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Algebra

See below for a selection of the latest books from Algebra category. Presented with a red border are the Algebra books that have been lovingly read and reviewed by the experts at Lovereading. With expert reading recommendations made by people with a passion for books and some unique features Lovereading will help you find great Algebra books and those from many more genres to read that will keep you inspired and entertained. And it's all free!

Algebraic Inequalities: In Mathematical Olympiad And Competitions

Algebraic Inequalities: In Mathematical Olympiad And Competitions

Author: Ji (Ningbo Univ, China) Chen, Chaocheng (Ningbo Middle Sch, China) Ji Format: Hardback Release Date: 29/08/2021

The focus of this book is algebraic inequalities. Not only is it the current Mathematical Olympiad hot topic, it is also the basis of geometric inequalities. In addition, the book involves some analysis on inequality.This book serves as a good reference in the field of algebraic inequalities as faced in problems found in a Mathematical Olympiad.

Algebraic Inequalities: In Mathematical Olympiad And Competitions

Algebraic Inequalities: In Mathematical Olympiad And Competitions

Author: Ji (Ningbo Univ, China) Chen, Chaocheng (Ningbo Middle Sch, China) Ji Format: Paperback / softback Release Date: 29/08/2021

The focus of this book is algebraic inequalities. Not only is it the current Mathematical Olympiad hot topic, it is also the basis of geometric inequalities. In addition, the book involves some analysis on inequality.This book serves as a good reference in the field of algebraic inequalities as faced in problems found in a Mathematical Olympiad.

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

Galois Theory and Its Algebraic Background

Galois Theory and Its Algebraic Background

Author: D. J. H. (University of Cambridge) Garling Format: Paperback / softback Release Date: 31/07/2021

Galois Theory, the theory of polynomial equations and their solutions, is one of the most fascinating and beautiful subjects of pure mathematics. Using group theory and field theory, it provides a complete answer to the problem of the solubility of polynomial equations by radicals: that is, determining when and how a polynomial equation can be solved by repeatedly extracting roots using elementary algebraic operations. This textbook contains a fully detailed account of Galois Theory and the algebra that it needs and is suitable both for those following a course of lectures and the independent reader (who is assumed to have no previous knowledge of Galois Theory). The second edition has been significantly revised and re-ordered; the first part develops the basic algebra that is needed, and the second a comprehensive account of Galois Theory. There are applications to ruler-and- compass constructions, and to the solution of classical mathematical problems of ancient times. There are new exercises throughout, and carefully-selected examples will help the reader develop a clear understanding of the mathematical theory.

Galois Theory and Its Algebraic Background

Galois Theory and Its Algebraic Background

Author: D. J. H. (University of Cambridge) Garling Format: Hardback Release Date: 31/07/2021

Galois Theory, the theory of polynomial equations and their solutions, is one of the most fascinating and beautiful subjects of pure mathematics. Using group theory and field theory, it provides a complete answer to the problem of the solubility of polynomial equations by radicals: that is, determining when and how a polynomial equation can be solved by repeatedly extracting roots using elementary algebraic operations. This textbook contains a fully detailed account of Galois Theory and the algebra that it needs and is suitable both for those following a course of lectures and the independent reader (who is assumed to have no previous knowledge of Galois Theory). The second edition has been significantly revised and re-ordered; the first part develops the basic algebra that is needed, and the second a comprehensive account of Galois Theory. There are applications to ruler-and- compass constructions, and to the solution of classical mathematical problems of ancient times. There are new exercises throughout, and carefully-selected examples will help the reader develop a clear understanding of the mathematical theory.

Thinking Algebraically

Thinking Algebraically

Author: Thomas Q. Sibley Format: Paperback / softback Release Date: 30/07/2021

Thinking Algebraically presents the insights of abstract algebra in a welcoming and accessible way. It succeeds in combining the advantages of rings-first and groups-first approaches while avoiding the disadvantages. After an historical overview, the first chapter studies familiar examples and elementary properties of groups and rings simultaneously to motivate the modern understanding of algebra. The text builds intuition for abstract algebra starting from high school algebra. In addition to the standard number systems, polynomials, vectors, and matrices, the first chapter introduces modular arithmetic and dihedral groups. The second chapter builds on these basic examples and properties, enabling students to learn structural ideas common to rings and groups: isomorphism, homomorphism, and direct product. The third chapter investigates introductory group theory. Later chapters delve more deeply into groups, rings, and fields, including Galois theory, and they also introduce other topics, such as lattices. The exposition is clear and conversational throughout. The book has numerous exercises in each section as well as supplemental exercises and projects for each chapter. Many examples and well over 100 figures provide support for learning. Short biographies introduce the mathematicians who proved many of the results. The book presents a pathway to algebraic thinking in a semester- or year-long algebra course.

Linear Algebra: Gateway to Mathematics

Linear Algebra: Gateway to Mathematics

Author: Robert Messer Format: Paperback / softback Release Date: 30/07/2021

Linear Algebra: Gateway to Mathematics uses linear algebra as a vehicle to introduce students to the inner workings of mathematics. The structures and techniques of mathematics in turn provide an accessible framework to illustrate the powerful and beautiful results about vector spaces and linear transformations. The unifying concepts of linear algebra reveal the analogies among three primary examples: Euclidean spaces, function spaces, and collections of matrices. Students are gently introduced to abstractions of higher mathematics through discussions of the logical structure of proofs, the need to translate terminology into notation, and efficient ways to discover and present proofs. Application of linear algebra and concrete examples tie the abstract concepts to familiar objects from algebra, geometry, calculus, and everyday life. Students will finish a course using this text with an understanding of the basic results of linear algebra and an appreciation of the beauty and utility of mathematics. They will also be fortified with a degree of mathematical maturity required for subsequent courses in abstract algebra, real analysis, and elementary topology. Students who have prior background in dealing with the mechanical operations of vectors and matrices will benefit from seeing this material placed in a more general context.

