Algebra Books
MP-AMM American Mathematical Invariant Theory
Book SynopsisPresents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples.Table of ContentsIntroduction Recollections: Linear representations of finite groups Rings and algebras Introduction and Gobel's bound: Rings of polynomial invariants Permutation representations Application: Decay of a spinless particle Application: Counting weighted graphs The first fundamental theorem of invariant theory and Noether's bound: Construction of invariants Noether's bound Some families of invariants Application: Production of fibre composites Application: Gaussian quadrature Noether's theorems: Modules Integral dependence and the Krull relations Noether's theorems Application: Self-dual codes Advanced counting methods and the Shephard-Todd-Chevalley theorem: Poincare series Systems of parameters Pseudoreflection representations Application: Counting partitions Appendix A: Rational invariants Suggestions for further reading Index.
£46.80
MP-AMM American Mathematical The Theory of Matrices
Book SynopsisOffers an easily accessible form a coherent account of matrix theory with a view to applications in mathematics, theoretical physics, statistics, and electrical engineering. This title includes individual chapters that have been kept as far as possible independent of each other.Table of ContentsVolume 1: I. Matrices and operations on matrices: 1. Matrices. Basic notation; 2. Addition and multiplication of rectangular matrices; 3. Square matrices; 4. Compound matrices. Minors of the inverse matrix II. The algorithm of Gauss and some of its applications: 1. Gauss's elimination method; 2. Mechanical interpretation of Gauss's algorithm; 3. Sylvester's determinant identity; 4. The decomposition of a square matrix into triangular factors; 5. The partition of a matrix into blocks. The technique of operating with partitioned matrices. The generalized algorithm of Gauss III. Linear operators in an $n$-dimensional vector space: 1. Vector spaces; 2. A linear operator mapping an $n$-dimensional space into an $m$-dimensional space; 3. Addition and multiplication of linear operators; 4. Transformation of coordinates; 5. Equivalent matrices. The rank of an operator. Sylvester's inequality; 6. Linear operators mapping an $n$-dimensional space into itself; 7. Characteristic values and characteristic vectors of a linear operator; 8. Linear operators of simple structure IV. The characteristic polynomial and the minimal polynomial of a matrix: 1. Addition and multiplication of matrix polynomials; 2. Right and left division of matrix polynomials; 3. The generalized Bezout theorem; 4. The characteristic polynomial of a matrix. The adjoint matrix; 5. The method of Faddeev for the simultaneous computation of the coefficients of the characteristic polynomial and of the adjoint matrix; 6. The minimal polynomial of a matrix V. Functions of matrices: 1. Definition of a function of a matrix; 2. The Lagrange-Sylvester interpolation polynomial; 3. Other forms of the definition of $f(A)$. The components of the matrix $A$; 4. Representation of functions of matrices by means of series; 5. Application of a function of a matrix to the integration of a system of linear differential equations with constant coefficients; 6. Stability of motion in the case of a linear system VI. Equivalent transformations of polynomial matrices. Analytic theory of elementary divisors: 1. Elementary transformations of a polynomial matrix; 2. Canonical form of a $\lambda$-matrix; 3. Invariant polynomials and elementary divisors of a polynomial matrix; 4. Equivalence of linear binomials; 5. A criterion for similarity of matrices; 6. The normal forms of a matrix; 7. The elementary divisors of the matrix $f(A)$; 8. A general method of constructing the transforming matrix; 9. Another method of constructing a transforming matrix VII. The structure of a linear operator in an $n$-dimensional space: 1. The minimal polynomial of a vector and a space (with respect to a given linear operator); 2. Decomposition into invariant subspaces with co-prime minimal polynomials; 3. Congruence. Factor space; 4. Decomposition of a space into cyclic invariant subspaces; 5. The normal form of a matrix; 6. Invariant polynomials. Elementary divisors; 7. The Jordan normal form of a matrix; 8. Krylov's method of transforming the secular equation VIII. Matrix equations: 1. The equation $AX=XB$; 2. The special case $A=B$. Commuting matrices; 3. The equation $AX-XB=C$; 4. The scalar equation $f(X)=0$; 5. Matrix polynomial equations; 6. The extraction of $m$-th roots of a non-singular matrix; 7. The extraction of $m$-th roots of a singular matrix; 8. The logarithm of a matrix IX. Linear operators in a unitary space: 1. General considerations; 2. Metrization of a space; 3. Gram's criterion for linear dependence of vectors; 4. Orthogonal projection; 5. The geometrical meaning of the Gramian and some inequalities; 6. Orthogonalization of a sequence of vectors; 7. Orthonormal bases; 8. The adjoint operator; 9. Normal operators in a unitary space; 10. The spectra of normal, hermitian, and unitary operators; 11. Positive-semidefinite and positive-definite hermitian operators; 12. Polar decomposition of a linear