Algebra Books

Book SynopsisAlgebraic Structure of Lattice-Ordered Rings presents an introduction to the theory of lattice-ordered rings and some new developments in this area in the last 10-15 years. It aims to provide the reader with a good foundation in the subject, as well as some new research ideas and topic in the field.This book may be used as a textbook for graduate and advanced undergraduate students who have completed an abstract algebra course including general topics on group, ring, module, and field. It is also suitable for readers with some background in abstract algebra and are interested in lattice-ordered rings to use as a self-study book.The book is largely self-contained, except in a few places, and contains about 200 exercises to assist the reader to better understand the text and practice some ideas.Table of ContentsPartially Ordered Sets; Lattices; Lattice-Ordered Groups; Vector Lattices; Lattice-Ordered Rings and Algebras; Lattice-Ordered Algebras with a d-Basis; Positive Derivations on Lattice-Ordered Rings; Recognition of Lattice-Ordered Matrix Rings with the Entrywise Order; Positive Cycles; Nonzero f-Elements in Lattice-Ordered Rings; Quotient Rings of Lattice-Ordered Ore Domains; Lattice-Ordered Matrix Algebras with Totally Ordered Integral Domains; d-Elements That Are Not Positive; Lattice-Ordered Triangular Matrix Rings; l-Ideals of Lattice-Ordered Rings with Positive Identity.

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Book SynopsisThis book gives a self- contained treatment of linear algebra with many of its most important applications. It is very unusual if not unique in being an elementary book which does not neglect arbitrary fields of scalars and the proofs of the theorems. It will be useful for beginning students and also as a reference for graduate students and others who need an easy to read explanation of the important theorems of this subject.It presents a self- contained treatment of the algebraic treatment of linear differential equation which includes all proofs. It also contains many different proofs of the Cayley Hamilton theorem. Other applications include difference equations and Markov processes, the latter topic receiving a more thorough treatment than usual, including the theory of absorbing states. In addition it contains a complete introduction to the singular value decomposition and related topics like least squares and the pseudo-inverse.Most major topics receive more than one discussion, one in the text and others being outlined in the exercises. The book also gives directions for using maple in performing many of the difficult algorithms.

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Book SynopsisThe content in Chapter 1-3 is a fairly standard one-semester course on local rings with the goal to reach the fact that a regular local ring is a unique factorization domain. The homological machinery is also supported by Cohen-Macaulay rings and depth. In Chapters 4-6 the methods of injective modules, Matlis duality and local cohomology are discussed. Chapters 7-9 are not so standard and introduce the reader to the generalizations of modules to complexes of modules. Some of Professor Iversen's results are given in Chapter 9. Chapter 10 is about Serre's intersection conjecture. The graded case is fully exposed. The last chapter introduces the reader to Fitting ideals and McRae invariants.

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Book SynopsisThis book presents methods for the computational solution of some important problems of linear algebra: linear systems, linear least squares problems, eigenvalue problems, and linear programming problems. The book also includes a chapter on the fast Fourier transform and a very practical introduction to the solution of linear algebra problems on modern supercomputers.The book contains the relevant theory for most of the methods employed. It also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs for solving linear algebraic problems. Highly readable FORTRAN and MATLAB codes are presented which solve all of the main problems studied.Table of ContentsReference Materials; Systems of Linear Equations; Linear Least Squares Problems; The Eigenvalue Problem; Linear Programming; The Fast Fourier Transform; Linear Algebra on Supercomputers;

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Book SynopsisThis book presents methods for the computational solution of some important problems of linear algebra: linear systems, linear least squares problems, eigenvalue problems, and linear programming problems. The book also includes a chapter on the fast Fourier transform and a very practical introduction to the solution of linear algebra problems on modern supercomputers.The book contains the relevant theory for most of the methods employed. It also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs for solving linear algebraic problems. Highly readable FORTRAN and MATLAB codes are presented which solve all of the main problems studied.Table of ContentsReference Materials; Systems of Linear Equations; Linear Least Squares Problems; The Eigenvalue Problem; Linear Programming; The Fast Fourier Transform; Linear Algebra on Supercomputers;

