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Gorenstein Homological Algebra

Gorenstein Homological Algebra

Gorenstein homological algebra is an important area of mathematics with applications in commutative and noncommutative algebra model category theory representation theory and algebraic geometry. While in classical homological algebra the existence of the projective injective and flat resolutions over arbitrary rings are well known things are a little different when it comes to Gorenstein homological algebra. The main open problems in this area deal with the existence of the Gorenstein injective Gorenstein projective and Gorenstein flat resolutions. Gorenstein Homological Algebra is especially suitable for graduate students interested in homological algebra and its applications.

GBP 150.00
1

Geometric Algebra and Applications to Physics

Geometric Algebra and Applications to Physics

Bringing geometric algebra to the mainstream of physics pedagogy Geometric Algebra and Applications to Physics not only presents geometric algebra as a discipline within mathematical physics but the book also shows how geometric algebra can be applied to numerous fundamental problems in physics especially in experimental situations. This reference begins with several chapters that present the mathematical fundamentals of geometric algebra. It introduces the essential features of postulates and their underlying framework; bivectors multivectors and their operators; spinor and Lorentz rotations; and Clifford algebra. The book also extends some of these topics into three dimensions. Subsequent chapters apply these fundamentals to various common physical scenarios. The authors show how Maxwell's equations can be expressed and manipulated via space-time algebra and how geometric algebra reveals electromagnetic waves' states of polarization. In addition they connect geometric algebra and quantum theory discussing the Dirac equation wave functions and fiber bundles. The final chapter focuses on the application of geometric algebra to problems of the quantization of gravity. By covering the powerful methodology of applying geometric algebra to all branches of physics this book provides a pioneering text for undergraduate and graduate students as well as a useful reference for researchers in the field.

GBP 59.99
1

Differential Equations A Linear Algebra Approach

Differential Equations A Linear Algebra Approach

Differential Equations: A Linear Algebra Approach follows an innovative approach of inculcating linear algebra and elementary functional analysis in the backdrop of even the simple methods of solving ordinary differential equations. The contents of the book have been made user-friendly through concise useful theoretical discussions and numerous illustrative examples practical and pathological. | Differential Equations A Linear Algebra Approach

GBP 105.00
1

Introduction to Linear Algebra

Introduction to Linear Algebra

Linear algebra provides the essential mathematical tools to tackle all the problems in Science. Introduction to Linear Algebra is primarily aimed at students in applied fields (e. g. Computer Science and Engineering) providing them with a concrete rigorous approach to face and solve various types of problems for the applications of their interest. This book offers a straightforward introduction to linear algebra that requires a minimal mathematical background to read and engage with. Features Presented in a brief informative and engaging style Suitable for a wide broad range of undergraduates Contains many worked examples and exercises

GBP 44.99
1

Computer Algebra Concepts and Techniques

Computer Algebra Concepts and Techniques

The goal of Computer Algebra: Concepts and Techniques is to demystify computer algebra systems for a wide audience including students faculty and professionals in scientific fields such as computer science mathematics engineering and physics. Unlike previous books the only prerequisites are knowledge of first year calculus and a little programming experience — a background that can be assumed of the intended audience. The book is written in a lean and lively style with numerous examples to illustrate the issues and techniques discussed. It presents the principal algorithms and data structures while also discussing the inherent and practical limitations of these systems | Computer Algebra Concepts and Techniques

GBP 44.99
1

Abstract Algebra

Abstract Algebra

Designed for an advanced undergraduate- or graduate-level course Abstract Algebra provides an example-oriented less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory polynomials finite fields as well as linear and multilinear algebra. This classroom-tested how-to manual takes a more narrative approach than the stiff formalism of many other textbooks presenting coherent storylines to convey crucial ideas in a student-friendly accessible manner. An unusual feature of the text is the systematic characterization of objects by universal mapping properties rather than by constructions whose technical details are irrelevant. Addresses Common Curricular Weaknesses In addition to standard introductory material on the subject such as Lagrange's and Sylow's theorems in group theory the text provides important specific illustrations of general theory discussing in detail finite fields cyclotomic polynomials and cyclotomic fields. The book also focuses on broader background including brief but representative discussions of naive set theory and equivalents of the axiom of choice quadratic reciprocity Dirichlet's theorem on primes in arithmetic progressions and some basic complex analysis. Numerous worked examples and exercises throughout facilitate a thorough understanding of the material.

GBP 59.99
1

Abstract Algebra A First Course

Abstract Algebra A First Course

When a student of mathematics studies abstract algebra he or she inevitably faces questions in the vein of What is abstract algebra or What makes it abstract? Algebra in its broadest sense describes a way of thinking about classes of sets equipped with binary operations. In high school algebra a student explores properties of operations (+ − × and ÷) on real numbers. Abstract algebra studies properties of operations without specifying what types of number or object we work with. Any theorem established in the abstract context holds not only for real numbers but for every possible algebraic structure that has operations with the stated properties. This textbook intends to serve as a first course in abstract algebra. The selection of topics serves both of the common trends in such a course: a balanced introduction to groups rings and fields; or a course that primarily emphasizes group theory. The writing style is student-centered conscientiously motivating definitions and offering many illustrative examples. Various sections or sometimes just examples or exercises introduce applications to geometry number theory cryptography and many other areas. This book offers a unique feature in the lists of projects at the end of each section. the author does not view projects as just something extra or cute but rather an opportunity for a student to work on and demonstrate their potential for open-ended investigation. The projects ideas come in two flavors: investigative or expository. The investigative projects briefly present a topic and posed open-ended questions that invite the student to explore the topic asking and to trying to answer their own questions. Expository projects invite the student to explore a topic with algebraic content or pertain to a particular mathematician’s work through responsible research. The exercises challenge the student to prove new results using the theorems presented in the text. The student then becomes an active participant in the development of the field. | Abstract Algebra A First Course