operator in a unitary space. Cayley's formulas; 13. Linear operators in a euclidean space; 14. Polar decomposition of an operator and the Cayley formulas in a euclidean space; 15. Commuting normal operators X. Quadratic and hermitian forms: 1. Transformation of the variables in a quadratic form; 2. Reduction of a quadratic form to a sum of squares. The law of inertia; 3. The methods of Lagrange and Jacobi of reducing a quadratic form to a sum of squares; 4. Positive quadratic forms; 5. Reduction of a quadratic form to principal axes; 6. Pencils of quadratic forms; 7. Extremal properties of the characteristic values of a regular pencil of forms; 8. Small oscillations of a system with $n$ degrees of freedom; 9. Hermitian forms; 10. Hankel forms; Bibliography Index Volume 2: XI. Complex symmetric, skew-symmetric, and orthogonal matrices: 1. Some formulas for complex orthogonal and unitary matrices; 2. Polar decomposition of a complex matrix; 3. The normal form of a complex symmetric matrix; 4. The normal form of a complex skew-symmetric matrix; 5. The normal form of a complex orthogonal matrix XII. Singular pencils of matrices: 1. Introduction; 2. Regular pencils of matrices; 3. Singular pencils. The reduction theorem; 4. The canonical form of a singular pencil of matrices; 5. The minimal indices of a pencil. Criterion for strong equivalence of pencils; 6. Singular pencils of quadratic forms; 7. Application to differential equations XIII. Matrices with non-negative elements: 1. General properties; 2. Spectral properties of irreducible non-negative matrices; 3. Reducible matrices; 4. The normal form of a reducible matrix; 5. Primitive and imprimitive matrices; 6. Stochastic matrices; 7. Limiting probabilities for a homogeneous Markov chain with a finite number of states; 8. Totally non-negative matrices; 9. Oscillatory matrices XIV. Applications of the theory of matrices to the investigation of systems of linear differential equations: 1. Systems of linear differential equations with variable coefficients. General concepts; 2. Lyapunov transformations; 3. Reducible systems; 4. The canonical form of a reducible system. Erugin's theorem; 5. The matricant; 6. The multiplicative integral. The infinitesimal calculus of Volterra; 7. Differential systems in a complex domain. General properties; 8. The multiplicative integral in a complex domain; 9. Isolated singular points; 10. Regular singularities; 11. Reducible analytic systems; 12. Analytic functions of several matrices and their application to the investigation of differential systems. The papers of Lappo-Danilevskii XV. The problem of Routh-Hurwitz and related questions: 1. Introduction; 2. Cauchy indices; 3. Routh's algorithm; 4. The singular case. Examples; 5. Lyapunov's theorem; 6. The theorem of Routh-Hurwitz; 7. Orlando's formula; 8. Singular cases in the Routh-Hurwitz theorem; 9. The method of quadratic forms. Determination of the number of distinct real roots of a polynomial; 10. Infinite Hankel matrices of finite rank; 11. Determination of the index of an arbitrary rational fraction by the coefficients of numerator and denominator; 12. Another proof of the Routh-Hurwitz theorem; 13. Some supplements to the Routh-Hurwitz theorem. Stability criterion of Lienard and Chipart; 14. Some properties of Hurwitz polynomials. Stieltjes' theorem. Representation of Hurwitz polynomials by continued fractions; 15. Domain of stability. Markov parameters; 16. Connection with the problem of moments; 17. Theorems of Markov and Chebyshev; 18. The generalized Routh-Hurwitz problem Bibliography Index.
£99.90
MP-CTM National Council of T Algebra Patterns Functions and Change Casebook
Book SynopsisPresents twenty-nine cases, written by teachers describing real situations and actual student thinking in their classrooms, that provide the basis of each session's investigation of specific mathematical concepts and teaching strategies.
£41.61
Cengage Learning Student Solutions Manual for Stewarts Essential
Book Synopsis
£98.06
Elements of Modern Algebra
Book SynopsisELEMENTS OF MODERN ALGEBRA, Eighth Edition, with its user-friendly format, provides you with the tools you need to succeed in abstract algebra and develop mathematical maturity as a bridge to higher-level mathematics courses. Strategy boxes give you guidance and explanations about techniques and enable you to become more proficient at constructing proofs. A summary of key words and phrases at the end of each chapter help you master the material. A reference section, symbolic marginal notes, an appendix, and numerous examples help you develop your problem-solving skills.
£999.99
John Wiley & Sons Linear Algebra with Applications
Book Synopsis
£137.70
Pearson Education College Algebra and Trigonometry Global Edition
Book SynopsisMarge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but af
£81.36
Springer London Graphs and Matrices
Book SynopsisTable of ContentsPreliminaries.- Incidence Matrix.- Adjacency Matrix.- Laplacian Matrix.- Cycles and Cuts.- Regular Graphs.- Line Graph of a Tree.- Algebraic Connectivity.- Distance Matrix of a Tree.- Resistance Distance.- Laplacian Eigenvalues of Threshold Graphs.- Positive Definite Completion Problem.- Matrix Games Based on Graphs.