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Book SynopsisThe book is about (associative, Lie and other) algebras, groups, semigroups presented by generators and defining relations. They play a great role in modern mathematics. It is enough to mention the quantum groups and Hopf algebra theory, the Kac-Moody and Borcherds algebra theory, the braid groups and Hecke algebra theory, the Coxeter groups and semisimple Lie algebra theory, the plactic monoid theory. One of the main problems for such presentations is the problem of normal forms of their elements. Classical examples of such normal forms give the Poincaré-Birkhoff-Witt theorem for universal enveloping algebras and Artin-Markov normal form theorem for braid groups in Burau generators.What is now called Gröbner-Shirshov bases theory is a general approach to the problem. It was created by a Russian mathematician A I Shirshov (1921-1981) for Lie algebras (explicitly) and associative algebras (implicitly) in 1962. A few years later, H Hironaka created a theory of standard bases for topological commutative algebra and B Buchberger initiated this kind of theory for commutative algebras, the Gröbner basis theory. The Shirshov paper was largely unknown outside Russia. The book covers this gap in the modern mathematical literature. Now Gröbner-Shirshov bases method has many applications both for classical algebraic structures (associative, Lie algebra, groups, semigroups) and new structures (dialgebra, pre-Lie algebra, Rota-Baxter algebra, operads). This is a general and powerful method in algebra.

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Book SynopsisIn the spirit of the author’s Basic Language of Mathematics, this companion volume is a careful exposition of the concepts and processes of Linear Algebra. It stresses cautious and clear explanations, avoiding reliance on co-ordinates as much as possible, and with special, but not exclusive, attention to the finite-dimensional situation. It is intended to also serve as a conceptual and technical background for use in geometry and analysis as well as other applications.Table of ContentsLinear Spaces and Linear Mappings; Properties of Linear Mappings; Linear Products and Coproducts; Families in Linear Spaces; Finite Dimension; Duality; Duality and Finite Dimension; Indexes;

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Book SynopsisIn an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.Table of ContentsPositive Definite Kernels and Radial Basis Functions; Reproducing Kernel Hilbert Spaces; Kriging; Green's Kernels; Generalized Sobolev Spaces; Alternate and Stable Interpolation Bases; Kernel Optimization; Examples in: Scattered Data Fitting, Surrogate Modeling, Spatial Statistics, Machine Learning, Boundary Value Problems, Finance;

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Book SynopsisThis volume is an outgrowth of the program Modular Representation Theory of Finite and p-Adic Groups held at the Institute for Mathematical Sciences at National University of Singapore during the period of 1-26 April 2013. It contains research works in the areas of modular representation theory of p-adic groups and finite groups and their related algebras. The aim of this volume is to provide a bridge — where interactions are rare between researchers from these two areas — by highlighting the latest developments, suggesting potential new research problems, and promoting new collaborations.It is perhaps one of the few volumes, if not only, which treats such a juxtaposition of diverse topics, emphasizing their common core at the heart of Lie theory.Table of ContentsRepresentation Theory and Cohomology of Khovanov-Lauda-Rouquier Algebras (Alexander S Kleshchev); p-Modular Representations of p-Adic Groups (Florian Herzig); Cyclotomic Quiver Hecke Algebras of Type A (Andrew Mathas); l-Modular Representations of p-Adic Groups (l <> p) (Vincent Secherre);

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Book SynopsisThis book introduces entirely new invariants never considered before, in homological algebra and commutative (and even non-commutative) algebra. The C-completion C(M), and higher C-completions, Cn(M), are defined for an arbitrary left module M over a topological ring A. Spectral sequences are defined that use these invariants. Given a left module over a topological ring A, under mild conditions the usual Hausdorff completion: M^ can be recovered from the C-completion C(M), by taking the quotient module by the closure of {0}.The new invariants and tools in this book are expected to be used in the study of p-adic cohomology in algebraic geometry; and also in the study of p-adic Banach spaces — by replacing the cumbersome 'complete tensor product' of p-adic Banach spaces, with the more sophisticated 'C-complete tensor product', discussed in this book.It is also not unlikely that the further study of these new invariants may well develop into a new branch of abstract mathematics - connected with commutative algebra, homological algebra, and algebraic topology.Table of ContentsAdmissible Topological Rings; C-completion of an Abstract Module over a Topological Ring; Topological Rings that are C-OK; The higher C-completions; the Spectral Sequence of the C-completion; Inverse Limits and Higher Inverse Limits; Direct Sum and Direct Limit; Image of the Direct Sum in the Direct Product; The Special Properties of Noetherian Rings; Ext and Tor in the Category of C-complete Left A-modules (and Related Spectral Sequences);

