Algebra Books
De Gruyter Fixed Point Theory and Functional Analysis
£138.22
Springer Spektrum Lineare Algebra
Book Synopsis
£23.74
Walter de Gruyter & Co Algebra and Geometry
Table of ContentsFrontmatter -- Introduction -- Contents -- 1. Elements of Mathematics (165) -- Preface (1) (164) -- Preface (2) (94a) -- 1. Introduction, on Mathematics in General -- 2. Sequences -- 3. The Fundamental Operations in Algebra -- 4. Factors -- 5. Negative Numbers -- 6. Fractional Quantities -- 7. Simple Equations -- 8. Ratios and Proportions -- 9. Surds -- 10. Topical Geometry -- 11. Graphics and Perspective -- 2. New Elements of Geometry Based on Benjamin Peirce’s Works and Teachings (94) -- Preface -- Book I. Fundamental Properties of Space -- Book II. Topology -- Book III. Graphics -- Book IV. Metrics -- 3. Topical Geometry (137) -- Topical Geometry (137) -- 4. Appendices -- A. On the Quadratic Equation (86) -- B. Rational Fractions (278a fragment) -- C. Numerical Equations (69) -- D. [Additional Definitions] (from 166 and 150) -- E. [A Gloss. Elliptic, Hyperbolic, and Parabolic Measurement] (150) -- F. A Geometrico-Logical Discussion (126) -- G. [Projective Space] (part of 114) -- H. [Logic of Number – Le Fevre] (229) -- I. [Additional Theorems] (150 and 266) -- J. Promptuarium of Analytical Geometry (part of 102) -- K. Pythagorean Triangles (109) -- L. Analysis of Time (part of 138) -- M. Plan of Geometry (132) -- N. [Non-Euclidean Representation] (105) -- O. An Attempt to State Systematically the Doctrine of the Census in Geometrical Topics or Topical Geometry, More Commonly known as ‘Topology’; Being, a Mathematico- Logical Recreation of C. S. Peirce. Following the Lead of J. B. Listing’s Paper in the Göttinger Abhandlungen (from 145) -- P. [“Census” from Century Dictionary with Model] -- Q. Chapter III The Nature of Logical Inquiry (608) -- R. Three Problems -- S. Comments on Cayley’s Memoir on Abstract Geometry from the Point of View of the Logic of Relatives (546) -- T. [Obituary. Prof. Arthur Cayley] -- U. [From an Address to National Academy of Sciences] (95) -- Key to Greek Terms -- Key to Contents of MS. 165 -- Key to Contents of MS. 94 -- Index of Names -- Subject Index
£172.90
McGraw-Hill Education Beginning Algebra ISE
Book SynopsisThe 6th Edition of Beginning Algebra continues the Miller/O''Neill/Hyde author team's approach in addressing the needs of developmental level students to help them get better results. Content updates include new end-of-section activities, prerequisite review exercises, and new study skills videos. This new edition is available in ALEKS 360. In a single platform, ALEKS provides a balance of adaptive practice for skill mastery and homework, tests, and quizzes for application and assessment so that you can create the assignments your students need to have the best outcome in your course. In addition to content updates to the text, we are continuously adding new features to ALEKS 360including new video assignments, an enhanced gradebook experience, end-of-chapter questions aligned to the text, and more.Table of ContentsChapter 1: The Set of Real NumbersChapter 2: Linear Equations and InequalitiesChapter 3: Graphing Linear Equations in Two VariablesChapter 4: Systems of Linear Equations in Two VariablesChapter 5: Polynomials and Properties of ExponentsChapter 6: Factoring PolynomialsChapter 7: Rational Expressions and EquationsChapter 8: RadicalsChapter 9: Quadratic Equations, Complex Numbers, and Functions
£72.89
Elsevier Science Vertex Operator Algebras and the Monster
Trade Review"This book is a detailed research monograph which contains the complete proofs of the authors' previously announced results. It is mostly self-contained and the exposition, given the technicalities involved, could not have been any better. It will be an asset to research mathematicians as well as physicists, and certainly deserves a place in every mathematics and physics library." --MATHEMATICAL REVIEWS "The present book shows how this group arises as the symmetry group of a certain vertex-operator algebra....'One fact, however, is undeniable. As the automorphism group of a distinguished conformal field theory, the Monster is fundamentally related to one of the most spectacular chapters of modern theoretical physics--string theroy." --N.J.A. SLoane, AT&T Laboratories quoted in AMERICAN SCIENTISTTable of ContentsLie Algebras. Formal Calculus: Introduction. Realizations of sl(2) by Twisted Vertex Operators. Realizations of sl(2) by Untwisted Vertex Operators. Central Extensions. The Simple Lie Algebras An, Dn, En. Vertex Operator Realizations of An, Dn, En. General Theory of Untwisted Vertex Operators. General Theory of Twisted Vertex Operators. The Moonshine Module. Triality. The Main Theorem. Completion of the Proof. Appendix: Complex Realization of Vertex Operator Algebras. Bibliography. Index of frequently used symbols. Index.
£62.69
Barcharts, Inc Algebraic Equations Quick Study Quizzer
Book SynopsisThis guide outlines basic algebraic equations, formulas, properties & operations.
£8.98
World Scientific Publishing Co Pte Ltd Linear Algebra Ii: Advanced Topics For
Book SynopsisThis is the second volume of the two-volume book on linear algebra in the University of Tokyo (UTokyo) Engineering Course.The objective of this second volume is to branch out from the standard mathematical results presented in the first volume to illustrate useful specific topics pertaining to engineering applications. While linear algebra is primarily concerned with systems of equations and eigenvalue problems for matrices and vectors with real or complex entries, this volumes covers other topics such as matrices and graphs, nonnegative matrices, systems of linear inequalities, integer matrices, polynomial matrices, generalized inverses, and group representation theory.The chapters are, for the most part, independent of each other, and can be read in any order according to the reader's interest. The main objective of this book is to present the mathematical aspects of linear algebraic methods for engineering that will potentially be effective in various application areas.
