Abstract Algebra: An Inquiry-Based Approach

Abstract Algebra: An Inquiry-Based Approach,Second Edition is a text that teaches abstract algebra and provides a deeper understanding of what mathematics is,how it is done,and how mathematicians think. It emphasizes active learning,introduces the ideas behind definitions and theorems,helps students understand how mathematics is done,and develops their abilities to effectively communicate mathematical ideas. The second edition has been streamlined,new investigations have been added,and more online Special Topics investigations and additional Appendices have been added.

Format: Hardback
Length: 525 pages
Publication date: 19 December 2023
Publisher: Taylor & Francis Ltd

Abstract Algebra: An Inquiry-Based Approach, Second Edition, is a comprehensive textbook that not only delves into the realm of abstract algebra but also offers a profound exploration of the essence of mathematics, its methodologies, and the thought processes of mathematicians. Building upon the success of its predecessor, this second edition enhances the learning experience by placing a strong emphasis on active learning, enabling students to acquire algebraic concepts through a gradual development of intuition and the ability to construct coherent proofs within contextual settings.

The primary objectives of this text are as follows:

Flexibility to Begin the Course with Either Groups or Rings: The text provides the flexibility to start the course with either groups or rings, allowing instructors to tailor the curriculum to their specific preferences and student needs.

Introducing the Ideas Behind Definitions and Theorems: The authors aim to help students develop a deeper intuition by introducing the ideas behind definitions and theorems. Students will engage in hands-on experimentation, form conjectures, and then refine or prove their conjectures through examples and rigorous reasoning.

Understanding How Mathematics is Done: The text endeavors to assist students in gaining a deeper understanding of the mathematical process. Students will actively participate in examples, make conjectures, and explore various approaches to problem-solving, fostering critical thinking and analytical skills.

Developing Effective Communication Skills in Mathematics: The text emphasizes the importance of effective communication in mathematics. Students will be encouraged to express their mathematical ideas clearly and concisely, both in written and oral formats.

Active Engagement of Students in Achieving These Goals: The text actively involves students in realizing each of these goals through a combination of in-class activities, common in-class intellectual experiences, and challenging problem sets. These engaging exercises promote active learning and help students develop a deeper understanding of abstract algebra.

Changes in the Second Edition:

Streamlining of Introductory Material: The second edition has streamlined the introductory material, ensuring a quicker transition to the core concepts of rings and groups. This allows students to focus more efficiently on the fundamental aspects of abstract algebra.

New Investigations on Extensions of Fields and Galois Theory: The book includes new investigations on extensions of fields and Galois theory, providing students with a deeper understanding of these important topics in abstract algebra.

Additional Exercises and Clarification: The text has been updated with additional exercises and revised sections to enhance clarity and improve the overall learning experience.

Online Special Topics Investigations: The book offers online Special Topics investigations, providing students with additional resources and opportunities to explore specialized topics in abstract algebra.

Additional Appendices: The second edition includes new appendices on other methods of proof and complex roots of unity, further enriching the content and providing valuable supplementary material.

Encouraging Students to Be Active Learners: Abstract Algebra: An Inquiry-Based Approach, Second Edition, aims to empower students to become active learners rather than passive recipients of information. The text emphasizes that the development of mathematics often differs from its presentation, with definitions, theorems, and proofs serving as building blocks. By exposing students to these foundational elements, the text fosters a deeper understanding of the subject matter.

In conclusion, Abstract Algebra: An Inquiry-Based Approach, Second Edition, is a remarkable textbook that offers a comprehensive and engaging exploration of abstract algebra and its broader implications. With its emphasis on active learning, effective communication skills, and a deep understanding of the mathematical process, this text empowers students to become confident and proficient abstract algebraists. Whether used in undergraduate or graduate courses, this textbook is an invaluable resource for anyone seeking to deepen their understanding of this fascinating branch of mathematics.

Weight: 1170g
Dimension: 254 x 178 (mm)
ISBN-13: 9780367555016
Edition number: 2 ed