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Book SynopsisThis volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry and numerical analysis. It consists of seven chapters that are loosely connected and interdependent. The choice of the topics is very personal and reflects the subjects that the author was actively working on in the last 40 years. Many results appear for the first time in the volume. Readers will encounter various properties of matrices with entries in integral domains, canonical forms for similarity, and notions of analytic, pointwise and rational similarity of matrices with entries which are locally analytic functions in one variable. This volume is also devoted to various properties of operators in inner product space, with tensor products and other concepts in multilinear algebra, and the theory of non-negative matrices. It will be of great use to graduate students and researchers working in pure and applied mathematics, bioinformatics, computer science, engineering, operations research, physics and statistics.Table of ContentsDomains, Modules and Matrices; Canonical Forms for Similarity; Functions of Matrices and Analytic Similarity; Inner Product Spaces; Elements of Multilinear Algebra; Nonnegative Matrices; Various Topics;

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Book SynopsisThe volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry. It presents the detailed Hecke algebra and braid representation to illustrate the original Jones polynomial (rather than the algebraic formal definition many other books and research articles use) and provides self-contained proofs of the Tait conjecture (one of the big achievements from the Jones invariant). It also presents explicit computations to the Casson-Lin invariant via braid representations.With the approach of an explicit computational point of view on knot invariants, this user-friendly volume will benefit readers to easily understand low-dimensional topology from examples and computations, rather than only knowing terminologies and theorems.

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Book SynopsisThe volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry. It presents the detailed Hecke algebra and braid representation to illustrate the original Jones polynomial (rather than the algebraic formal definition many other books and research articles use) and provides self-contained proofs of the Tait conjecture (one of the big achievements from the Jones invariant). It also presents explicit computations to the Casson-Lin invariant via braid representations.With the approach of an explicit computational point of view on knot invariants, this user-friendly volume will benefit readers to easily understand low-dimensional topology from examples and computations, rather than only knowing terminologies and theorems.

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Book SynopsisIn China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they won the first place almost every year.The authors are coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book explains many basic techniques for proving inequalities such as direct comparison, method of magnifying and reducing, substitution method, construction method, and so on.

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Book SynopsisThe book gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel, and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as 'group' and 'field'. A brief discussion of the fundamental theorems of modern Galois theory and complete proofs of the quoted results are provided, and the material is organized in such a way that the more technical details can be skipped by readers who are interested primarily in a broad survey of the theory.In this second edition, the exposition has been improved throughout and the chapter on Galois has been entirely rewritten to better reflect Galois' highly innovative contributions. The text now follows more closely Galois' memoir, resorting as sparsely as possible to anachronistic modern notions such as field extensions. The emerging picture is a surprisingly elementary approach to the solvability of equations by radicals, and yet is unexpectedly close to some of the most recent methods of Galois theory.

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Book SynopsisThe volume is a collection of 20 refereed articles written in connection with lectures presented at the 12th International Conference on Finite Fields and Their Applications ('Fq12') at Skidmore College in Saratoga Springs, NY in July 2015. Finite fields are central to modern cryptography and secure digital communication, and hence must evolve rapidly to keep pace with new technologies. Topics in this volume include cryptography, coding theory, structure of finite fields, algorithms, curves over finite fields, and further applications.Contributors will include: Antoine Joux (Fondation Partenariale de l'UPMC, France); Gary Mullen (Penn State University, USA); Gohar Kyureghyan (Otto-von-Guericke Universität, Germany); Gary McGuire (University College Dublin, Ireland); Michel Lavrauw (Università degli Studi di Padova, Italy); Kirsten Eisentraeger (Penn State University, USA); Renate Scheidler (University of Calgary, Canada); Michael Zieve (University of Michigan, USA).

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Book SynopsisThe aim of this book is to give a systematic exposition of results in some important cases where p-adic families and p-adic L-functions are studied. We first look at p-adic families in the following cases: general linear groups, symplectic groups and definite unitary groups. We also look at applications of this theory to modularity lifting problems. We finally consider p-adic L-functions for GL(2), the p-adic adjoint L-functions and some cases of higher GL(n).Table of ContentsAn Overview of Serre's p-Adic Modular Forms (Miljan Brakocevic and R Sujatha); p-Adic Families of Ordinary Siegel Cusp Forms (Jacques Tilouine); Ordinary Families on Definite Unitary Groups (Baskar Balasubramanyam and Dipramit Majumdar); Modularity Lifting Theorems for Ordinary Galois Representations (David Geraghty); p-Adic L-Functions for GL(2) (Mladen Dimitrov); Arithmetic of Adjoint L-Values (Haruzo Hida); p-Adic L-Functions for GL(n) (Debargha Banerjee and A Raghuram); Non-Triviality of Generalised Heegner Cycles Over Anticyclotomic Towers: A Survey (Ashay Burungale); The Euler System of Heegner Points and p-Adic L-Functions (Ming-Lun Hsieh); Non-Commutative q-Expansions (Mahesh Kakde);

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Book SynopsisThis is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.