£61.74
MP-AMM American Mathematical Brauer Groups Tamagawa Measures and Rational
Book SynopsisThe central theme of this book is the study of rational points on algebraic varieties of Fano and intermediate type - both in terms of when such points exist and, if they do, their quantitative density. The book presents the state of the art in computational arithmetic geometry for higher-dimensional algebraic varieties.Table of Contents Introduction Heights The concept of a height Conjectures on the asymptotics of points of bounded height The Brauer group On the Brauer group of a scheme An application: The Brauer-Manin obstruction Numerical experiments The Diophantine equation x4+2y4=z4+4w4 Points of bounded height on cubic and quartic threefolds On the smallest point on a diagonal cubic surface Appendix Bibliography Index
£103.50
MP-AMM American Mathematical Conformal Symmetry Breaking Differential
Book Synopsis
£68.40
MP-AMM American Mathematical Homotopy of Operads and GrothendieckTeichmuller
Book SynopsisTable of Contents From operads to Grothendieck-Teichmuller groups. The general theory of operads: The basic concepts of the theory of operads The definition of operadic composition structures revisited Symmetric monoidal categories and operads Braids and $E_n$-operads: The little discs model of $E_n$-operads Braids and the recognition of $E_2$-operads The magma and parenthesized braid operators Hopf algebras and the Malcev completion: Hopf algebras The Malcev completion for groups The Malcev completion for groupoids and operads The operadic definition of the Grothendieck-Teichmuller group: The Malcev completion of the braid operads and Drinfeld's associators The Grothendieck-Teichmuller group A glimpse at the Grothendieck program Appendices: Trees and the construction of free operads The cotriple resolution of operads Glossary of notation Bibliography Index
£103.50
MP-AMM American Mathematical Bounded Littlewood Identities
Book Synopsis
£68.40
MP-AMM American Mathematical Discrete Painleve Equations
Book SynopsisProvides introductory material to give the reader an accessible entry point to this vast subject matter. Instead of technical theorems or complete proofs, the book relies on providing essential points of many arguments through explicit examples, with the hope that they will be useful for applied mathematicians and physicists.Table of Contents Introduction A dynamical systems approach Initial value spaces Foliated initial value spaces Cremona mappings Asymptotic analysis Lax pairs Riemann-Hilbert problems Foliations and vector bundles Projective spaces Reflection groups Lists of discrete-Painleve equations Asymptotics of discrete equations Bibliography Index.
£999.99
MP-AMM American Mathematical Mathematics
Book SynopsisTrade ReviewThe book under review contains six chapters that can be read independently, each one surveying one mathematical topic. ... It is carefully written, and it is better than a collection of lecture notes. Such books are needed for students, as a complement to the standard textbooks and to present more specialized applications of classical mathematics. The reviewer wishes there were many more such books." - Athanase Papadopoulos, Zentralblatt MATH"This book has its origins, we are told, in the authors' experiences teaching graduate students in computer science, who needed background in certain mathematical topics. Since these topics were not covered in the basic courses that these students had taken, the authors undertook to introduce them in courses spanning several semesters, the lecture notes of which, suitably expanded, became this text. ... I like expository books, because I think, particularly in these days of increasing specialization, that they serve a valuable purpose, not only for students but also professionals who want to see what's going on in other areas, or who need some background in one area for research in another. This book is a fine example of that genre." - Mark Hunacek, MAA ReviewsTable of Contents Measaure and integral High-dimensional geometry and measure concentration Fourier analysis Representations of finite groups Polynomials Topology Index
£47.70
MP-AMM American Mathematical Localization for THHku and the Topological
Book SynopsisThe authors develop a theory of $THH$ and $TC$ of Waldhausen categories and prove the analogues of Waldhausen's theorems for $K$-theory. They resolve the longstanding confusion about localization sequences in $THH$ and $TC$, and establish a specialized devissage theorem.
£67.50
MP-AMM American Mathematical Lectures on Finite Fields
Book SynopsisThe theory of finite fields encompasses algebra, combinatorics, and number theory and has furnished widespread applications in other areas of mathematics and computer science. This book covers basic facts about finite fields, polynomials over finite fields, Gauss sums, algebraic number theory and cyclotomic fields, zeros of polynomials over finite fields, and classical groups over finite fields.Table of Contents Polynomials over finite fields Gauss sums Algebraic number theory Zeros of polynomials over finite fields Classical groups Bibliography List of notation Index
£106.20
MP-AMM American Mathematical Fundamental Factorization of a GLSM Part I
Book SynopsisWe define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases these invariants recover both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan using cosection localization as well as the FJRW type invariants constructed by Polishchuk-Vaintrob.
