--- title: Abstract Algebra description: Abstract algebra is the study of algebraic structures such as groups, rings, fields, and vector spaces. Learners will understand algebraic proofs and symmetry, allowing them to analyze abstract mathematical systems and solve advanced algebraic equations. category: mathematics subcategory: algebra difficulty: beginner, intermediate, advanced url: /subject/abstract-algebra --- # Abstract Algebra Abstract algebra is the study of algebraic structures such as groups, rings, fields, and vector spaces. Learners will understand algebraic proofs and symmetry, allowing them to analyze abstract mathematical systems and solve advanced algebraic equations. ## Available Resources 1 Videos • 3 Books • 3 Courses • 3 Websites ## Courses ### 1. Introduction to Abstract Algebra Learn the fundamentals of abstract algebra! This course by Trefor Bazett covers groups, rings, fields and more. **Difficulty:** Advanced | **Price:** Free **Link:** https://www.youtube.com/playlist?list=PLbRMhDVUMngdVprk_HvTKA_F1pe9UPlEy **Tags:** abstract-algebra, group-theory, ring-theory, fields, video-lectures ### 2. Abstract Algebra Learn abstract algebra with Socratica's free video course! Explore groups, rings, and fields. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/playlist?list=PLi01XoE8jYoi3SgnnGorR_XOW3IcK-TP6 **Tags:** abstract-algebra, group-theory, ring-theory, fields, video-lectures ### 3. Harvard MATH E-222: Abstract Algebra **Author:** Benedict Gross Recorded Harvard Extension School lectures by Benedict Gross, following Michael Artin's textbook Algebra. Covers groups and group actions, vector spaces and linear operators, rings, and fields, with proofs throughout. Viewers gain a rigorous first grounding in algebraic structures and symmetry. **Difficulty:** Intermediate | **Price:** Free **Link:** https://www.youtube.com/playlist?list=PLzUeAPxtWcqzr80lS25FrzMn7a36BuXhj **Tags:** abstract algebra, group theory, group actions, linear algebra, rings and fields ## Videos ### 1. Euler's Formula with Introductory Group Theory **Author:** Grant Sanderson 3Blue1Brown video introducing groups through symmetry actions, then using the multiplicative and additive groups of numbers to explain why exponentials turn addition into multiplication and what Euler's formula means geometrically, building visual intuition for group actions and homomorphisms. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/watch?v=mvmuCPvRoWQ **Tags:** group-theory, symmetry-groups, homomorphisms, eulers-formula, visual-math ## Books ### 1. Algebra : 211- Serge Lang **Author:** Serge Lang Graduate reference covering groups, rings, modules, fields, Galois theory, homological algebra, and representation theory in one volume. Terse and comprehensive; suited to readers who already know the basics and want a definitive source to work through or consult. **Difficulty:** Advanced | **Language:** English | **Price:** Paid **Link:** https://amzn.to/4qQgWt4 **Tags:** abstract-algebra, graduate-mathematics, galois-theory, commutative-algebra, reference ### 2. A Book of Abstract Algebra **Author:** Charles C. Pinter An undergraduate introduction that builds group and ring theory from scratch with short chapters and graded exercise sets. Readers finish able to work with groups, homomorphisms, quotient structures, rings, and fields, and to read proofs in the subject. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0486474178?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, mathematics ### 3. Contemporary Abstract Algebra **Author:** Joseph A. Gallian A standard first course text on groups, rings, and fields, heavy on worked examples, applications, and biographical notes. Provides enough exercises and computational practice to carry a student through a two-semester undergraduate algebra sequence. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0669194964?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, algebra ## Websites ### 1. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ### 2. math.stackexchange.com Math Stack Exchange is a community Q&A site for mathematics where users ask, answer, and discuss problems across topics from algebra to advanced theory. It features a large archive of math questions with detailed explanations, proofs, examples, and peer-voted high-quality answers. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://math.stackexchange.com **Tags:** websites, mathematics-statistics, mathematics ### 3. groupprops.subwiki.org GroupProperties Subwiki is a collaborative reference for abstract algebra focused on group theory, cataloguing the many properties a group can possess (e.g., abelian, finite, nilpotent, solvable, simple). Each page provides definitions, examples, and notes on how properties relate and differ, making it a handy learning resource and quick reference. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://groupprops.subwiki.org **Tags:** websites, mathematics-statistics, mathematics --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/abstract-algebra