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Book SynopsisThe purpose of this book is to provide a concise yet detailed account of fundamental concepts in modern algebra. The target audience for this book is first-year graduate students in mathematics, though the first two chapters are probably accessible to well-prepared undergraduates. The book covers a broad range of topics in modern algebra and includes chapters on groups, rings, modules, algebraic extension fields, and finite fields. Each chapter begins with an overview which provides a road map for the reader showing what material will be covered. At the end of each chapter we collect exercises which review and reinforce the material in the corresponding sections. These exercises range from straightforward applications of the material to problems designed to challenge the reader. We also include a list of 'Questions for Further Study' which pose problems suitable for master's degree research projects.

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Book SynopsisThis is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.

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Book SynopsisThe purpose of this book is to provide a concise yet detailed account of fundamental concepts in modern algebra. The target audience for this book is first-year graduate students in mathematics, though the first two chapters are probably accessible to well-prepared undergraduates. The book covers a broad range of topics in modern algebra and includes chapters on groups, rings, modules, algebraic extension fields, and finite fields. Each chapter begins with an overview which provides a road map for the reader showing what material will be covered. At the end of each chapter we collect exercises which review and reinforce the material in the corresponding sections. These exercises range from straightforward applications of the material to problems designed to challenge the reader. We also include a list of 'Questions for Further Study' which pose problems suitable for master's degree research projects.

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Book SynopsisThis second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.

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Book SynopsisThis second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.

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Book SynopsisThis is the first book that focuses on practical algorithms for polynomial inequality proving and discovering. It is a summary of the work by the authors and their collaborators on automated inequality proving and discovering in recent years. Besides brief introduction to some classical results and related work in corresponding chapters, the book mainly focuses on the algorithms initiated by the authors and their collaborators, such as real root counting, real root classification, improved CAD projection, dimension-decreasing algorithm, difference substitution, and so on. All the algorithms were rigorously proved and the implementations are demonstrated by lots of examples in various backgrounds such as algebra, geometry, biological science, and computer science.See Press Release: A collection of practical algorithms for polynomial inequality proving and discoveringTable of ContentsIntroduction; Basics of Elimination Method; Zero Decomposition for Polynomial System; Triangularization of Semi-Algebraic System; Real Root Counting; Real Root Isolation; Real Root Classification; Polynomial Optimization Based on Improved CAD Projection; Dimension-Decreasing Algorithm; Difference Substitution; SOS Decomposition; Inequality Proving Beyond the Tarski Model;

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Book Synopsis“It is a nice to have a collection at hand taking together some of the main fundamental papers of a rapidly developing subject. ”Mathematics Abstracts This volume reviews the subject of Kac-Moody and Virasoro Algebras. It serves as a reference book for physicists with commentary notes and reprints.

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Book Synopsis“It is a nice to have a collection at hand taking together some of the main fundamental papers of a rapidly developing subject. ”Mathematics Abstracts This volume reviews the subject of Kac-Moody and Virasoro Algebras. It serves as a reference book for physicists with commentary notes and reprints.

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Book Synopsis“For anyone interested in the rapidly developing field of string theory (graduate students with the proper physics background), Siegel's book is a particularly good introduction.”>/p>Choice, USA“Siegel has played a major role in the application of BRST formalisms for quantization to string theory … Siegel's book is of great interest for those who intend to do research in string field theory.”Foundations of Physics, USA This volume covers the most up-to-date findings on string field theory. It is presented in a new approach as a result of insights gained from the theory. This includes the use of a universal method for treating free field theories, which allows the derivation of a single, simple, free, local, Poincare-invariant, gauge-invariant action that can be applied directly to any fields.