£68.40
MP-AMM American Mathematical Singularities Mirror Symmetry and the Gauged
Book SynopsisContains the proceedings of the workshop ‘Crossing the Walls in Enumerative Geometry’, held in May 2018. The volume features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model.Table of Contents R. Webb, Quasimaps and some examples of stacks for everybody E. Clader, Introduction to the gauged linear sigma model D. Ross, Localization and mirror symmetry W.-P. Li, A brief introduction to cosection localization and $P$-fields M. Shoemaker, Virtual classes for hypersurfaces via two-periodic complexes J. Oh, Localized Chern characters for 2-periodic complexes and virtual cycles T. Milanov, Singularity theory and mirror symmetry U. Whitcher, Counting points with Berglund-Hubsch-Kravitz mirror symmetry H. Fan and Y.-P. Lee, Variations on the theme of quantum Lefschetz R. Mi, Type II extremal transitions in Gromov-Witten theory C.-C. M. Liu, A lecture on holomorphic anomaly equations and extended holomorphic anomaly equation
£96.30
MP-AMM American Mathematical An Invitation to Arithmetic Geometry
Book Synopsis
£999.99
MP-AMM American Mathematical Groups and Topological Dynamics
Book SynopsisFocuses on group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and dynamical systems.Table of Contents Dynamical systems Group actions Groupoids Iterated monodromy groups Groups from groupoids Growth and amenability Bibliography Index
£67.50
MP-AMM American Mathematical Compactifications Configurations and Cohomology
Book SynopsisFocuses on new and existing connections between three types of compactifications, thereby setting the stage for further research. The book draws on the discipline-specific expertise of all contributors, and at the same time gives a unified, self-contained reference for compactifications and related constructions in different contexts.Table of ContentsA. Balibanu, A quasi-Poisson structure on the multiplicative Grothendieck-Springer resolution; P. Brosnan, Volumes of definable sets in o-minimal expansions and affine GAGA theorems; P. Crooks and R. Roser, Hessenberg varieties and Poisson slices; G. Denham and A. Steiner, Geometry of logarithmic derivations of hyperplane arrangements; I. Halacheva, Shift of argument algebras and de Concini-Procesi spaces; B. Knudsen, Projection spaces and twisted Lie algebras; A. I. Suciu, Cohomology, Bocksteins, and resonance varieties in characteristic 2.
£103.50
MP-AMM American Mathematical Number Systems An Introduction to Algebra and
Book SynopsisOffers a rigorous and coherent introduction to the five basic number systems of mathematics - natural numbers, integers, rational numbers, real numbers, and complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.Table of Contents Natural numbers Integers Rational numbers Real numbers Complex numbers Sets, relations, functions Bibliography Index
£63.00
MP-AMM American Mathematical Organized Collapse An Introduction to Discrete
Book SynopsisProvides a gentle introduction into discrete Morse theory. Using a combinatorial approach, the author emphasizes acyclic matchings as the central object of study. The first two parts of the book can be used as a stand-alone introduction to homology, the last two parts delve into the core of discrete Morse theory.Table of Contents Preamble Preface The idea of homology The idea of discrete Morse theory A sample application How to use this book Prerequisites Guide to the literature Part 1 . Introduction to Homology Chapter 1. The First Steps Chapter 2. Simplicial Homology Chapter 3. Beyond the Simplicial Setting Part 2 . Further Aspects of Homology Theory Chapter 4. Category of Chain Complexes Chapter 5. Chain Homotopy Chapter 6. Connecting Homomorphism Chapter 7. Singular Homology Chapter 8. Cellular Homology Suggested further reading for Parts 1 and 2 Part 3 . Basic Discrete Morse Theory Chapter 9. Simplicial Collapses Chapter 10. Organizing Collapsing Sequences Chapter 11. Internal Collapses and Discrete Morse Theory Chapter 12. Explicit Homology Classes Associated to Critical Cells Chapter 13. The Critical Morse Complex Chapter 14. Implications and Variations Suggested further reading for Part 3 Part 4 . Extensions of Discrete Morse Theory Chapter 15. Algebraic Morse Theory Chapter 16. Discrete Morse Theory for Posets Chapter 17. Discrete Morse Theory for CW Complexes Chapter 18. Discrete Morse Theory and Persistence Suggested further reading for Part 4 Index List of Figures List of Tables Bibliography Index Preview Material Preface Table of Contents
£70.20
MP-AMM American Mathematical Topics in Hyperplane Arrangements
Book SynopsisStudies the interplay between various algebraic, geometric and combinatorial aspects of real hyperplane arrangements. This volume provides a careful, organised and unified treatment of several recent developments in the field, and brings forth many new ideas and results. It has two parts, each divided into eight chapters, and five appendices with background material.Table of Contents Part I: Hyperplane arrangements Cones Lunes Category of lunes Reflection arrangements Braid arrangement and related examples Descent and lune equations Distance functions and Varchenko matrix Part II: Birkhoff algebra and Tits algebra Lie and Zie elements Eulerian idempotents Diagonalizability and characteristic elements Loewy series and Peirce decompositions Dynkin idempotents Incidence algebras Invariant Birkhoff algebra and invariant Tits algebra Appendices: Regular cell complexes Posets Incidence algebras of posets Algebras and modules Bands References: Bibliography Notation index Subject index.