£999.99
Pearson Intermediate Algebra Books a la Carte Edition
Book Synopsis
£218.09
Pearson Introductory and Intermediate Algebra Books a la
Book Synopsis
£228.10
Pearson Mylab Math for Prealgebra Introductory Algebra
Book Synopsis
£125.99
Pearson Prealgebra Introductory Algebra Books a La Carte
Book Synopsis
£230.63
Pearson College Mathematics for Trades and Technologies
Book Synopsis
£233.99
Pearson College Algebra with Intermediate Algebra A
Book Synopsis
£203.98
Oxford University Press Invitation to Discrete Mathematics
Book SynopsisA clear and self-contained introduction to discrete mathematics for undergraduates and early graduates.Trade ReviewReview from previous edition 'The book is a self-contained introduction to discrete mathematics, and in particular to combinatorics and graph theory. It is aimed at undergraduate and early graduate students and encourages an active, problem-solving approach to the material. The book treats selected topics in unusual depth and from several points of view.' * Zentralblatt fur Didaktik der Mathematik *'...a far-from-traditional textbook and...a joy to read. The text is lucid and sprinkled with small jokes and background stories.' * Times Higher Education Supplement, Friday 26th November 1999 *Table of ContentsPREFACE TO THE SECOND EDITION; PREFACE TO THE FIRST EDITION; APPENDIX; BIBLIOGRAPHY; HINTS TO SELECTED EXERCISES; INDEX
£90.86
Birkhauser Boston Trigonometry Gelfand Mathematical Seminar Series
Book SynopsisIt leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. Trigonometry is an important introduction to calculus, where one stud ies what mathematicians call analytic properties of functions.Trade Review"Cover[s] all of the basic topics that a high school or beginning university student should be expected to know.... There are...some nice touches; for example, a nice informal discussion showing that the sine of an angle in a right triangle does not depend on whether the sides are measured in inches or centimeters..." —Choice "Covers all the basics of the subject through beautiful illustrations and examples…. Throughout, the treatment stimulates the reader to think of mathematics as a unified subject." — L'enseignement Mathématique "As a teacher I enjoyed this book enormously and I will doubtless borrow many of the plums to spice up my lessons…. [For] that ideal student who is to be prepared to be challenged to think what the subject is really about, and has the patience to excavate the basic ideas for all they are worth before jumping on to the next chapter, it should prove to be a godsend." —The Mathematical Gazette "The authors tried to explain the results of trigonometry as simply as possible…. The exercises include a few problems of each routine type. Most of the problems exhibit a new aspect of the technique or object under discussion. One of the goals of this book is to prepare students for a course in calculus. We recommend it for teachers and students." —Publicationes MathematicaeTable of Contents0 Trigonometry.- 1 Trigonometric Ratios in a Triangle.- 2 Relations among Trigonometric Ratios.- 3 Relationships in a Triangle.- 4 Angles and Rotations.- 5 Radian Measure.- 6 The Addition Formulas.- 7 Trigonometric Identities.- 8 Graphs of Trigonometric Functions.- 9 Inverse Functions and Trigonometric Equations.
£29.99
Birkhauser Boston Lie Groups Beyond an Introduction Progress in
Book SynopsisThis book takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics.Trade Review"Anthony Knapp's Lie Groups Beyond an Introduction, 2nd edition, is a beautiful introduction to this area of mathematics, appropriate for a variety different audiences.... The book is well-organized with concise, focused introductions to each chapter, a very thorough index of notation, and appendices.... In addition, there are hints to the hundreds of exercises, and a section on historical notes.... Knapp's writing is clear, and he avoids excessive notation. The first few chapters comprise a standard introductory course in Lie theory, while numerous second courses could be taught out of the later chapters. Its breadth of coverage and extensive tables also make the book a valuable reference for researchers in representation theory." —MAA Reviews (review of the second edition) "The first edition of the present book appeared in 1996, and quickly became one of the standard references on the subject…. The present edition has been perfected even further, apart from straightening occasional errors…and making various revisions throughout, by adding a new introduction and two new chapters [IX and X]…. Chapter IX contains a treatment of induced representations and branching theorems…. Chapter X is largely about actions of compact Lie groups on polynomial algebras, pointing toward invariant theory and some routes to infinite-dimensional representation theory…. This is an excellent monograph, which, as with the previous edition, can be recommended both as a textbook or for reference to anyone interested in Lie theory." —Mathematical Bohemica (review of the second edition) "The important feature of the present book is that it starts from the beginning (with only a very modest knowledge assumed) and covers all important topics.... The book is very carefully organized [and] ends with 20 pages of useful historic comments. Such a comprehensive and carefully written treatment of fundamentals of the theory will certainly be a basic reference and text book in the future." —Newsletter of the EMS (review of the first edition) "Each chapter begins with an excellent summary of the content and ends with an exercise section.... This is really an outstanding book, well written and beautifully produced. It is both a graduate text and a monograph, so it can be recommended to graduate students as well as to specialists." —Publicationes Mathematicae (review of the first edition) "This is a wonderful choice of material. Any graduate student interested in Lie groups, differential geometry, or representation theory will find useful ideas on almost every page. Each chapter is followed by a long collection of problems [that] are interesting and enlightening [and] there are extensive hints at the back of the book. The exposition...is very careful and complete.... Altogether this book is delightful and should serve many different audiences well. It would make a fine text for a second graduate course in Lie theory." —Bulletin of the AMS (review of the first edition) "This is a fundamental book and none, beginner or expert, could afford to ignore it. Some results are really difficult to be found in other monographs, while others are for the first time included in a book." —Mathematica (review of the first edition) "The book is written in a very clear style, with detailed treatment of many relevant examples. . . . The book is eminently suitable as a text from which to learn Lie theory." —Mathematical Reviews (review of the first edition) "The important feature of the present book is that it starts from the beginning (with only a very modest knowledge assumed) and covers all important topics... The book is very carefully organized [and] ends with 20 pages of useful historic comments. Such a comprehensive and carefully written treatment of fundamentals of the theory will certainly be a basic reference and textbook in the future." —Newsletter of the EMS (review of the first edition) "It is a pleasure to read this book. It should serve well different audiences. It perfectly suits as a text book to learn Lie theory, including Lie groups, representation theory, and structure theory of Lie algebras. The absense of misprints and errors as well as the long collection of problems including hints at the back of the book make it suitable for self-study. . . At the end there are a lot of enlightening historical remarks, references, and additional results which can serve as a guide for further reading. The book has two good indices. Specialists will be able to use it as a reference for formulation and proofs of the basic results but also for details concerning examples of semisimple groups." ---ZAATable of ContentsPreface to the Second Edition * Preface to the First Edition * List of Figures * Prerequisites by Chapter * Standard Notation * Introduction: Closed Linear Groups * Lie Algebras and Lie Groups * Complex Semisimple Lie Algebras * Universal Enveloping Algebra * Compact Lie Groups * Finite-Dimensional Representations * Structure Theory of Semisimple Groups * Advanced Structure Theory * Integration * Induced Representations and Branching Theorems * Prehomogeneous Vector Spaces * Appendices * Hints for Solutions of Problems * Historical Notes * References * Index of Notation * Index
£104.49
MP-AMM American Mathematical Kvant Selecta Part 1
Book SynopsisPresents the Russian tradition of expository mathematical writing. Suitable for students and teachers who want to study its various aspects, this book includes topics in number theory. It treats diverse aspects of analysis and algebra.Table of ContentsThe arithmetic of binomial coefficients by D. B. Fuchs and M. B. Fuchs Do you like messing around with integers? by M. I. Bashmakov On Bertrand's conjecture by M. I. Bashmakov On best approximations. I by D. B. Fuchs and M. B. Fuchs On best approximations. II by D. B. Fuchs and M. B. Fuchs On a certain property of binomial coefficients by A. I. Shirshov On $n!$ and the number $e$ (Several approaches to a certain problem) by L. G. Limanov Rational approximations and transcendence by D. B. Fuchs and M. B. Fuchs Close fractions by V. N. Vaguten On the equation $\binom{n}{m} = \binom{n+1}{m-1}$ by A. I. Shirshov On regular polygons, Euler's function, and Fermat numbers by A. Kirillov 2-adic numbers by B. Bekker, S. Vostokov, and Yu. Ionin On the number $e$ by E. Kuzmin and A. Shirshov Markov's Diophantine equation by M. G. Krein The arithmetic of Gaussian integers by A. B. Goncharov Three formulas of Ramanujan by V. S. Shevelev Amazing adventures in the land of repeating decimals by V. G. Stolyar, E. A. Kuraev, Z. K. Silogadze, G. A. Galperin, and A. V. Korlyukov.