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Book SynopsisJohn Tobey received his BA in mathematics from Wheaton College in Wheaton, Illinois, in 1965, his MA in mathematics education from Harvard University in 1966, and his PhD in mathematics education from Boston University in 1980. He has taught in the mathematics department at the United States Military Academy at West Point and served as the Mathematics Department Chairman at North Shore Community College in Danvers, Massachusetts, for five years. John has served as the president of the New England Mathematics Association of Two Year Colleges. He has received the NISOD award for outstanding teaching from the University of Texas at Austin. John is the author of seven mathematics books published by Pearson Education. John has spoken to many mathematics departments and at many professional meetings throughout the country on the topic of developmental mathematics education and distance learning in mathematics. He lives in Massachusetts. Jeffrey SlaterTable of ContentsTable of Contents Whole Numbers 1.1 Understanding Whole Numbers 1.2 Adding Whole Numbers 1.3 Subtracting Whole Numbers 1.4 Multiplying Whole Numbers 1.5 Dividing Whole Numbers 1.6 Exponents and Order of Operations 1.7 Rounding and Estimating 1.8 Solving Applied Problems Involving Whole Numbers Career Explorations Chapter 1 Organizer Chapter 1 Review Problems Chapter 1 Test Math Coach Fractions 2.1 Understanding Fractions 2.2 Simplifying Fractions 2.3 Converting Between Improper Fractions and Mixed Numbers 2.4 Multiplying Fractions and Mixed Numbers 2.5 Dividing Fractions and Mixed Numbers 2.6 The Least Common Denominator and Creating Equaivalent Fractions 2.7 Adding and Subtracting Fractions 2.8 Adding and Subtracting Mixed Numbers and the Order of Operations 2.9 Solving Applied Problems Involving Fractions Career Explorations Chapter 2 Organizer Chapter 2 Review Problems Chapter 2 Test Math Coach Decimals 3.1 Using Decimal Notation 3.2 Comparing, Ordering, and Rounding Decimals 3.3 Adding and Subtracting Decimals 3.4 Multiplying Decimals 3.5 Dividing Decimals 3.6 Converting Fractions to Decimals and the Order of Operations 3.7 Estimating and Solving Applied Problems Involving Decimals Career Explorations Chapter 3 Organizer Chapter 3 Review Problems Chapter 3 Test Math Coach Ratio and Proportion 4.1 Ratios and Rates 4.2 The Concept of Proportions 4.3 Solving Proportions 4.4 Solving Applied Problems Involving Proportions Career Explorations Chapter 4 Organizer Chapter 4 Review Problems Chapter 4 Test Math Coach Percent 5.1 Understanding Percent 5.2 Changing Between Percents, Decimals, and Fractions 5.3A Solving Percent Problems Using Equations 5.3B Solving Percent Problems Using Proportions 5.4 Solving Applied Percent Problems 5.5 Solving Commission, Percent Increase or Decrease, and Interest Problems Career Explorations Chapter 5 Organizer Chapter 5 Review Problems Chapter 5 Test Math Coach Measurement 6.1 American Units 6.2 Metric Measurements: Length 6.3 Metric Measurements: Volume and Weight 6.4 Converting Units 6.5 Solving Applied Measurements Problems Career Explorations Chapter 6 Organizer Chapter 6 Review Problems Chapter 6 Test Math Coach Geometry 7.1 Angles 7.2 Rectangles and Squares 7.3 Parallelograms, Trapezoids, and Rhombuses 7.4 Triangles 7.5 Square Roots 7.6 The Pythagorean Theorem 7.7 Circles 7.8 Volume 7.9 Similar Geometric Features 7.10 Solving Applied Problems in Geometry Career Explorations Chapter 7 Organizer Chapter 7 Review Problems Chapter 7 Test Math Coach Statistics 8.1 Circle Graphs 8.2 Bar Graphs and Line Graphs 8.3 Histograms 8.4 Mean, Median, and Mode Career Explorations Chapter 8 Organizer Chapter 8 Review Problems Chapter 8 Test Math Coach Signed Numbers 9.1 Adding Signed Numbers 9.2 Subtracting Signed Numbers 9.3 Multiplying and Dividing Signed Numbers 9.4 Order of Operations with Signed Numbers 9.5 Scientific Notation Career Explorations Chapter 9 Organizer Chapter 9 Review Problems Chapter 9 Test Math Coach Introduction to Algebra 10.1 Variables and Like Terms 10.2 The Distributive Property 10.3 Solving Equations Using the Addition Property 10.4 Solving Equations Using the Division or Multiplication Property 10.5 Solving Equations Using Two Properties 10.6 Translating English to Algebra 10.7 Solving Applied Problems Career Explorations Chapter 10 Organizer Chapter 10 Review Problems Chapter 10 Test Math Coach

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Book SynopsisTable of Contents 1 - Linear Equations And Matrices 2 - Solving Linear Systems 3 - Determinants 4 - Real Vector Spaces 5 - Inner Product Spaces 6 - Linear Transformations and Matrices 7 - Eigenvalues and Eigenvectors 8 - Applications of Eigenvalues and Eigenvectors (Optional) 9 - MATLAB for Linear Algebra 10 - MATLAB Exercises

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