£133.20
MP-AMM American Mathematical Spaces of Constant Curvature
Book SynopsisThis book is the sixth edition of the classic Spaces of Constant Curvature, first published in 1967, with the previous (fifth) edition published in 1984. It illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups. Part I is a brief introduction to differentiable manifolds, covering spaces, and riemannian and pseudo-riemannian geometry. It also contains a certain amount of introductory material on symmetry groups and space forms, indicating the direction of the later chapters. Part II is an updated treatment of euclidean space form. Part III is Wolf's classic solution to the Clifford-Klein Spherical Space Form Problem. It starts with an exposition of the representation theory of finite groups. Part IV introduces riemannian symmetric spaces and extends considerations of spherical space forms to space forms of riemannian symmetric spaces. Finally, Part V examines space form problems on pseudo-riemannian symmetric spaces. At the end of Chapter 12 there is a new appendix describing some of the recent work on discrete subgroups of Lie groups with application to space forms of pseudo-riemannian symmetric spaces. Additional references have been added to this sixth edition as well.Table of Contents Riemannian geometry: Affine differential geometry Riemannian curvature The Euclidean space form problem: Flat Riemannian manifolds The spherical space form problem: Representations of finite groups Vincent's work on the spherical space form problem The classification of fixed point free groups The solution to the spherical space form problem Space form problems on symmetric spaces: Riemannian symmetric spaces Space forms of irreducible symmetric spaces Locally symmetric spaces of non-negative curvature Space form problems on indefinite metric manifolds: Spaces of constant curvature Locally isotropic manifolds Appendix to Chapter 12 References Additional references Index
£48.60
Arcler Education Inc An Introduction to Algebraic and Combinatorial
Book SynopsisAn Introduction to Algebraic and Combinatorial Coding Theory is a comprehensive book that offers a thorough exploration of the principles and techniques of coding theory. It serves as a valuable resource for readers interested in gaining a deeper understanding of error detection and correction in communication systems. With its well-structured chapters covering coding theory fundamentals, algebraic codes, cyclic codes, block codes, and advanced coding techniques, this book caters to the needs of students, researchers, and professionals in the field. It provides a solid foundation in coding theory and showcases its practical applications in various domains, including telecommunications, data storage, and cryptography.Table of Contents Chapter 1 Introduction Chapter 2 Digital Image Information Hiding Algorithm Research Based on LDPC Code Chapter 3 Rate-Adaptive BCH Codes for Distributed Source Coding Chapter 4 Reducing the Overhead of BCH Codes: New Double Error Correction Codes Chapter 5 Ideals of Numerical Semigroups and Error-Correcting Codes Chapter 6 Turbo Codes for Multi-Hop Wireless Sensor Networks with Decode-and-Forward Mechanism Chapter 7 Entanglement-Assisted Quantum Codes from Cyclic Codes Chapter 8 Low-Complexity Chase Decoding of Reed–Solomon Codes Using Channel Evaluation Chapter 9 How Reed-Solomon Codes Can Improve Steganographic Schemes Chapter 10 A New Minimize Matrix Computation Coding Method for Distributed Storage Systems Chapter 11 Permutation-Based Block Code for Short Packet Communication Systems Chapter 12 A Simple Neural-Network-Based Decoder for Short Binary Linear Block Codes Chapter 13 An Analytical Approach to Error Detection and Correction for Onboard Nanosatellites Chapter 14 Application of Forward Error Correction (FEC) Codes in Wireless Acoustic Emission Structural Health Monitoring on Railway Infrastructures Chapter 15 Blind Recognition of Forward Error Correction Codes Based on Recurrent Neural Network
£158.40
Mathematical Association of America Learning Modern Algebra
Book SynopsisMuch of modern algebra arose from attempts to prove Fermat's Last Theorem, which in turn has its roots in Diophantus' classification of Pythagorean triples. This book, designed for prospective and practising mathematics teachers, makes explicit connections between the ideas of abstract algebra and the mathematics taught at high-school level. Algebraic concepts are presented in historical order, and the book also demonstrates how other important themes in algebra arose from questions related to teaching. The focus is on number theory, polynomials, and commutative rings. Group theory is introduced near the end of the text to explain why generalisations of the quadratic formula do not exist for polynomials of high degree, allowing the reader to appreciate the work of Galois and Abel. Results are motivated with specific examples, and applications range from the theory of repeating decimals to the use of imaginary quadratic fields to construct problems with rational solutions.Trade ReviewThis book covers abstract algebra from a historical perspective by using mathematics from attempts to prove Fermat's last theorem, as the title indicates. The target audience is high school mathematics teachers. However, typical undergraduate students will also derive great benefit by studying this text. The book is permeated with fascinating mathematical nuggets that are clearly explained." - D. P. Turner, CHOICE"This book is destined for college students in the U.S. who intend to teach mathematics in high school. The reviewer finds it even more apt as a text for algebra courses. Special features in the book are side notes given and printed prominently at the margins of the pages, like: How to think about it, Historical notes, Etymology of notions and words. … The reviewer considers the book a refreshing read among the vast amount of books dealing with similar topics." - Robert W. van der Waall, Zentrallblatt MATH"Although this book is designed for college students who want to teach in high school," its mathematical richness fits it admirably as a text for a first abstract algebra course or a handbook for assiduous students working on their own. While definitions, examples, theorems and their proofs are organized formally, the book is enhanced by substantial historical notes, advice on "how to think about it," marginal comments, connections and etymology that are designed to "balance experience and formality." The book is tightly organized with the goal of elucidating developments leading to the solution of the Fermat conjecture and the theory of solvability by radicals." - E. J. Barbeau, Mathematical Reviews"The primary intended audience of the book is future high school teachers. The authors take great pains to relate the material covered here to subjects that are taught in high school mathematics classes. … In writing this book, the authors have obviously kept the needs of the student reader firmly in mind at all times. The writing style is not just clear; iit is often conversational and humorous. … There are lots of exercises covering a wide range of difficulty, some with hints (but none with complete solutions) and there is a pretty good 39-entry bibliography. … What might be a very interesting use for this book would be as a text for a senior seminar or “topics” course for students who already have some prior exposure to abstract algebra. And, of course, whatever may be the applicability of this book as a text for undergraduate course, it seems clear to me that it belongs in any good undergraduate library." - Mark Hunacek, MAA ReviewsTable of ContentsPreface; Some features of this book; A note to students; A note to instructors; Notation; 1. Early number theory; 2. Induction; 3. Renaissance; 4. Modular arithmetic; 5. Abstract algebra; 6. Arithmetic of polynomials; 7. Quotients, fields, and classical problems; 8. Cyclotomic integers; 9. Epilogue; References; Index.