£38.90
Taylor & Francis Ltd (Sales) Logic and Algebra 180 Lecture Notes in Pure and
Book SynopsisAttempts to unite the fields of mathematical logic and general algebra. Presents a collection of refereed papers inspired by the International Conference on Logic and Algebra held in Siena, Italy, in honor of the late Italian mathematician Roberto Magari, a leading force in the blossoming of research in mathematical logic in Italy since the 1960s.Trade Review"Many papers in this volume are valuable contributions to mathematical logic, universal algebra, and category theory, and the volume is recommended to researchers in these fields. "---Studia Scientiarum Mathematicarum HungaricaTable of ContentsPreface, Acknowledgments, List o f Participants, Invited Papers, Contributed Papers,
£276.25
CRC Press Concise Introduction to Linear Algebra
Book SynopsisConcise Introduction to Linear Algebra deals with the subject of linear algebra, covering vectors and linear systems, vector spaces, orthogonality, determinants, eigenvalues and eigenvectors, singular value decomposition. It adopts an efficient approach to lead students from vectors, matrices quickly into more advanced topics including, LU decomposition, orthogonal decomposition, Least squares solutions, Gram-Schmidt process, eigenvalues and eigenvectors, diagonalizability, spectral decomposition, positive definite matrix, quadratic forms, singular value decompositions and principal component analysis. This book is designed for onesemester teaching to undergraduate students.Table of ContentsVectors and linear systems. Solving linear systems. Vector spaces. Orthogonality. Determinants. Eigenvalues and Eigenvectors. Singular value decomposition.
£84.99
Taylor & Francis Ltd Topological Methods for Differential Equations
Book SynopsisTopological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis. Table of ContentsIntroduction. 1 Background in Multi-valued Analysis. 2 Hausdor□-Pompeiu Metric Topology. 3 Measurable Multifunctions. Measurable selection. 4 Continuous Selection Theorems. 5 Linear Multivalued Operators. 6 Fixed Point Theorems. 7 Generalized Metric and Banach Spaces. 8 Fixed Point Theorems in Vector Metric and Banach Spaces. 9 Random □xed point theorem. 10 Semigroups. 11 Systems of Impulsive Di□erential Equations on the Half-line. 12 Di□erential Inclusions. 13 Random Systems of Di□erential Equations. 14 Random Fractional Di□erential Equations via Hadamard Fractional Derivatives. 15 Existence Theory for Systems of Discrete Equations. 16 Discrete Inclusions. 17 Semilinear System of Discrete Equations. 18 Discrete Boundary Value Problems. 19 Appendix.
£155.00
Taylor & Francis Ltd An Introduction to Linear Algebra
Book SynopsisThe techniques of linear algebra are used extensively across the applied sciences, and in many different areas of algebra such as group theory, module theory, representation theory, ring theory, and Galois theory. Written by experienced researchers with a decades of teaching experience, Introduction to Linear Algebra is a clear and rigorous introductory text on this key topic for students of both applied sciences and pure mathematics. Table of ContentsLinear Vector Spaces. Matrices. Determinants. Invertible Matrices. Linear Systems. LU Factorization. Linear Dependence and Independence. Bases and Dimension. Coordinates and Isomorphisms. Rank of a Matrix. Linear Mappings. Matrix Representation of Linear Mappings. Inner Products and Orthogonality. Linear Functionals. Eigenvalues and Eigenvectors. Normed Linear Spaces. Diagonalization. Singular Value Decomposition. Differential and Difference Systems. Least Squares Approximation. Quadratic Forms. Positive Definite Matrices. Moore–Penrose Inverse.Special Matrices.
£84.99
Pearson Education Algebra and Trigonometry Global Edition MyLab
Book SynopsisBob Blitzer is a native of Manhattan and received aBachelor of Arts degree with dual majors in mathematics and psychology (minor:English literature) from the City College of New York. His unusual combinationof academic interests led him toward a Master of Arts in mathematics from theUniversity of Miami and a doctorate in behavioral sciences from NovaUniversity. Bob's love for teaching mathematics was nourished for nearly 30years at Miami Dade College, where he received numerous teaching awards,including Innovator of the Year from the League for Innovations in theCommunity College and an endowed chair based on excellence in the classroom. Inaddition to Algebra and Trigonometry, Bob has written textbookscovering developmental mathematics, introductory algebra, intermediate algebra,trigonometry, precalculus, and liberal arts mathematics, all published byPearson. When not secluded in his Northern California writer's cabin, Bob canbe found hikin
£76.04
CRC Press Advanced Linear Algebra for Engineers with MATLAB
Book SynopsisArming readers with both theoretical and practical knowledge, Advanced Linear Algebra for Engineers with MATLAB provides real-life problems that readers can use to model and solve engineering and scientific problems in fields ranging from signal processing and communications to electromagnetics and social and health sciences. Facilitating a unique understanding of rapidly evolving linear algebra and matrix methods, this book: Outlines the basic concepts and definitions behind matrices, matrix algebra, elementary matrix operations, and matrix partitions, describing their potential use in signal and image processing applications Introduces concepts of determinants, inverses, and their use in solving linear equations that result from electrical and mechanical-type systems Presents special matrices, linear vector spaces, and fundamental principles of orthogonality, using an appropriate blend of abstract and concreteTable of Contents Matrices, Matrix Algebra, and Elementary Matrix Operations. Determinants, Matrix Inversion and Solutions to Systems of Linear Equations. Linear Vector Spaces. Eigenvalues and Eigenvectors. Matrix Polynomials and Functions of Square Matrices. Introduction to Optimization. Appendix A: The Laplace Transform. Appendix B: The z-Transform. Bibliography. Index.
