rule. Basic linear algebra topics, such as vectors, dot product, cross product, and vector projection are explored, as well as a unique variety of more advanced topics including rotations in space, 'rolling' a circle along a curve, and the TNB Frame. Subsequent chapters feature coverage of linear transformations from Rn to Rm, the geometry of linear and affine transformations, with an exploration of their effect on arclength, area, and volume, least squares fits, and pseudoinverses. Mathematica is used to enhance concepts and is seamlessly integrated throughout the book through symbolic manipulations, numerical computations, graphics in two and three dimensions, animations, and programming. Each section concludes with standard problems in addition to problems that were specifically designed to be solved with Mathematica, allowing readers to test their comprehension of the presented material. All related Mathematica code is available on a corresponding website, along with solutions to problems and additional topical resources. Extensively class-tested to ensure an accessible presentation, Principles of Linear Algebra with Mathematica is an excellent book for courses on linear algebra at the undergraduate level. The book is also an ideal reference for students and professionals who would like to gain a further understanding of the use of Mathematica to solve linear algebra problems.

Post Modern Algebra

Author : Jonathan D. H. Smith
ISBN : 9781118030837
Genre : Mathematics
File Size : 55. 83 MB
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Advanced algebra in the service of contemporary mathematical research-- a unique introduction. This volume takes an altogether new approach to advanced algebra. Its intriguing title, inspired by the term postmodernism, denotes a departure from van der Waerden's Modern Algebra--a book that has dominated the field for nearly seventy years. Post-Modern Algebra offers a truly up-to-date alternative to the standard approach, explaining topics from an applications-based perspective rather than by abstract principles alone. The book broadens the field of study to include algebraic structures and methods used in current and emerging mathematical research, and describes the powerful yet subtle techniques of universal algebra and category theory. Classical algebraic areas of groups, rings, fields, and vector spaces are bolstered by such topics as ordered sets, monoids, monoid actions, quasigroups, loops, lattices, Boolean algebras, categories, and Heyting algebras. The text features: * A clear and concise treatment at an introductory level, tested in university courses. * A wealth of exercises illustrating concepts and their practical application. * Effective techniques for solving research problems in the real world. * Flexibility of presentation, making it easy to tailor material to specific needs. * Help with elementary proofs and algebraic notations for students of varying abilities. Post-Modern Algebra is an excellent primary or supplementary text for graduate-level algebra courses. It is also an extremely useful resource for professionals and researchers in many areas who must tackle abstract, linear, or universal algebra in the course of their work.

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