£59.40
Springer Nature Switzerland AG Geometric Multivector Analysis: From Grassmann to
Book SynopsisThis book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of M. Riesz and L. Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Möbius maps in arbitrary dimensions.The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes’s theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20th-century mathematics.The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis. Trade Review“The book is carefully prepared and well presented, and I recommend the book … for students who have just mastered vector calculus and Maxwellian electromagnetism.” (Hirokazu Nishimura, zbMATH 1433.58001, 2020)Table of ContentsPrelude: Linear algebra.- Exterior algebra.- Clifford algebra.- Mappings of inner product spaces.- Spinors in inner product spaces.- Interlude: Analysis.- Exterior calculus.- Hodge decompositions.- Hypercomplex analysis.- Dirac equations.- Multivector calculus on manifolds.- Two index theorems.
£999.99
Springer Nature Switzerland AG Linear Algebra and Optimization for Machine
Book SynopsisThis textbook introduces linear algebra and optimization in the context of machine learning. Examples and exercises are provided throughout the book. A solution manual for the exercises at the end of each chapter is available to teaching instructors. This textbook targets graduate level students and professors in computer science, mathematics and data science. Advanced undergraduate students can also use this textbook. The chapters for this textbook are organized as follows:1. Linear algebra and its applications: The chapters focus on the basics of linear algebra together with their common applications to singular value decomposition, matrix factorization, similarity matrices (kernel methods), and graph analysis. Numerous machine learning applications have been used as examples, such as spectral clustering, kernel-based classification, and outlier detection. The tight integration of linear algebra methods with examples from machine learning differentiates this book from generic volumes on linear algebra. The focus is clearly on the most relevant aspects of linear algebra for machine learning and to teach readers how to apply these concepts.2. Optimization and its applications: Much of machine learning is posed as an optimization problem in which we try to maximize the accuracy of regression and classification models. The “parent problem” of optimization-centric machine learning is least-squares regression. Interestingly, this problem arises in both linear algebra and optimization, and is one of the key connecting problems of the two fields. Least-squares regression is also the starting point for support vector machines, logistic regression, and recommender systems. Furthermore, the methods for dimensionality reduction and matrix factorization also require the development of optimization methods. A general view of optimization in computational graphs is discussed together with its applications to back propagation in neural networks. A frequent challenge faced by beginners in machine learning is the extensive background required in linear algebra and optimization. One problem is that the existing linear algebra and optimization courses are not specific to machine learning; therefore, one would typically have to complete more course material than is necessary to pick up machine learning. Furthermore, certain types of ideas and tricks from optimization and linear algebra recur more frequently in machine learning than other application-centric settings. Therefore, there is significant value in developing a view of linear algebra and optimization that is better suited to the specific perspective of machine learning. Trade Review“Based on the topics covered and the excellent presentation, I would recommend Aggarwal's book over these other books for an advanced undergraduate or beginning graduate course on mathematics for data science.” (Brian Borchers, MAA Reviews, March 28, 2021)“This book should be of interest to graduate students in engineering, applied mathematics, and other fields requiring an understanding of the mathematical underpinnings of machine learning.” (IEEE Control Systems Magazine, Vol. 40 (6), December, 2020)Table of ContentsPreface.- 1 Linear Algebra and Optimization: An Introduction.- 2 Linear Transformations and Linear Systems.- 3 Eigenvectors and Diagonalizable Matrices.- 4 Optimization Basics: A Machine Learning View.- 5 Advanced Optimization Solutions.- 6 Constrained Optimization and Duality.- 7 Singular Value Decomposition.- 8 Matrix Factorization.- 9 The Linear Algebra of Similarity.- 10 The Linear Algebra of Graphs.- 11 Optimization in Computational Graphs.- Index.