£115.00
Taylor & Francis Ltd Factoring Groups into Subsets
Book SynopsisDecomposing an abelian group into a direct sum of its subsets leads to results that can be applied to a variety of areas, such as number theory, geometry of tilings, coding theory, cryptography, graph theory, and Fourier analysis. Focusing mainly on cyclic groups, Factoring Groups into Subsets explores the factorization theory of abelian groups. The book first shows how to construct new factorizations from old ones. The authors then discuss nonperiodic and periodic factorizations, quasiperiodicity, and the factoring of periodic subsets. They also examine how tiling plays an important role in number theory. The next several chapters cover factorizations of infinite abelian groups; combinatorics, such as Ramsey numbers, Latin squares, and complex Hadamard matrices; and connections with codes, including variable length codes, error correcting codes, and integer codes. The final chapter deals with several classical problems of Fuchs.EncompassTrade ReviewThe book under review was written by two leading experts in this field.… The exposition is clear and detailed—it is enriched with examples and exercises—making the book, as envisioned by the authors, readily accessible to non-experts in the field.—Mathematical Reviews, Issue 2010hTable of ContentsIntroduction. New Factorizations from Old Ones. Nonperiodic Factorizations. Periodic Factorizations. Various Factorizations. Factoring by Many Factors. Group of Integers. Infinite Groups. Combinatorics. Codes. Some Classical Problems. References. Index.
£204.25
Taylor & Francis Inc MATLAB Primer
Book SynopsisHighlighting the new aspects of MATLAB 7.10 and expanding on many existing features, MATLAB Primer, Eighth Edition shows you how to solve problems in science, engineering, and mathematics. Now in its eighth edition, this popular primer continues to offer a hands-on, step-by-step introduction to using the powerful tools of MATLAB.New to the Eighth Edition A new chapter on object-oriented programming Discussion of the MATLAB File Exchange window, which provides direct access to over 10,000 submissions by MATLAB users Major changes to the MATLAB Editor, such as code folding and the integration of the Code Analyzer (M-Lint) into the Editor Explanation of more powerful Help tools, such as quick help popups for functions via the Function Browser The new bsxfun function A synopsis of each of the MATLAB Top 500 most frequently used functions, operators, andTrade Review This primer is a useful little booklet. It presents language features in a progressive manner, with the easy things first and more sophisticated features built onto these. … it also serves as a reference work and is a useful supplement to the online help that comes with MATLAB itself. … The presentation throughout is clear and concise, with the text enlivened by illustrative examples where appropriate. Altogether, the book is a complete course in MATLAB, including a careful introduction to object-oriented programming and other advanced and powerful features. I highly recommend this book to MATLAB users at all levels of expertise.—J.C. Butcher, Computing Reviews, October 2011 After many years away from MATLAB, I am now picking it up again to do some research in signal processing strategies for cochlear implants. As I got into it, I realized that I had forgotten enough of the details as to be pretty useless so I got this book and started from scratch. I love this book! Extremely well written. I especially like the examples that the author intentionally ‘botched’ in order to make teaching points.—J. Mark Elder, M.D., Ph.D., Aztek Networks, Inc, Boulder, Colorado, USA Table of ContentsGetting Started. The MATLAB Desktop. Matrices and Matrix Operations. Submatrices and Colon Notation. MATLAB Functions. M-Files. Control Flow Statements. Advanced Data Structures. Object-Oriented Programming. Advanced M-File Features. Code Development Tools. Calling C from MATLAB. Calling Fortran from MATLAB. Calling Java from MATLAB. Two-Dimensional Graphics. Three-Dimensional Graphics. Advanced Graphics. Sparse Matrix Computations. The Symbolic Math Toolbox. Polynomials, Interpolation, and Integration. Solving Equations. Displaying Results. Cell Publishing. Appendices. Index.
£30.57
Taylor & Francis Inc Linear and Complex Analysis for Applications
Book SynopsisLinear and Complex Analysis for Applications aims to unify various parts of mathematical analysis in an engaging manner and to provide a diverse and unusual collection of applications, both to other fields of mathematics and to physics and engineering. The book evolved from several of the author's teaching experiences, his research in complex analysis in several variables, and many conversations with friends and colleagues. It has three primary goals: to develop enough linear analysis and complex variable theory to prepare students in engineering or applied mathematics for advanced work, to unify many distinct and seemingly isolated topics, to show mathematics as both interesting and useful, especially via the juxtaposition of examples and theorems. The book realizes these goals by beginning with reviews of Linear Algebra, Complex Numbers, and topics frTable of ContentsChapter 1. Linear algebra; Chapter 2. Complex numbers; Chapter 3. Vector analysis; Chapter 4. Complex analysis; Chapter 5. Transform methods; Chapter 6. Hilbert spaces; Chapter 7. Examples and applications; Chapter 8. Appendix: The language of mathematics; References; Index
£84.99
Taylor & Francis Inc Iterative Methods and Preconditioning for Large
Book SynopsisThis book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems.The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.Trade ReviewThe book can be used for a Master and/or Ph.D. level graduate course in science and engineering and can be useful to researchers from any eld of engineering, health, physical, chemical and biological sciences.-Constantin Popa, Zentralblatt MATHTable of ContentsIntroduction and Motivations; Some iterative algorithms for linear systems; General purpose preconditioning strategies; Preconditioners for some structured linear systems; Appendix A: A Review of Numerical Linear Algebra; Appendix B: Data sets and software codes
£147.25
Taylor & Francis Inc Bounds for Determinants of Linear Operators and
Book SynopsisThis book deals with the determinants of linear operators in Euclidean, Hilbert and Banach spaces. Determinants of operators give us an important tool for solving linear equations and invertibility conditions for linear operators, enable us to describe the spectra, to evaluate the multiplicities of eigenvalues, etc. We derive upper and lower bounds, and perturbation results for determinants, and discuss applications of our theoretical results to spectrum perturbations, matrix equations, two parameter eigenvalue problems, as well as to differential, difference and functional-differential equations.Trade Review "[This] book is well written and some long computations are presented in a convincing manner. This book will surely be useful to specialists in operator theory, as well as to those interested in its applications, especially for the treatment of the determinants associated to Nakano and Orlicz type operators, among others. Graduate students may also be interested in some chapters of this work, in particular those containing improvements of certain classical results."- F.-H. Vasilescu, Mathematical Reviews, August 2017"[This] book is well written and some long computations are presented in a convincing manner. This book will surely be useful to specialists in operator theory, as well as to those interested in its applications, especially for the treatment of the determinants associated to Nakano and Orlicz type operators, among others. Graduate students may also be interested in some chapters of this work, in particular those containing improvements of certain classical results."- F.-H. Vasilescu, Mathematical Reviews, August 2017Table of ContentsPreliminaries. Determinants of Schatten-Von Neumann Operators. Determinants of Nakano Type Operators. Determinants of Orlicz Type Operators. Determinants of p-summing Operators. Multiplicative Representations of Resolvents. Inequalities Between Determinants and Resolvents. Bounds for Eigenvalues and Determinants Via Self-commutators.Discrete Spectra of Compactly Perturbed Bounded Operators. Operators on Tensor Products of Euclidean Spaces and Matrix Equations. Two-parameter Matrix Eigenvalue Problem. Differential, Difference and Functional-differential equations
