This book combines concepts from algebraic geometry and differential geometry. Building on classical foundations. Many applied problems center around metric questions, such as optimization with respect to distances.

This book covers a combination of classical algebra and analytic geometry, with an introduction to the transcendental exponential and logarithmic functions. If mathematics is the language of science, then algebra is the grammar of that language.

More than merely a succession of definition-theorem-proofs, this text put results and ideas in context so that students can appreciate why a certain topic is being studied, and where definitions originate.

This open access textbook presents a comprehensive treatment of the arithmetic theory of Quaternion Algebras and orders, a subject with applications in diverse areas of mathematics. Numerous pathways offer explorations in many different directions.

Written and reviewed by a team of highly experienced instructors, this book provides a comprehensive and multilayered exploration of algebraic principles. It is suitable for a typical introductory algebra course, and was developed to be used fexibly.

This book provides a comprehensive and multi-layered exploration of algebraic principles. It is suitable for a typical introductory Algebra & Trigonometry course, and was developed to be used flexibly. The book meets the needs of a variety of programs.

A proven motivator for readers of diverse mathematical backgrounds, this book explores mathematics within the context of real life using understandable, realistic applications consistent with the abilities of any reader.

This is a book on linear algebra and matrix theory. It gives a self- contained treatment of linear algebra with many of its most important applications which does not neglect arbitrary fields of scalars and the proofs of the theorems.

This textbook covers linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. Each chapter has three or four discussions of additional topics and applications.

This book is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications.

This book provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today, with discrete explanations from functions to quadratic and linear equations, etc.

This book is a unique approach and presentation, the author demonstrates how software can be used as a problem-solving tool for algebra. It includes many computations, both as examples and as exercises.

This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. It covers the basics of number theory, abstract algebra and discrete probability theory.

This book is dealing with a broad range of topics, ranging from algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic to computer algebra problems in quantum computing.

A college (or advanced high school) level text dealing with the basic principles of matrix and linear algebra. It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations.

This is a course in matrix algebra, with a focus on concepts that are often used in probability and statistics. Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory.

This book is designed to introduce students to the use of Linear Algebra to solve real-world problems. These materials were developed specifically for students and instructors that emphasizes hands-on problem-solving activities.

Thoroughly details matrix computations and the accompanying theory alongside the author's useful insights, This book provides a clear and thorough introduction to matrix computations,a key component of scientific computing.

The tensor trigonometry is development of the flat scalar trigonometry from Leonard Euler classic forms into general multi-dimensional tensor forms with vector and scalar orthoprojections and with step by step increasing complexity and opportunities.

This detailed exposition makes the rich legacy of classical algebraic geometry accessible to modern algebraic geometers and to others who are interested in applying classical results. Topics include plane algebraic curves of low degree, etc.

This book is intended as a text for a graduate course that focuses on applications of linear algebra and on the algorithms used to solve the problems that arise in those applications. It uses matrix theory to understand the workings of the algorithms.

The focus is on numerical linear algebra, the study of how theory, algorithms, and computer arithmetic interact. These materials keep the learner engaged by intertwining text, videos, exercises, and programming activities in consumable chunks.

This book is an introduction to the basic concepts of linear algebra, along with an introduction to the techniques of formal mathematics. It begins with systems of equations and matrix algebra before moving into the advanced topics.

This undergraduate textbook on Linear Algebra and n-Dimensional Geometry, in a self-teaching style, is invaluable for sophomore level undergraduates in mathematics, engineering, business, and the sciences.

This 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.

This is a modern presentation of the fundamental notions of Group Theory is chosen, where the language of commutative diagrams and universal properties, so necessary in Modern Mathematics, in Physics and Computer Science, among other disciplines.

This book explores the use of symmetries through descriptions of the techniques of Lie groups and Lie algebras. It develops the models, theoretical framework, and mathematical tools to understand these symmetries.

This book aims to express properties of graphs in algebraic terms, then to deduce theorems about them. It tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix, using the Sage.

Linear Algebra: Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets.

The aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students.

Combines straightforward explanations with a wealth of practical examples to offer an innovative approach to teaching linear algebra. Requiring no prior knowledge of the subject, it covers the aspects of linear algebra - vectors, matrices, and least squares

These books use a teacherly writing style and a careful blend of skills development and conceptual questions to meet the unique needs of the developmental math student. It takes advantage of experiences in the classroom and an editing eye to offer one of the most well-rounded series available, written with the developmental learner in mind.

This textbook on linear algebra is written to be easy to digest by non-mathematicians. It introduces the concepts of vector spaces and mappings between them without too much theorems and proofs. Various applications of the formal theory are discussed as well.

This textbook contains a collection of six high-quality chapters. The techniques are illustrated by a wide sample of applications. This book is devoted to Linear Mathematics by presenting problems in Applied Linear Algebra of general or special interest.

This book includes content found in a typical algebra course, along with introductions to curve-fitting and display of data. The authors focus on three core themes throughout their textbook: Modeling, Functions, and Graphs.

It introduces the basic notions of group theory by a thorough treatment of important examples, including complex numbers, modular arithmetic, symmetries, and permutations, also applications to communications, cryptography, and coding theory.

