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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!

Fundamentals of Numerical Mathematics for Physicists and Engineers

Fundamentals of Numerical Mathematics for Physicists and Engineers

Author: Alvaro Meseguer Format: Hardback Release Date: 19/07/2020

Introduces the fundamentals of numerical mathematics and illustrates its applications to a wide variety of disciplines in physics and engineering Applying numerical mathematics to solve scientific problems, this book helps readers understand the mathematical and algorithmic elements that lie beneath numerical and computational methodologies in order to determine the suitability of certain techniques for solving a given problem. It also contains examples related to problems arising in classical mechanics, thermodynamics, electricity, and quantum physics. Fundamentals of Numerical Mathematics for Physicists and Engineers is presented in two parts. Part I addresses the root finding of univariate transcendental equations, polynomial interpolation, numerical differentiation, and numerical integration. Part II examines slightly more advanced topics such as introductory numerical linear algebra, parameter dependent systems of nonlinear equations, numerical Fourier analysis, and ordinary differential equations (initial value problems and univariate boundary value problems). Chapters cover: Newton's method, Lebesgue constants, conditioning, barycentric interpolatory formula, Clenshaw-Curtis quadrature, GMRES matrix-free Krylov linear solvers, homotopy (numerical continuation), differentiation matrices for boundary value problems, Runge-Kutta and linear multistep formulas for initial value problems. Each section concludes with Matlab hands-on computer practicals and problem and exercise sets. This book: Provides a modern perspective of numerical mathematics by introducing top-notch techniques currently used by numerical analysts Contains two parts, each of which has been designed as a one-semester course Includes computational practicals in Matlab (with solutions) at the end of each section for the instructor to monitor the student's progress through potential exams or short projects Contains problem and exercise sets (also with solutions) at the end of each section Fundamentals of Numerical Mathematics for Physicists and Engineers is an excellent book for advanced undergraduate or graduate students in physics, mathematics, or engineering. It will also benefit students in other scientific fields in which numerical methods may be required such as chemistry or biology.

Hot Topics in Linear Algebra

Hot Topics in Linear Algebra

Author: Ivan Kyrchei Format: Hardback Release Date: 17/07/2020

Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. Systems of linear equations with several unknowns are naturally represented using the formalism of matrices and vectors. So we arrive at the matrix algebra, etc. Linear algebra is central to almost all areas of mathematics. Many ideas and methods of linear algebra were generalized to abstract algebra. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Linear algebra is also used in most sciences and engineering areas because it allows for the modeling of many natural phenomena, and efficiently computes with such models. ''Hot Topics in Linear Algebra'' presents original studies in some areas of the leading edge of linear algebra. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum. Topics discussed herein include recent advances in analysis of various dynamical systems based on the Gradient Neural Network; Cramer's rules for quaternion generalized Sylvester-type matrix equations by using noncommutative row-column determinants; matrix algorithms for finding the generalized bisymmetric solution pair of general coupled Sylvester-type matrix equations; explicit solution formulas of some systems of mixed generalized Sylvester-type quaternion matrix equations; new approaches to studying the properties of Hessenberg matrices by using triangular tables and their functions; researching of polynomial matrices over a field with respect to semi-scalar equivalence; mathematical modeling problems in chemistry with applying mixing problems, which the associated MP-matrices; and some visual apps, designed in Scilab, for the learning of different topics of linear algebra.

Basic Representation Theory of Algebras

Basic Representation Theory of Algebras

Author: Ibrahim Assem, Flavio U. Coelho Format: Hardback Release Date: 13/07/2020

This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander-Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander-Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.

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: 29/06/2020

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: 29/06/2020

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.

Linear Algebra And Its Applications

Linear Algebra And Its Applications

Author: T.T. (Purdue Univ, Usa) Moh Format: Hardback Release Date: 29/06/2020

From Tzuong-Tsieng Moh, a long-time expert in algebra, comes a new book for students to better understand linear algebra. Writing from an experienced standpoint, Moh touches on the many facets surrounding linear algebra, including but not limited to, echelon forms, matrix algebra, linear transformations, determinants, dual space, inner products, the Gram-Schmidt Theorem, Hilbert space, and more. It is ideal for both newcomers and seasoned readers who want to attain a deeper understanding on both the basics and advanced topics of linear algebra and its vast applications. The wide range of topics combined with the depth of each discussion make it essential to be on the shelf of every mathematical beginner and enthusiast.