£155.00
Society for Industrial & Applied Mathematics,U.S. Numerical Linear Algebra
Book SynopsisSince its original appearance in 1997, Numerical Linear Algebra has been a leading textbook in its field, used in universities around the world. It is noted for its 40 lecture-sized short chapters and its clear and inviting style. It is reissued here with a new foreword by James Nagy and a new afterword by Yuji Nakatsukasa about subsequent developments.Trade ReviewA beautifully written textbook offering a distinctive and original treatment.""- Nicholas J. Higham, University of Manchester""Offers a rarely seen integration of computation and theory, illuminated by judiciously chosen examples.""- Ilse Ipsen, North Carolina State University""Almost the perfect text to introduce graduate students to the subject.""- Daniel Szyld, Temple University""An ideal book for a graduate course in numerical linear algebra.""- Suely Oliveira, University of Iowa
£32.36
Springer Nature Switzerland AG The Brauer–Grothendieck Group
Book SynopsisThis monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was discovered soon after this group was introduced by Grothendieck. The Brauer–Manin obstruction plays a crucial role in the study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to establish the irrationality of many new classes of algebraic varieties. The book covers the vast theory underpinning these and other applications. Intended as an introduction to cohomological methods in algebraic geometry, most of the book is accessible to readers with a knowledge of algebra, algebraic geometry and algebraic number theory at graduate level. Much of the more advanced material is not readily available in book form elsewhere; notably, de Jong’s proof of Gabber’s theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer–Manin obstruction, and proof of the finiteness theorem for the Brauer group of abelian varieties and K3 surfaces over finitely generated fields. The book surveys recent work but also gives detailed proofs of basic theorems, maintaining a balance between general theory and concrete examples. Over half a century after Grothendieck's foundational seminars on the topic, The Brauer–Grothendieck Group is a treatise that fills a longstanding gap in the literature, providing researchers, including research students, with a valuable reference on a central object of algebraic and arithmetic geometry.Trade Review“The book gives a comprehensive, clear, up-to date presentation of the theory, including most proofs. A particular strength is that it nicely collects many results, examples and counterexamples from various areas of algebraic and arithmetic geometry … . the book fills a wide gap and is a most welcome addition to the literature.” (Stefan Schröer, zbMATH 1490.14001, 2022)“This book has collected in one place much of the fundamental cohomological theory of the Brauer group, along with excellent references. It then gives some coverage of further results, especially on the two important topics of obstructions to rationality and obstructions to the Hasse principle. For whatever is not included in this book, it gives a thorough and coherent overview of the relevant literature. Approximately four hundred references are given.” (Thomas Benedict Williams, Mathematical Reviews, September, 2022)Table of Contents1 Galois Cohomology.- 2 Étale Cohomology.- 3 Brauer Groups of Schemes.- 4 Comparison of the Two Brauer Groups, II.- 5 Varieties Over a Field.- 6 Birational Invariance.- 7 Severi–Brauer Varieties and Hypersurfaces.- 8 Singular Schemes and Varieties.- 9 Varieties with a Group Action.- 10 Schemes Over Local Rings and Fields.- 11 Families of Varieties.- 12 Rationality in a Family.- 13 The Brauer–Manin Set and the Formal Lemma.- 14 Are Rational Points Dense in the Brauer–Manin Set?.- 15 The Brauer–Manin Obstruction for Zero-Cycles.- 16 Tate Conjecture, Abelian Varieties and K3 Surfaces.- Bibliography.- Index.
£999.99
Springer Nature Switzerland AG Topics in Groups and Geometry: Growth,
Book SynopsisThis book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today.The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.Table of Contents- Foreword.- Preface.- Part I Algebraic Theory: 1. Free Groups.- 2. Nilpotent Groups.- 3. Residual Finiteness and the Zassenhaus Filtration.- 4. Solvable Groups.- 5. Polycyclic Groups.- 6. The Burnside Problem.- Part II Geometric Theory: 7. Finitely Generated Groups and Their Growth Functions.- 8. Hyperbolic Plane Geometry and the Tits Alternative.- 9. Topological Groups, Lie Groups, and Hilbert Fifth Problem.- 10. Dimension Theory.- 11. Ultrafilters, Ultraproducts, Ultrapowers, and Asymptotic Cones.- 12. Gromov’s Theorem.- Part III Analytic and Probabilistic Theory: 13. The Theorems of Polya and Varopoulos.- 14. Amenability, Isoperimetric Profile, and Følner Functions.- 15. Solutions or Hints to Selected Exercises.- References.- Subject Index.- Index of Authors.
£999.99
Springer International Publishing AG Algebraic Number Theory
Book SynopsisThis undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform.The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.Trade Review“Undergraduate mathematics students need both to develop facility with numerical and symbolic calculation and comfort with abstraction. Algebraic number theory offers an ideal context for encountering the synthesis of these goals. One could compile a shelf of graduate-level expositions of algebraic number theory, and another shelf of undergraduate general number theory texts that culminate with a first exposure to it. … Summing Up: Highly recommended. Upper-division undergraduates.” (D. V. Feldman, Choice, Vol. 52 (8), April, 2015)“In this book, the author leads the readers from the theorem of unique factorization in elementary number theory to central results in algebraic number theory. … This book is designed for being used in undergraduate courses in algebraic number theory; the clarity of the exposition and the wealth of examples and exercises (with hints and solutions) also make it suitable for self-study and reading courses.” (Franz Lemmermeyer, zbMATH, Vol. 1303, 2015)Table of ContentsUnique factorisation in the natural numbers.- Number fields.- Fields, discriminants and integral bases.- Ideals.- Prime ideals and unique factorisation.- Imaginary quadratic fields.- Lattices and geometrical methods.- Other fields of small degree.- Cyclotomic fields and the Fermat equation.- Analytic methods.- The number field sieve.
£29.99
Springer International Publishing AG An Excursion through Elementary Mathematics,
Book SynopsisThis book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This third and last volume covers Counting, Generating Functions, Graph Theory, Number Theory, Complex Numbers, Polynomials, and much more.As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level.The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.Table of Contents
£999.99
Springer International Publishing AG An Excursion through Elementary Mathematics,
Book SynopsisThis book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This first volume covers Real Numbers, Functions, Real Analysis, Systems of Equations, Limits and Derivatives, and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.Trade Review“This book develops several basic concepts in elementary mathematics and which are needed in the preparation of mathematical Olympiads around the world. … Throughout the book, the author puts great emphasis on explaining the issues discussed. … The presentation is pedagogical and coherent throughout with emphasis on concepts and underlying ideas … . The author has succeeded in crafting a comprehensive book to give a well-rounded picture of the role of real numbers and functions in elementary mathematics.” (Teodora Liliana Rădulescu, zbMATH 1371.97002, 2017)Table of ContentsChapter 1 The Set of Real Numbers.- Chapter 2 Algebraic Identities, Equations and Systems.- Chapter 3 Elementary Sequences.- Chapter 4 Induction and the Binomial Formula.- Chapter 5 Elementary Inequalities.- Chapter 6 The Concept of Function.- Chapter 7 More on Real Numbers.- Chapter 8 Continuous Functions.- Chapter 9 Limits and Derivatives.- Chapter 10 Riemann’s Integral.- Chapter 11 Series of Functions.- Bibliography.- Appendix A Glossary.- Appendix B Hints and Solutions.
