Basic Algebra I

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.

A classic text and standard reference for a generation, this volume covers all undergraduate algebra topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition.

"Explores all of the topics typically covered in undergraduate courses including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra"--Cover p. 4

Relations between groups and sets, results and methods of abstract algebra in terms of number theory and geometry, and noncommutative and homological algebra. Solutions. 2006 edition.

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters 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. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.

If you have bought any of my books on Simplified Algebra (Volume 1 to 4), then this book might not be for you because this book is an edited version with some corrections and inclusion of solutions to the exercises. However, if you have not bought any of my books on Simplified Algebra (Volume 1 to 4), then you will find this book very useful for learning the basics of Algebra. Simplified Basic Algebra: A Self-Teaching Book for High Schools and Colleges provides an easy way to gain a solid understanding of the basics of algebra in Mathematics. Assuming no background knowledge of the subject, this clear and self teaching guide explains solved problems in ways that are easy to understand. Exercises are given at the end of each chapter for students to use to asses their understanding of the topic. Solutions to the exercises are provided at the end of the book. This maths book is an ideal resource for high school students and college students taking algebra courses, for students taking higher level courses needing to refresh their knowledge, and for those preparing for admission and need to take entrance test or exam. Topics covered in this e-book include: Basic arithmetic operations Laws of indices Linear and quadratic equations Change of subject of formulae Simultaneous equations Word problems forming linear, simultaneous and quadratic equations Introductory logical reasoning Variation Linear and quadratic inequality Introductory vector algebra ...and more! A self-guided approach which enables you to move through the material at your own pace―gradually building upon your knowledge while you strengthen your critical thinking and problem-solving skills. This powerful learning resource features: A step-by-step method proven to increase your understanding of the fundamental concepts in algebra Emphasis on important basics, with clear explanations to ensure that you comprehend the material quickly Many worked examples with concise, student-friendly approach to the worked examples Exercises at the end of each chapter. Solutions to the exercises are at the end of the book so that students can asses their understanding of each topic. Simplified Basic Algebra: A Self-Teaching Book for High Schools and Colleges breaks down difficult calculations into simpler steps. Whether you are studying Algebra in school and you are looking for a little help making sense of what is being taught in class, or you are just into learning new things, Simplified Basic Algebra gets you rolling with all the basics you need. This worked examples-packed math book puts you on the fast-track to mastering the basics of algebra.

This is the first volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. This volume covers the important results of algebra. Readers should have some knowledge of linear algebra, groups and fields, although all the essential facts and definitions are recalled.

This book provides a complete abstract algebra course, enabling instructors to select the topics for use in individual classes.

Wholeheartedly recommended to every student and user of mathematics, this is an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields studied in every university maths course, through Lie groups to cohomology and category theory, the author shows how the origins of each concept can be related to attempts to model phenomena in physics or in other branches of mathematics. Required reading for mathematicians, from beginners to experts.

This book is the first volume of an intensive “Russian-style” two-year graduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses. This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.