Linear Algebra for 21st Century Applications

Linear Algebra for 21st Century Applications

Customarily, much of traditional mathematics curricula was predicated on 'by hand' calculation. However, ubiquitous computing requires us to refresh what we teach and how it is taught. This is especially true in the rapidly broadening fields of Data Mining and Artificial Intelligence, and also in fields such as Bioinformatics, which all require the use of Singular Value Decomposition (SVD). Indeed SVD is sometimes called the jewel in the crown of linear algebra. Linear Algebra for 21st Century Applications adapts linear algebra to best suit modern teaching and application, and it places the SVD as central to the text early on to empower science and engineering students to learn and use potent practical and theoretical techniques. No rigour is lost in this new route as the text demonstrates that most theory is better proved with an SVD. In addition to this, there is earlier introduction, development, and emphasis on orthogonality that is vital in so many applied disciplines throughout science, engineering, computing and increasingly within the social sciences. A strong graphical emphasis takes advantage of the power of visualisation in the human brain and examples are included to exhibit modern applications of linear algebra, such as GPS, text mining, and image processing. Active learning is encouraged with exercises throughout that are aimed to enhance lectures, quizzes, or 'flipped' teaching.

Linear Algebra for 21st Century Applications

Linear Algebra for 21st Century Applications

Customarily, much of traditional mathematics curricula was predicated on 'by hand' calculation. However, ubiquitous computing requires us to refresh what we teach and how it is taught. This is especially true in the rapidly broadening fields of Data Mining and Artificial Intelligence, and also in fields such as Bioinformatics, which all require the use of Singular Value Decomposition (SVD). Indeed SVD is sometimes called the jewel in the crown of linear algebra. Linear Algebra for 21st Century Applications adapts linear algebra to best suit modern teaching and application, and it places the SVD as central to the text early on to empower science and engineering students to learn and use potent practical and theoretical techniques. No rigour is lost in this new route as the text demonstrates that most theory is better proved with an SVD. In addition to this, there is earlier introduction, development, and emphasis on orthogonality that is vital in so many applied disciplines throughout science, engineering, computing and increasingly within the social sciences. A strong graphical emphasis takes advantage of the power of visualisation in the human brain and examples are included to exhibit modern applications of linear algebra, such as GPS, text mining, and image processing. Active learning is encouraged with exercises throughout that are aimed to enhance lectures, quizzes, or 'flipped' teaching.

Algebra For Parents: A Book For Grownups About Middle School Mathematics

Algebra For Parents: A Book For Grownups About Middle School Mathematics

Author: Ron (Technion, Israel Inst Of Tech, Israel) Aharoni Format: Hardback Release Date: 13/05/2020

The book goes through middle school mathematics and techniques and methods of its teaching. It is meant to aid parents who wish to be involved in the mathematical education of their children, as well as teachers who wish to learn principles of mathematics and of its teaching.

Algebra For Parents: A Book For Grownups About Middle School Mathematics

Algebra For Parents: A Book For Grownups About Middle School Mathematics

Author: Ron (Technion, Israel Inst Of Tech, Israel) Aharoni Format: Paperback / softback Release Date: 13/05/2020

The book goes through middle school mathematics and techniques and methods of its teaching. It is meant to aid parents who wish to be involved in the mathematical education of their children, as well as teachers who wish to learn principles of mathematics and of its teaching.

An Invitation To Algebraic Numbers And Algebraic Functions

An Invitation To Algebraic Numbers And Algebraic Functions

Author: Franz (University of Graz, Austria) Halter-Koch Format: Hardback Release Date: 08/05/2020

The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekind's ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of differents, discriminants, and higher ramification. The theory of function fields is based on the ideal and valuation theory developed before; it presents the Riemann-Roch theorem on the basis of Weil differentials and highlights in detail the connection with classical differentials. The theory of congruence zeta functions and a proof of the Hasse -Weil theorem represent the culminating point of the volume. The volume is accessible with a basic knowledge in algebra and elementary number theory. It empowers the reader to follow the advanced number-theoretic literature, and it is a solid basis for the study of the forthcoming volume on the foundations and main results of class field theory. Key features: A thorough presentation of the theory of Algebraic Numbers and Algebraic Functions on an ideal- and valuation-theoretic basis. Several of the topics both in the number field and in the function field case were not presented before in this context. Despite the wealth of presented advanced topics the text is easily readable.

Vectors, Pure and Applied A General Introduction to Linear Algebra

Vectors, Pure and Applied A General Introduction to Linear Algebra

Author: T. W. Korner Format: Paperback / softback Release Date: 01/05/2020

Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online.