£999.99
Springer International Publishing AG The Moment Problem
Book SynopsisThis advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments. In both the one-dimensional and multidimensional cases, the full and truncated moment problems are carefully treated separately. Fundamental concepts, results and methods are developed in detail and accompanied by numerous examples and exercises. Particular attention is given to powerful modern techniques such as real algebraic geometry and Hilbert space operators. A wide range of important aspects are covered, including the Nevanlinna parametrization for indeterminate moment problems, canonical and principal measures for truncated moment problems, the interplay between Positivstellensätze and moment problems on semi-algebraic sets, the fibre theorem, multidimensional determinacy theory, operator-theoretic approaches, and the existence theory and important special topics of multidimensional truncated moment problems. The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study.Trade Review“The virtue of Schmüdgen's graduate textbook is that it lays solid foundations for any further explorations, theoretical or applied, in the complex and dynamical realm of moment problems. … This volume will definitely be the reference to moment problems for several future generations.” (Mihai Putinar,Mathematical Reviews, 2018)“The bibliography includes many older and newer titles, the author being one of the main contributors in the last forty years. The book is well-written and it can be considered as an up-to day reference book for the use of both beginners and confirmed researchers, oriented not only to the domain of moment problems but also to other branches of analysis, or of mathematics, in general.” (Florian-Horia Vasilescu, zbMATH, 2018)Table of ContentsPreface and Overview.- 1 Integral representations of linear functionals.- 2 Moment problems on abelian *-semigroups.- Part I The one dimensional moment problem.- 3 One dimensional moment problems on intervals: existence.- 4 One dimensional moment problems: determinacy.- 5 Orthogonal polynomials and Jacobi operators.- 6 The operator-theoretic approach to the Hamburger moment problem.- 7 The indeterminate Hamburger moment problem.- 8 The operator-theoretic approach to the Stieltjes moment problem.- Part II The one dimensional truncated moment problem.- 9 The one-dimensional truncated Hamburger and Stieltjes moment problems.- 10 The one-dimensional truncated moment problem on a bounded interval.- 11 The moment problem on the unit circle.- Part III The multidimensional moment problem.- 12 The moment problem on compact semi-algebraic sets.- 13 The moment problem on closed semi-algebraic sets: existence.- 14 The multidimensional moment problem: determinacy.- 15 The complex moment problem.- 16 Semidefinite programming and polynomial optimization.- Part IV The multidimensional truncated moment problem.- 17 Multidimensional truncated moment problems: existence criteria.- 18 Multidimensional truncated moment problems: basic concepts and special topics.- 19 The truncated moment problem for homogeneous polynomials.
£49.49
Springer International Publishing AG Algebras and Representation Theory
Book SynopsisThis carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers.The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.Trade Review“The book under review is a text-book for higher undergraduate mathematics students or graduate students who have previous knowledge of results from linear algebra, and basic properties of rings and groups. … It is also useful for non-experts (in representation theory of quivers), they may benefit from this book in several ways: by examining the numerous worked examples, or by working out the many exercises.” (Bin Zhu, zbMATH 1429.16001, 2020)Table of Contents1 Introduction.- 2 Algebras.- 3 Modules and Representations.- 4 Simple Modules in the Jordan-Hölder Theorem.- 5 Semisimple Modules and Semisimple Algebras.- 6 The Structure of Semisimple ALgebras - The Artin-Wedderburn Theorem.- 7 Semisimple Group Algebras and Maschke's Theorem.- 8 Indecomposable Modules.- 9 Representation Type.- 10 Representations of Quivers.- 11 Diagrams and Roots.- 12 Gabriel's Theorem.- 13 Proofs and Background.- 14 Appendix A: Induced Modules for Group Algebras.- 15 Appendix B: Solutions to Selected Exercises.- Index.
£23.74
Springer Fachmedien Wiesbaden Lineare Algebra mit Mathematica und Maple:
Book SynopsisTable of ContentsVektorrechnung im V^3 - Komplexe Zahlen - Vektorräume - Matrizen - Lineare Gleichungssysteme und Determinanten - Eigenwerte und Eigenvektoren - Sachwortverzeichnis - Mathematica-Befehle - Maple-Befehle
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Algèbre commutative: Chapitres 8 et 9
Book SynopsisCe volume du Livre d’Algèbre commutative, septième Livre du traité, comprend les chapitres: 8. Dimension ; 9. Anneaux locaux noethériens complets. Le chapitre 8 traite de diverses notions de dimension en algèbre commutative, telles que la dimension de Krull d’un anneau. Ces notions jouent un rôle capital en géometrie algébrique. Le chapitre 9 introduit, quant à lui, les vecteurs de Witt et les anneaux japonais.Table of ContentsDimension.- Anneaux locaux noethériens complets.
£54.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Categories and Sheaves
Book SynopsisCategories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.Trade ReviewFrom the reviews: "This book of Kashiwara and Schapira, recognized specialists in algebraic analysis, is a detailed full-scale exposition of categories, homological algebra and sheaves. These notions are presented from scratch up to the most recent (sometimes new) results … ." (Corrado Marastoni, Mathematical Reviews, Issue 2006 k)Table of ContentsThe Language of Categories.- Limits.- Filtrant Limits.- Tensor Categories.- Generators and Representability.- Indization of Categories.- Localization.- Additive and Abelian Categories.- ?-accessible Objects and F-injective Objects.- Triangulated Categories.- Complexes in Additive Categories.- Complexes in Abelian Categories.- Derived Categories.- Unbounded Derived Categories.- Indization and Derivation of Abelian Categories.- Grothendieck Topologies.- Sheaves on Grothendieck Topologies.- Abelian Sheaves.- Stacks and Twisted Sheaves.
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Commutative Algebra: Chapters 1-7
Book SynopsisThis is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and filtrations). Chapter 4 studies associated prime ideals and the primary decomposition. Chapter 5 deals with integers, integral closures and finitely generated algebras over a field (including the Nullstellensatz). Chapter 6 studies valuation (of any rank), and the last chapter focuses on divisors (Krull, Dedekind, or factorial domains) with a final section on modules over integrally closed Noetherian domains, not usually found in textbooks. Useful exercises appear at the ends of the chapters.Table of ContentsFlat Modules; Localization; Graduations, Filtrations and Topologies; Associated Prime Ideals and Primary Decomposition, Integers, Valuations, Divisors, Exercises
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Algebra I: Chapters 1-3
Book SynopsisThis softcover reprint of the 1974 English translation of the first three chapters of Bourbaki’s Algebre gives a thorough exposition of the fundamentals of general, linear, and multilinear algebra. The first chapter introduces the basic objects, such as groups and rings. The second chapter studies the properties of modules and linear maps, and the third chapter discusses algebras, especially tensor algebras.Table of ContentsAlgebraic Structures.- Linear Algebra.- Tensor Algebras, Exterior Algebras.- Symmetric Algebras.- Historical Notes.
