Abstract Algebra: A First Course

Abstract algebra is a branch of mathematics that studies properties of operations without specifying what types of number or object we work with. It is a student-centered textbook that introduces groups, rings, and fields, with a balanced introduction to groups, rings, and fields or a course that primarily emphasizes group theory. It also offers lists of projects at the end of each section, with ideas for investigative and expository projects. The exercises challenge the student to prove new results using the theorems presented in the text.

Format: Hardback
Length: 557 pages
Publication date: 05 July 2022
Publisher: Taylor & Francis Ltd

Abstract algebra is a branch of mathematics that studies properties of operations without specifying what types of number or object we work with. It is a way of thinking about classes of sets equipped with binary operations, such as (+, -, ×, and ÷) on real numbers. This textbook intends to serve as a first course in abstract algebra, with a balanced introduction to groups, rings, and fields or a course that primarily emphasizes group theory. The writing style is student-centered, motivating definitions and offering many illustrative examples. Various sections or sometimes just examples or exercises introduce applications to geometry, number theory, cryptography, and many other areas.

The book offers a unique feature in the lists of projects at the end of each section. The author does not view projects as just something extra or cute, but rather an opportunity for a student to work on and demonstrate their potential for open-ended investigation. The projects ideas come in two flavors: investigative or expository. The investigative projects briefly present a topic and posed open-ended questions that invite the student to explore the topic, asking and trying to answer their own questions.

Expository projects invite the student to explore a topic with algebraic content or pertain to a particular application. The book is an excellent resource for students who want to learn abstract algebra and gain a deeper understanding of the subject.

Weight: 1211g
Dimension: 234 x 156 (mm)
ISBN-13: 9781032289397
Edition number: 2 ed