French mathematician Evariste Galois developed the Galois theory of groups-one of the most penetrating concepts in modem mathematics. The elements of the theory are clearly presented in this lectures delivered by noted mathematician Emil Artin.

This book is on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry.

This book is on Preliminaries about the Integers, Polynomials, and Matrices; Vector Spaces over Q, R, and C; Inner-Product Spaces; Groups and Group Actions; Theory of a Single Linear Transformation; Multilinear Algebra; Advanced Group Theory; etc.

This book brings out how sets in algebraic structures can be used to construct the most generalized algebraic structures, like set linear algebra / vector space, set ideals in groups and rings and semigroups, and topological set vector spaces.

This book surveys fundamental algebraic structures and maps between these structures. Its techniques are used in many areas of mathematics, with applications to physics, engineering, and computer science as well.

This introduction to modern or abstract algebra addresses the conventional topics of groups, rings, and fields with symmetry as a unifying theme, while it introduces readers to the active practice of mathematics.

This book starts by gently training you in the fundamental mental skills. It then shows how to apply them mathematically, with a focus on algebra.

An brief overview of pre-algebra and introductory algebra topics, written in a style meant to give you the basic facts in a way that is easy to understand, suitable for high-school Algebra I, or for anyone who wants to learn introductory algebra.

This book is an informal and readable introduction to higher algebra at the post-calculus level with focus on infinite algebras; ; infinite-Operads; Algebras and Modules over infinte-Operads; Associative Algebras and Their Modules; etc.

This textbook is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course.

The book presents an introduction to the fascinating subject of linear algebra. As the title suggests, this text is designed as a first course in linear algebra for students who have a reasonable understanding of basic algebra.

This book aims to bridge the gap between the mainly computation-oriented lower division undergraduate classes and the abstract mathematics encountered in more advanced mathematics courses.

This book contains selected topics in linear algebra, which represent the recent contributions in the most famous and widely problems. It includes a wide range of theorems and applications in different branches of linear algebra, etc.

Focus on the mathematical framework that underlies linear systems arising in physics, engineering and applied mathematics - from the theory of linear transformation on finite dimensional vector space to the infinite dimensional vector spaces.

This book avoids the traditional definition-theorem-proof format; instead a fresh approach introduces a variety of problems and examples all in a clear and informal style.

This book presents the elements of analysis and linear algebra used in financial models and in microeconomics. Functions of one and several variables and matrices are developed as well as vector spaces, linear mappings and optimization methods, etc.

Assuming little mathematical background, this short introduction to Category Theory is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time.

Using databases as an entry to Category Theory, this book explains category theory by examples, and shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences.

This book introduces Category Theory at a level appropriate for computer scientists and provides practical examples in the context of programming language design.

Anyone need to use algorithms in polynomials should have a copy of this! This is definitely one of the best! It covers almost everything anyone need in computation with systems of polynomial equations: Grobner Basis, Resultants, Characteristic Set, etc.

This book provides a systematic and focused treatment of a collection of core problemsthe computational equivalents of the classical Fundamental Problem of Algebra and its derivatives.

Super Linear Algebras are built using super matrices. These new structures can be applied to all fields in which linear algebras are used. Super characteristic values exist only when the related super matrices are super square diagonal super matrices.

This book is intended for researchers in applied mathematics and scientific computing as well as for practitioners interested in understanding the theory of numerical methods used for eigenvalue problems.

This unique text presents the new domain of consistent non-linear counterparts for all basic objects and tools of linear algebra, and develops an adequate calculus for solving non-linear algebraic and differential equations.

The monograph gives a self-contained detailed exposition of the algorithmic real algebraic geometry. It will be useful both for beginners and for advanced readers, who work in real algebraic geometry or apply its methods in other fields.

The book begins with an introduction to model theory. It then broadens into three components: pure model theory, geometry, and the model theory of fields.

This book presents a thorough treatment of many algorithms concerning the arithmetic of elliptic curves with remarks on computer implementation.

It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.

TThis book is a standalone version of part of From Arithmetic To Differential Calculus (A2DC), a course of study developed to allow a significantly higher percentage of students to complete Differential Calculus in three semesters.

This book is to present a complete course on global analysis topics and establish some orbital applications of the integration on topological groups and their algebras to harmonic analysis and induced representations in representation theory.

In 1900, David Hilbert asked whether each locally euclidean topological group admits a Lie group structure. This was the fifth of his famous 23 questions which foreshadowed much of the mathematical creativity of the twentieth century.

This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally.

This book is both a comprehensive introduction to the subject and a valuable reference source for researchers. An introductory chapter provides the reader with all the necessary background material.

You will find algebra exercises and problems, grouped by chapters, intended for higher grades in high schools or middle schools of general education. Its purpose is to facilitate training in mathematics for students in all high school categories.

This book presents the elements of analysis and linear algebra used in financial models and in microeconomics.

The theory of equations is not only a necessity in the subsequent mathematical courses and their applications, but furnishes an illuminating sequel to geometry, algebra and analytic geometry. A useful supplement to differential calculus.