GBP 99.99
1

Algebra & Geometry An Introduction to University Mathematics

Algebra & Geometry An Introduction to University Mathematics

Algebra & Geometry: An Introduction to University Mathematics Second Edition provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations polynomial equations and quadratic forms. The first few chapters cover foundational topics including the importance of proofs and a discussion of the properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solutions of different kinds of algebraic equations the nature of the solutions and the interplay between geometry and algebra. New to the second edition Several updated chapters plus an all-new chapter discussing the construction of the real numbers by means of approximations by rational numbers Includes fifteen short ‘essays’ that are accessible to undergraduate readers but which direct interested students to more advanced developments of the material Expanded references Contains chapter exercises with solutions provided online at www. routledge. com/9780367563035 | Algebra & Geometry An Introduction to University Mathematics

GBP 52.99
1

Linear Algebra

Linear Algebra

Linear Algebra is intended primarily as an undergraduate textbook but is written in such a way that it can also be a valuable resource for independent learning. The narrative of the book takes a matrix approach: the exposition is intertwined with matrices either as the main subject or as tools to explore the theory. Each chapter contains a description of its aims a summary at the end of the chapter exercises and solutions. The reader is carefully guided through the theory and techniques presented which are outlined throughout in How to… text boxes. Common mistakes and pitfalls are also pointed out as one goes along. Features Written to be self-contained Ideal as a primary textbook for an undergraduate course in linear algebra Applications of the general theory which are of interest to disciplines outside of mathematics such as engineering

GBP 52.99
1

Computational Linear Algebra with Applications and MATLAB Computations

Computational Linear Algebra with Applications and MATLAB Computations

Courses on linear algebra and numerical analysis need each other. Often NA courses have some linear algebra topics and LA courses mention some topics from numerical analysis/scientific computing. This text merges these two areas into one introductory undergraduate course. It assumes students have had multivariable calculus. A second goal of this text is to demonstrate the intimate relationship of linear algebra to applications/computations. A rigorous presentation has been maintained. A third reason for writing this text is to present in the first half of the course the very important topic on singular value decomposition SVD. This is done by first restricting consideration to real matrices and vector spaces. The general inner product vector spaces are considered starting in the middle of the text. The text has a number of applications. These are to motivate the student to study the linear algebra topics. Also the text has a number of computations. MATLAB® is used but one could modify these codes to other programming languages. These are either to simplify some linear algebra computation or to model a particular application. | Computational Linear Algebra with Applications and MATLAB® Computations

GBP 44.99
1

Exploring Linear Algebra Labs and Projects with MATLAB

Exploring Linear Algebra Labs and Projects with MATLAB

Exploring Linear Algebra: Labs and Projects with MATLAB® is a hands-on lab manual that can be used by students and instructors in classrooms every day to guide the exploration of the theory and applications of linear algebra. For the most part labs discussed in the book can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections. The exercise sections integrate problems using Mathematica demonstrations (an online tool that can be used with a browser with Java capabilities) and MATLAB® coding. This allows students to discover the theory and applications of linear algebra in a meaningful and memorable way. Features: The book’s inquiry-based approach promotes student interaction Each chapter contains a project set which consists of application-driven projects emphasizing the chapter’s materials Adds a project component to any Linear Algebra course Explores many applications to a variety of fields that can promote research projects Employs MATLAB® to calculate and explore concepts and theories of linear algebra | Exploring Linear Algebra Labs and Projects with MATLAB®

GBP 44.99
1

Concise Introduction to Linear Algebra

Concise Introduction to Linear Algebra

Concise 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.

GBP 44.99
1

Abstract Algebra A Gentle Introduction

Abstract Algebra A Gentle Introduction

Abstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller less expensive and brief introductions to primary courses. The authors move away from the ‘everything for everyone’ approach so common in textbooks. Instead they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra. Through a careful selection of topics supported by interesting applications the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majorswho need to have an introduction to the topic. As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a gentle introduction meant to provide enough for a course yet also enough to encourage them toward future study of the topic. FeaturesGroups before rings approachInteresting modern applicationsAppendix includes mathematical induction the well-ordering principle sets functions permutations matrices and complex nubers. Numerous exercises at the end of each sectionChapter Hint and Partial Solutions offers built in solutions manual | Abstract Algebra A Gentle Introduction

GBP 42.99
1

A Modern Introduction to Linear Algebra

A Modern Introduction to Linear Algebra

Useful Concepts and Results at the Heart of Linear AlgebraA one- or two-semester course for a wide variety of students at the sophomore/junior undergraduate levelA Modern Introduction to Linear Algebra provides a rigorous yet accessible matrix-oriented introduction to the essential concepts of linear algebra. Concrete easy-to-understand examples motivate the theory. The book first discusses vectors Gaussian elimination and reduced row echelon forms. It then offers a thorough introduction to matrix algebra including defining the determinant naturally from the PA=LU factorization of a matrix. The author goes on to cover finite-dimensional real vector spaces infinite-dimensional spaces linear transformations and complex vector spaces. The final chapter presents Hermitian and normal matrices as well as quadratic forms. Taking a computational algebraic and geometric approach to the subject this book provides the foundation for later courses in higher mathematics. It also shows how linear algebra can be used in various areas of application. Although written in a pencil and paper manner the text offers ample opportunities to enhance learning with calculators or computer usage. Solutions manual available for qualifying instructors

GBP 59.99
1