£52.24
Birkhäuser Prüfungstraining Lineare Algebra
Book Synopsis Fundamentales über lineare Abbildungen.- Diagonalisierung.- Anwendungen der Diagonalisierung.- Invariante Unterräume und Trigonalisierung.- Jordan- Normalform (JNF).- Vektorräume mit Skalarprodukt.- Lineare Abbildungen auf Vektorräumen mit Skalarprodukt.- Spektralsätze.- Singulärwertzerlegung (SWZ).- Ausgleichsrechnung.- Bilineare Abbildungen und Bilinearformen.- Hauptsachentrasformation.- Dualraum.- Einführung in Tensorprodukte.- Prüfungstrainer.
£28.49
Spektrum Akademischer Verlag Zahlbereiche
Book Synopsis
£26.59
Elsevier Science Publishing Co Inc A Concrete Approach to Abstract Algebra
Book SynopsisExamines familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials. This title shows how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems. It builds on relatively familiar material (Integers and polynomials).Table of ContentsIntroduction; What This Book Is about and Who This Book Is for; Proof and Intuition; The Integers; Rational Numbers and the Real Numbers; The Complex Numbers; The fundamental Theorem of Algebra; The Integers Modulo n; Group Theory; Polynomials over the Integers and Rationals; Roots of Polynomials of Degree Less than 5; Rational Values of Trigonometric Functions; Polynomials over Arbitrary Fields; Difference Functions and Partial Fractions; An Introduction to Linear Algebra and Vector Spaces; Degrees and Galois Groups of Field Extensions; Geometric Constructions; The Insolvability of the Quintic; Bibliography; Index
£75.99
Elsevier Science Elementary Linear Algebra
Book Synopsis
£107.00
Taylor & Francis Ltd Practical Linear Algebra
Book SynopsisLinear algebra is growing in importance. 3D entertainment, animations in movies and video games are developed using linear algebra. Animated characters are generated using equations straight out of this book. Linear algebra is used to extract knowledge from the massive amounts of data generated from modern technology.The Fourth Edition of this popular text introduces linear algebra in a comprehensive, geometric, and algorithmic way. The authors start with the fundamentals in 2D and 3D, then move on to higher dimensions, expanding on the fundamentals and introducing new topics, which are necessary for many real-life applications and the development of abstract thought. Applications are introduced to motivate topics.The subtitle, A Geometry Toolbox, hints at the book's geometric approach, which is supported by many sketches and figures. Furthermore, the book covers applications of triangles, polygons, conics, and curves. Examples demonstrate each topTable of Contents1. Descartes' Discovery. 1.1. Local and Global Coordinates: 2D. 1.2. Going from Global to Local. 1.3. Local and Global Coordinates: 3D. 1.4. Stepping Outside the Box. 1.5. Application: Creating Coordinates. 1.6. Exercises. 2. Here and There: Points and Vectors in 2D. 2.1. Points and Vectors. 2.2. What's the Difference? 2.3. Vector Fields. 2.4. Length of a Vector. 2.5. Combining Points. 2.6. Independence. 2.7. Dot Product. 2.8. Application: Lighting Model. 2.9. Orthogonal Projections. 2.10. Inequalities. 2.11. Exercises. 3. Lining Up: 2D Lines. 3.1. Defining a Line. 3.2. Parametric Equation of a Line. 3.3. Implicit Equation of a Line. 3.4. Explicit Equation of a Line. 3.5. Converting Between Line Forms. 3.6. Distance of a Point to a Line. 3.7. The Foot of a Point. 3.8. A Meeting Place: Computing Intersections. 3.9. Application: Closest Point of Approach. 3.10. Exercises. 4. Changing Shapes: Linear Maps in 2D. 4.1. Skew Target Boxes. 4.2. The Matrix Form. 4.3. Linear Spaces. 4.4. Scalings. 4.5 Reflections. 4.6. Rotations. 4.7. Shears. 4.8. Projections. 4.9. Application: Free-form Deformations. 4.10. Areas and Linear Maps: Determinants. 4.11. Composing Linear Maps. 4.12. More on Matrix Multiplication. 4.13. Matrix Arithmetic Rules. 4.14. Exercises. 5. 2 x 2 Linear Systems. 5.1. Skew Target Boxes Revisited. 5.2. The Matrix Form. 5.3. A Direct Approach: Cramer's Rule. 5.4. Gauss Elimination. 5.5. Pivoting. 5.6. Unsolvable Systems. 5.7. Underdetermined Systems. 5.8. Homogeneous Systems. 5.9. Kernel. 5.10. Undoing Maps: Inverse Matrices. 5.11. Defining a Map. 5.12. Change of Basis. 5.13. Application: Intersecting Lines. 5.14. Exercises. 6. Moving Things Around: Affine Maps in 2D. 6.1. Coordinate Transformations. 6.2. Affine and Linear Maps. 6.3. Translations. 6.4. Application: Animation. 6.5. Mapping Triangles to Triangles. 6.6. Composing Affine Maps. 6.7. Exercises. 7. Eigen Things. 7.1. Fixed Directions. 7.2. Eigenvalues. 7.3. Eigenvectors. 7.4. Striving for More Generality. 7.5. The Geometry of Symmetric Matrices and the Eigendecomposition. 7.6. Quadratic Forms. 7.7. Repeating Maps. 7.8. Exercises. 8. 3D Geometry. 8.1. From 2D to 3D. 8.2. Cross Product. 8.3. Lines. 8.4. Planes. 8.5. Scalar Triple Product. 8.6. Application: Lighting and Shading. 8.7. Exercises. 9. Linear Maps in 3D. 9.1. Matrices and Linear Maps. 9.2. Linear Spaces. 9.3. Scalings. 9.4. Reflections. 9.5 Shears. 9.6. Rotations. 9.7. Projections. 9.8. Volumes and Linear Maps: Determinants. 9.9. Combining Linear Maps. 9.10. Inverse Matrices. 9.11. Application: Mapping Normals. 9.12. More on Matrices. 9.13. Exercises. 10. Affine Maps in 3D. 10.1. Affine Maps. 10.2. Translations. 10.3. Mapping Tetrahedra. 10.4. Parallel Projections. 10.5. Homogeneous Coordinates and Perspective Maps. 10.6. Application: Building Instance Models. 10.7. Exercises. 11. Interactions in 3D. 11.1. Distance Between a Point and a Plane. 11.2. Distance Between Two Lines. 11.3. Lines and Planes: Intersections. 11.4. Intersecting a Triangle and a Line. 11.5. Reflections. 11.6. Intersecting Three Planes. 11.7. Intersecting Two Planes. 