£999.99
Springer Nature Switzerland AG Einführung in die mathematische Behandlung der
Book SynopsisDieses Lehrbuch ist ein idealer Begleitband für eine vierstündige Vorlesung mit Übungen für angehende Naturwissenschaftlerinnen und Naturwissenschaftler, kann aber auch für eine Einführungsvorlesung in die höhere Mathematik in anderen Disziplinen eingesetzt werden. Aufbauend auf Vorkenntnissen aus dem Gymnasium werden zunächst die wichtigsten Begriffe nochmals repetiert. Im Hauptteil werden Vektoren, Differential- und Integralrechnung sowie Differentialgleichungen eingeführt und ausführlich behandelt. Abschließend wird auf Funktionen mehrerer Variablen eingegangen. Zahlreiche Übungsaufgaben mit Lösungen zu jedem Kapitel helfen, den Stoff zu festigen. Neben den Erklärungen für alle Leserinnen und Leser werden in speziell markierten Teilen weiterführende Fragen vertieft behandelt, welche nicht zwingend für das Verständnis notwendig sind, aber interessante Einblicke geben. Das Buch und Übungskonzept ist eine weitgehend überarbeitete Neuausgabe des Texts einer über ein Jahrzehnt erfolgreich gelehrten Vorlesung.Table of ContentsA. Vektorrechnung.- 1. Vektoren und ihre geometrische Bedeutung.- 2. Vektorrechnung mit Koordinaten.- B. Differentialrechnung.- 3. Beispiele zum Begriff der Ableitung.- 4. Die Ableitung.- 5. Technik des Differenzierens.- 6. Anwendungen der Ableitung.- 7. Linearisierung und das Differential.- 8. Die Ableitung einer Vektorfunktion.- C. Integralrechnung.- 9. Einleitende Beispiele zum Begriff des Integrals.- 10. Das bestimmte Integral.- 11. Der Hauptsatz der Differential- und Integralrechnung.- 12. Stammfunktionen und das unbestimmte Integral.- 13. Weitere Integrationsmethoden.- 14. Integration von Vektorfunktionen.- D. Differentialgleichungen.- 15. Der Begriff der Differentialgleichung.- 16. Einige Lösungsmethoden.- E. Ausbau der Infinitesimalrechnung.- 17. Umkehrfunktionen.- 18. Einige wichtige Funktionen und ihre Anwendungen.- 19. Potenzreihen.- 20. Uneigentliche Integrale.- 21. Numerische Methoden.- F. Funktionen von Mehreren Variablen.- 22. Allgemeines über Funktionen von mehreren Variablen.- 23. Differentialrechnung von Funktionen von mehreren Variablen.- 24. Das totale Differential.- 25. Mehrdimensionale Integrale.- G. Anhang.- 26. Zusammenstellung einiger Grundbegriffe.- 27. Einige Ergänzungen.- 28. Lösungen der Aufgaben.
£999.99
Springer Nature Switzerland AG Hamilton’s Principle in Continuum Mechanics
Book SynopsisThis revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton’s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton’s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.Table of ContentsMechanics of Systems of Particles .- Mathematical Preliminaries.- Mechanics of Continuous Media.- Motions and Comparison Motions of a Mixture.- Singular Surfaces.- Index.
£98.99
Birkhauser Verlag AG Semi-Infinite Algebraic Geometry of
Book SynopsisSemi-Infinite Geometry is a theory of "doubly infinite-dimensional" geometric or topological objects. In this book the author explains what should be meant by an algebraic variety of semi-infinite nature. Then he applies the framework of semiderived categories, suggested in his previous monograph titled Homological Algebra of Semimodules and Semicontramodules, (Birkhäuser, 2010), to the study of semi-infinite algebraic varieties. Quasi-coherent torsion sheaves and flat pro-quasi-coherent pro-sheaves on ind-schemes are discussed at length in this book, making it suitable for use as an introduction to the theory of quasi-coherent sheaves on ind-schemes. The main output of the homological theory developed in this monograph is the functor of semitensor product on the semiderived category of quasi-coherent torsion sheaves, endowing the semiderived category with the structure of a tensor triangulated category. The author offers two equivalent constructions of the semitensor product, as well as its particular case, the cotensor product, and shows that they enjoy good invariance properties. Several geometric examples are discussed in detail in the book, including the cotangent bundle to an infinite-dimensional projective space, the universal fibration of quadratic cones, and the important popular example of the loop group of an affine algebraic group.Table of Contents- 1. Ind-Schemes and Their Morphisms. - 2. Quasi-Coherent Torsion Sheaves. - 3. Flat Pro-Quasi-Coherent Pro-Sheaves. - 4. Dualizing Complexes on Ind-Noetherian Ind-Schemes. - 5. The Cotensor Product. - 6. Ind-Schemes of Ind-Finite Type and the factorial !-Tensor Product. - 7. X-Flat Pro-Quasi-Coherent Pro-Sheaves on Y. - 8. The Semitensor Product. - 9. Flat Affine Ind-Schemes over Ind-Schemes of Ind-Finite Type. - 10. Invariance Under Postcomposition with a Smooth Morphism. - 11. Some Infinite-Dimensional Geometric Examples.
£98.99
Springer International Publishing AG Banach Function Algebras Arens Regularity and BSE
Book SynopsisThis book is about semisimple Banach algebras with a focus on those that are commutative. Some of the questions dealt with in the book are: Whether the introduced Banach algebras are BSE-algebras, whether they have BSE norms, whether they have the separating ball property or some variant of it, and whether they are Arens regular.
£98.99
de Gruyter Languages and Automata
Book Synopsis
£140.00
De Gruyter Combinatorial Number Theory
Book Synopsis
£148.20
De Gruyter Tabellen reduzierter positiver ternärer
Book Synopsis
£134.09
de Gruyter Kategorielle Algebra
Book Synopsis
£134.09
Grin Verlag Lineare Gleichungen und Funktionen für die 10.
