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An Inquiry-Based Approach to Abstract Algebra
This free and open-source textbook is designed to used with an inquiry-based learning (IBL) approach to a first-semester undergraduate abstract algebra course. The textbook starts with groups (up to the First Isomorphism Theorem) and finishes with an introduction to rings (up to quotients by maximal and prime ideals). While the textbook covers many of the standard topics, the focus is on building intuition and emphasizes visualization.
- Author
- Dana Ernst
- Publisher
- Northern Arizona University
- Source
- LibreTexts
- License
- CC BY-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 41 sections
- 01: Introduction
- 1.01: What is Abstract Algebra
- 1.02: What Should You Expect
- 1.03: An Inquiry-Based Approach
- 1.04: Structure of the Textbook
- 1.05: Some Minimal Guidance
- 02: Introduction to Groups
- 2.01: A First Example
- 2.02: Binary Operation
- 2.03: Groups
- 2.04: Generating Sets
- 2.05: Group Tables
- 2.06: Cayley Diagrams
- 03: Subgroups and Isomorphisms
- 3.01: Subgroups
- 3.02: Subgroup Lattices
- 3.03: Isomorphisms
- 04: Families of Groups
- 4.01: Cyclic Groups
- 4.02: Dihedral Groups
- 4.03: Symmetric Groups
- 4.04: Alternating Groups
- 05: Cosets Lagranges Theorem and Normal Subgroups
- 5.01: Cosets
- 5.02: Lagrange's Theorem
- 5.03: Normal Subgroups
- 06: Products and Quotients of Groups
- 6.01: Products of Groups
- 6.02: Quotients of Groups
- 07: Homomorphisms and the Isomorphism Theorems
- 7.01: Homomorphisms
- 7.02: The Isomorphism Theorems
- 08: An Introduction to Rings
- 8.01: Definitions and Examples
- 8.02: Ring Homomorphisms
- 8.03: Ideals and Quotient Rings
- 8.04: Maximal and Prime Ideals
- 09: Appendix
- 9.01: A.1- Elements of Style for Proofs
- 9.02: A.2- Fancy Mathematical Terms
- 9.03: A.3- Definitions in Mathematics