11.8. Creating Orthonormal Coordinate Systems. 11.9. Application: Camera Model. 11.10. Exercises. 12. Gauss for Linear Systems. 12.1. The Problem. 12.2. The Solution via Gauss Elimination. 12.3. Homogeneous Linear Systems. 12.4. Inverse Matrices. 12.5. LU Decomposition. 12.6. Determinants. 12.7. Least Squares. 12.8. Application: Fitting Data from a Femoral Head. 12.9. Exercises. 13. Alternative System Solvers. 13.1. The Householder Method. 13.2. Vector Norms. 13.3. Matrix Norms. 13.4. The Condition Number. 13.5. Vector Sequences. 13.6. Iterative Methods: Gauss-Jacobi and Gauss-Seidel. 13.7. Application: Mesh Smoothing. 13.8. Exercises. 14. General Linear Spaces. 14.1. Basic Properties of Linear Spaces. 14.2. Linear Maps. 14.3. Inner Products. 14.4. Gram-Schmidt Orthonormalization. 14.5. QR Decompositon. 14.6. A Gallery of Spaces. 14.7. Least Squares. 14.8. Application: Music Analysis. 14.9. Exercises. 15. Eigen Things Revisited. 15.1. The Basics Revisited. 15.2. Similarity and Diagonalization. 15.3. Quadratic Forms. 15.4. The Power Method. 15.5. Application: Google Eigenvector. 15.6. QR Algorithm. 15.7. Eigenfunctions. 15.8. Application: Inuenza Modelling. 15.9. Exercises. 16. The Singular Value Decomposition. 16.1. The Geometry of the 2 x 2 Case. 16.2. The General Case. 16.3. SVD Steps. 16.4. Singular Values and Volumes. 16.5. The Pseudoinverse. 16.6. Least Squares. 16.7. Application: Image Compression. 16.8. Principal Components Analysis. 16.9. Application: Face Authentication. 16.10. Exercises. 17. Breaking It Up: Triangles. 17.1. Barycentric Coordinates. 17.2. Affine Invariance. 17.3. Some Special Points. 17.4. 2D Triangulations. 17.5. A Data Structure. 17.6. Application: Point Location. 17.7. 3D Triangulations. 17.8. Exercises. 18. Putting Lines Together: Polylines and Polygons. 18.1 Polylines. 18.2. Polygons. 18.3. Convexity. 18.4. Types of Polygons. 18.5. Unusual Polygons. 18.6. Turning Angles and Winding Numbers. 18.7. Area. 18.8. Application: Planarity Test. 18.9. Application: Inside or Outside? 18.10. Exercises. 19. Conics. 19.1. The General Conic. 19.2. Analyzing Conics. 19.3. General Conic to Standard Position. 19.4. The Action Ellipse. 19.5. Exercises. 20. Curves. 20.1. Parametric Curves. 20.2. Properties of Bézier Curves. 20.3. The Matrix Form. 20.4. Derivatives. 20.5. Composite Curves. 20.6. The Geometry of Planar Curves. 20.7. Application: Moving along a Curve. 20.8. Exercises. A. Applications. B. Glossary. C. Selected Exercises Solutions. Bibliography.
£82.99
Taylor & Francis Ltd Introduction to Traveling Waves
Book SynopsisThis book focuses on traveling waves for undergraduate and masters level students. Traveling waves are not typically covered in the undergraduate curriculum, and topics related to traveling waves are usually only covered in research papers, except for a few texts designed for students. Table of Contents1. Nonlinear Traveling Waves. 1.1. Traveling Waves. 1.2. Reaction-Diffusion Equations. 1.3. Traveling Waves as Solutions of Reaction-Diffusion Equations. 1.4. Planar Waves. 1.5. Examples of Reaction-Diffusion Equations. 1.6. Other Partial Differential Equations that Support Waves. 2. Systems of Reaction-Diffusion Equations posed on Infinite Domains. 2.1. Systems of Reaction-Diffusion Equations. 2.2. Examples of Reaction-Diffusion Systems. 3. Existence of Fronts, Pulses, and Wavetrains. 3.1. Traveling Waves as Orbits in the Associated Dynamical Systems. 3.2. Dynamical Systems Approach: Equilibrium Points. 3.3. Existence of Fronts in Fisher-KPP Equation: Trapping Region Technique. 3.4. Existence of Fronts in Solid Fuel Combustion Model. 3.5. Wavetrains. 4. Stability of Fronts and Pulses. 4.1. Stability: Introduction. 4.2. A Heuristic Presentation of Spectral Stability for Front and Pulse Traveling Wave Solutions. 4.3. Location of the Point Spectrum. 4.4. Beyond Spectral Stability.
£87.39
Taylor & Francis Ltd Student Solutions Manual for Gallians
Book SynopsisWhereas many partial solutions and sketches for the odd-numbered exercises appear in the book, the Student Solutions Manual, written by the author, has comprehensive solutions for all odd-numbered exercises and large number of even-numbered exercises. This Manual also offers many alternative solutions to those appearing in the text. These will provide the student with a better understanding of the material.This is the only available student solutions manual prepared by the author of Contemporary Abstract Algebra, Tenth Edition and is designed to supplement that text.Table of ContentsIntegers and Equivalence Relations0. Preliminaries Groups1. Introduction to Groups 2. Groups 3. Finite Groups; Subgroups 4. Cyclic Groups 5. Permutation Groups 6. Isomorphisms 7. Cosets and Lagrange''s Theorem 8. External Direct Products 9. Normal Subgroups and FactorTable of ContentsIntegers and Equivalence Relations. 0. Preliminaries. Groups. 1. Introduction to Groups. 2. Groups. 3. Finite Groups; Subgroups. 4. Cyclic Groups. 5. Permutation Groups. 6. Isomorphisms. 7. Cosets and Lagrange's Theorem. 8. External Direct Products. 9. Normal Subgroups and Factor Groups. 10. Group Homomorphisms. 11. Fundamental Theorem of Finite Abelian Groups. Rings. 12. Introduction to Rings. 13. Integral Domains. 14. Ideals and Factor Rings. 15. Ring Homomorphisms. 16. Polynomial Rings. 17. Factorization of Polynomials. 18. Divisibility in Integral Domains Fields. Fields. 19. Extension Fields. 20. Algebraic Extensions. 21. Finite Fields. 22. Geometric Constructions. Special Topics. 23. Sylow Theorems. 24. Finite Simple Groups. 25. Generators and Relations. 26. Symmetry Groups. 27. Symmetry and Counting. 28. Cayley Digraphs of Groups. 29. Introduction to Algebraic Coding Theory. 30. An Introduction to Galois Theory. 31. Cyclotomic Extensions.
£43.69