Book Synopsis
£20.96
Springer Fachmedien Wiesbaden Elementare Zahlentheorie
Book SynopsisDiese Einführung in die Zahlentheorie wendet sich an Studierende sowie an Lehrerinnen und Lehrer aller Schulformen mit dem Fach Mathematik. Besonderheiten: - Schnupperkurs motiviert durch spannende Problemstellungen zur aktiven Auseinandersetzung mit der Zahlentheorie - Über 200 Aufgaben mit Lösungshinweisen ermöglichen eine selbstständige Erarbeitung vieler Fragestellungen - Aktuelle und ergiebige Internetadressen - Einsatz von Computeralgebrasystemen wie DERIVE wird am Beispiel des RSA-Verschlüsselungssystems realitätsnah dargestellt.Table of Contents
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Elementary Galois Theory: A Constructive Approach
Book SynopsisWhy is the squaring of the circle, why is the division of angles with compass and ruler impossible? Why are there general solution formulas for polynomial equations of degree 2, 3 and 4, but not for degree 5 or higher?This textbook deals with such classical questions in an elementary way in the context of Galois theory. It thus provides a classical introduction and at the same time deals with applications. The point of view of a constructive mathematician is consistently adopted: To prove the existence of a mathematical object, an algorithmic construction of that object is always given. Some statements are therefore formulated somewhat more cautiously than is classically customary; some proofs are more elaborately conducted, but are clearer and more comprehensible. Abstract theories and definitions are derived from concrete problems and solutions and can thus be better understood and appreciated.The material in this volume can be covered in a one-semester lecture on algebra right at the beginning of mathematics studies and is equally suitable for first-year students at the Bachelor's level and for teachers.The central statements are already summarised and concisely presented within the text, so the reader is encouraged to pause and reflect and can repeat content in a targeted manner. In addition, there is a short summary at the end of each chapter, with which the essential arguments can be comprehended step by step, as well as numerous exercises with an increasing degree of difficulty.Table of Contents1. introduction.- 2. the fundamental theorem of algebra.- 3. impossibility of squaring the circle.- 4. impossibility of cube doubling and angle division.- 5. on the constructability of regular n-corners.- 6. on the solvability of polynomial equations.- A constructive mathematics.- B linear algebra.- C analysis.
£40.49
Jainendra K Jain K-Theory
Book SynopsisThis volume contains the proceedings of the international colloquium organized by the Tata Institute of Fundamental Research in January 2016, one of a series of colloquia going back to 1956.The talks at the colloquium covered a wide spectrum of mathematics, ranging over algebraic geometry, topology, algebraic $K$-theory and number theory. Algebraic theory, $\mathbb{A}^1$-homotopy theory and topological $K$-theory formed important sub-streams in this colloquium. Several branches of $K$-theory, like algebraic cycles, triangulated categories of motives, motivic cohomology, motivic homotopy theory, Chow groups of varieties, Euler class theory, equivariant $K$-theory as well as classical $K$-theory have developed considerably in recent years, giving rise to newer directions to the subject as well as proving results of ``classical'' interest. The colloquium brought together experts in these various branches and their talks covered this wide spectrum, highlighting the interconnections and giving a better perspective of the whole subject area.This volume contains refereed articles by leading experts in these fields and includes original results as well as expository materials in these areas.
£158.40
Springer Verlag, Singapore Applied Linear Algebra, Probability and
Book SynopsisThis book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on generalized inverses, matrix analysis, matrices and graphs, applied probability and statistics, and the history of ancient mathematics, this book offers a diverse array of mathematical results, techniques and applications. The book promises to be especially rewarding for readers with an interest in the focus areas of applied linear algebra, probability and statistics.Table of ContentsChapter 1. On Some Matrix Versions of Covariance, Harmonic Mean and other Inequalities: An Overview.- Chapter 2. The Impact of Professor C. R. Rao's Research used in solving problems in Applied Probability.- Chapter 3. Upper ounds for the Euclidean distances between the BLUEs under the partitioned linear fixed model and the corresponding mixed model.- Chapter 4. Nucleolus Computation for some Structured TU Games via Graph Theory and Linear Algebra.- Chapter 5. From Linear System of Equations to Artificial Intelligence - The evolution Journey of Computer Tomographic Image Reconstruction Algorithms.- Chapter 6. Shapley Value and other Axiomatic Extensions to Shapley Value.- Chapter 7. An Accelerated Block Randomized Kaczmarz Methos.- Chapter 8. Nullity of Graphs - A Survey and Some New Results.- Chapter 9. Some Observations on Algebraic Connectivity of Graphs.- Chapter 10. Orthogonality for iadjoints f Operators.- Chapter 11. Permissible covariance structures for simultaneous retention of BLUEs in small and big linear models.- Chapter 12. On some Special Matrices and its Applications in Linear Complementarity Problem.- Chapter 3. On Nearest Matrix with Partially Specified Eigen Structure.- Chapter 14. Equality of BLUEs for Full, Small, and Intermediate Linear Models under Covariance Change, with links to Data Confidentiality and Encryption.-Chapter 15. Statistical Inference for Middle Censored Data with Applications. etc
£999.99
