|Statement||[the M433 Course Team]. Course guide.|
|Series||Mathematics and computing : a fourth level course, M433 -- course guide|
|Contributions||Open University. Aspects of Abstract Algebra Course Team.|
|The Physical Object|
This book really focuses on groups, rings and fields, and other more specialized aspects of abstract algebra that a lot of modern books and textbooks don’t really dive into – at least not in the kind of comprehensive depth that this title focuses on. This book is a survey of abstract algebra with emphasis on linear algebra. It is intended for students in mathematics, computer science, and the physical sciences. The rst three or four chapters can stand alone as a one semester course in abstract algebra. However they are structured to provide the background for the chapter on linear algebra. Book Description This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. This book is a gentle introduction to abstract algebra. It is ideal as a text for a one semester course designed to provide a rst exposure of the subject to students in mathematics, science, or engineering. Covered topics are: Divisibility in the Integers, Rings and Fields, Vector Spaces, Spaces, Groups, Sets, Functions, and Relations.
Portions of the book may also be used for various one-semester topics courses in advanced algebra, each of which would provide a solid background for a follow-up course delving more deeply into one of many possible areas: algebraic number theory, algebraic topology, algebraic geometry, representation theory, Lie groups, s: This is likely not going to be a popular suggestion, since it's relatively unknown, but I think the perfect book for you is Allan Clark's Elements of Abstract Algebra. It's a unique book that covers the basics of group theory, ring theory, and even a tiny bit of Galois Theory, but it does it almost entirely through problems. While its perhaps a bit more basic than some of the others posted here, Charles C. Pinter's "A Book of Abstract Algebra" is really a great book for both a first course in abstract algebra and a first course in proofs. The book is divided into Aspects of abstract algebra: Module code: M Module dates: Module status: This course is closed and no longer in presentation. Faculty: Faculty of Mathematics Computing and Technology: Keyword(s): M, Aspects of abstract algebra, Undergraduate course, Open University + Show more OU level: OU Level 3 Advanced: OU credits:
This book focuses on the study of the noncommutative aspects of rings and modules, and the style will make it accessible to anyone with a background in basic abstract algebra. Covered topics are: Rings, Modules, Structure Of Noncommutative Rings, Representations Of Finite Groups. of abstract algebra. A basic knowledge of set theory, mathematical induction, equivalence relations, and matrices is a must. Even more important is the ability to read and understand mathematical proofs. In this chapter we will outline the background needed for a course in abstract algebra. A Short Note on Proofs. This book takes a "group-first" approach to introductory abstract algebra with rings, fields, vector spaces, and Boolean algebras introduced later. Throughout the textbook, in addition to the examples and theory, there are several practical applications of abstract algebra with a particular emphasis on computer science, such as cryptography and coding theory. Unusually for an abstract algebra text, five chapters on linear algebra are also included, making the text a self-contained introduction to undergraduate algebra. The book will be of use throughout.