Introduction to Lattice Algebra

Introduction to Lattice Algebra

Author: Gerhard X. Ritter, Gonzalo Urcid Format: Hardback Release Date: 27/07/2021

Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various applications outside the domain of pure mathematics. These applications range from electronic communication theory and gate array devices that implement Boolean logic to artificial intelligence and computer science in general. Introduction to Lattice Theory: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks lays emphasis on two subjects, the first being lattice algebra and the second the practical applications of that algebra. This textbook is intended to be used for a special topics course in artificial intelligence with focus on pattern recognition, multispectral image analysis, and biomimetic artificial neural networks. The book is self-contained and - depending on the student's major - can be used at a senior undergraduate level or a first-year graduate level course. The book is also an ideal self-study guide for researchers and professionals in the above-mentioned disciplines. Features Filled with instructive examples and exercises to help build understanding Suitable for researchers, professionals and students, both in mathematics and computer science Every chapter consists of exercises with solution provided online at www.Routledge.com/9780367720292

Practical Linear Algebra

Practical Linear Algebra

Linear algebra is growing in importance. 3D entertainment, animations in movies and video games are developed using linear algebra. Animated characters are generated using equations straight out of this book. Linear algebra is used to extract knowledge from the massive amounts of data generated from modern technology. The Fourth Edition of this popular text introduces linear algebra in a comprehensive, geometric, and algorithmic way. The authors start with the fundamentals in 2D and 3D, then move on to higher dimensions, expanding on the fundamentals and introducing new topics, which are necessary for many real-life applications and the development of abstract thought. Applications are introduced to motivate topics. The subtitle, A Geometry Toolbox, hints at the book's geometric approach, which is supported by many sketches and figures. Furthermore, the book covers applications of triangles, polygons, conics, and curves. Examples demonstrate each topic in action. This practical approach to a linear algebra course, whether through classroom instruction or self-study, is unique to this book. New to the Fourth Edition: Ten new application sections. A new section on change of basis. This concept now appears in several places. Chapters 14-16 on higher dimensions are notably revised. A deeper look at polynomials in the gallery of spaces. Introduces the QR decomposition and its relevance to least squares. Similarity and diagonalization are given more attention as are eigenfunctions. A longer thread on least squares, running from orthogonal projections to a solution via SVD and the pseudoinverse. More applications for PCA have been added. More examples, exercises, and more on the kernel and general linear spaces. A list of applications has been added in Appendix A. The book gives instructors the option of tailoring the course for the primary interests of their students: mathematics, engineering, science, computer graphics, and geometric modeling. Table of Contents Preface Descartes' Discovery Here and There: Points and Vectors in 2D Lining Up: 2D Lines Changing Shapes: Linear Maps in 2D 2 x 2 Linear Systems Moving Things Around: Affine Maps in 2D Eigen Things 3D Geometry Linear Maps in 3D Affine Maps in 3D Interactions in 3D Gauss or Linear Systems Alternative System Solvers General Linear Spaces Eigen Things Revisited The Singular Value Decomposition Breaking It Up: Triangles Putting Lines Together: Polylines and Polygons Conics Curves Appendices Applications Glossary Select Exercise Solutions Bibliography Biography Gerald Farin (deceased) was a professor in the School of Computing, Informatics, and Design Systems Engineering (CIDSE) at Arizona State University. He received his doctoral degree in mathematics from the University of Braunschweig, Germany. His extensive experience in geometric design started at Daimler-Benz. He was a founding member of the editorial board for the journal Computer-Aided Geometric Design (Elsevier), and he served as co-editor in chief for more than 20 years. He published more than 100 research papers. Gerald also organized numerous conferences and authored or edited 29 books. This includes his much read and referenced textbook Curves and Surfaces for CAGD and his book on NURBS. In addition to this book, Gerald and Dianne co-authored The Essentials of CAGD, Mathematical Principles for Scientific Computing and Visualization both also published by AK Peters/CRC Press. Dianne Hansford, received her Ph.D. from Arizona State University. Her research interests are in the field of geometric modeling with a focus on industrial curve and surface applications related to mathematical definitions of shape. Together with Gerald Farin (deceased), she delivered custom software solutions, advisement on best practices, and taught on-site courses as a consultant. She is a co-founder of 3D Compression Technologies. She is now lecturer in the School of Computing, Informatics, and Design Systems Engineering (CIDSE) at Arizona State University, primarily teaching geometric design, computer graphics, and scientific computing and visualization. In addition to this book, Gerald and Dianne co-authored The Essentials of CAGD, Mathematical Principles for Scientific Computing and Visualization both also published by AK Peters/CRC Press.

Algebra and Applications 1

Algebra and Applications 1

Author: Abdenacer Makhlouf Format: Hardback Release Date: 05/07/2021

This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the first of three volumes specifically focusing on algebra and its applications. Algebra and Applications 1 centers on non-associative algebras and includes an introduction to derived categories. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Jordan superalgebras, Lie algebras, composition algebras, graded division algebras, non-associative C*- algebras, H*-algebras, Krichever-Novikov type algebras, preLie algebras and related structures, geometric structures on 3-Lie algebras and derived categories are all explored. Algebra and Applications 1 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.

The Manga Guide To Linear Algebra

The Manga Guide To Linear Algebra

Author: Shin Takahashi Format: Paperback / softback Release Date: 29/06/2021