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Abstract Algebra II The Next Step in Algebraic Thinking - OneDDL - 09-20-2025
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Free Download Abstract Algebra II The Next Step in Algebraic Thinking
Published 9/2025
Created by Science Academy,Andrew Misseldine
MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz, 2 Ch
Level: Intermediate | Genre: eLearning | Language: English | Duration: 123 Lectures ( 31h 16m ) | Size: 9.3 GB
aster the deeper layers of algebraic theory with a focus on rings, fields, and polynomial symmetries.
What you'll learn
How groups act on sets, and how orbits, stabilizers, and isotropy subgroups reveal group structure
The Class Equation, Cauchy's Theorem, and the Sylow Theorems-cornerstones of finite group theory
The concept of automorphisms, including inner automorphisms and automorphisms of abelian groups
How to classify and analyze simple groups, including nonabelian examples and group orders
The structure and behavior of rings, including subrings, matrix rings, polynomial rings, and group rings
Deep understanding of integral domains, principal ideal domains (PIDs), Euclidean domains, and unique factorization domains (UFDs)
The theory of ideals, including prime, maximal, and principal ideals, and the isomorphism theorems for rings
How to construct and work with fields, division rings, and field extensions
The logic behind algebraic closures, constructible numbers, and splitting fields
The structure of finite fields, Galois fields, and their applications in coding theory
The fundamentals of Galois theory, including automorphisms, fixed fields, and the Fundamental Theorem of Galois Theory
How to determine solvability by radicals, and the connection between group theory and polynomial equations
An introduction to lattices, Boolean algebras, and their algebraic properties and applications
Requirements
Completion of Abstract Algebra I or equivalent knowledge of groups, rings, and basic proofs
Familiarity with set theory, functions, and basic linear algebra
A willingness to engage with abstract reasoning and formal mathematical logic
Description
Abstract Algebra II: Group Actions, Rings, Fields & Galois TheoryExplore the Deep Structures of Algebra That Shape Modern MathematicsAbstract Algebra II is not just a continuation-it's a transformation in how you understand mathematics. If Abstract Algebra I introduced you to the foundational concepts of groups, rings, and fields, this course takes you into the core of algebraic reasoning, where structure, symmetry, and abstraction converge.This is the mathematics that underpins cryptography, coding theory, quantum mechanics, and algebraic geometry. It's the language of automorphisms, field extensions, and Galois groups-tools that mathematicians use to solve equations that defy classical methods and to understand the deep relationships between algebraic objects.You'll begin with group actions, a powerful framework for understanding how groups interact with sets, leading to insights about symmetry, orbits, and stabilizers. From there, you'll explore automorphisms, the internal symmetries of algebraic structures, and how they relate to the Class Equation, Sylow Theorems, and the classification of simple groups.Then, the course shifts into ring theory, where you'll study subrings, ideals, and homomorphisms, and discover how structures like principal ideal domains (PIDs) and Euclidean domains govern factorization and divisibility. You'll learn how polynomial rings behave over different domains, and how tools like Gauss' Lemma and Eisenstein's Criterion help identify irreducible elements.The second half of the course is devoted to field theory and Galois theory-the crown jewel of classical algebra. You'll explore field extensions, splitting fields, and finite fields, and learn how Galois groups encode the solvability of polynomials. You'll see how solvability by radicals connects group theory to the age-old question of solving equations, and how constructible numbers relate to geometric problems like trisecting angles and squaring the circle.Finally, the course introduces lattices and Boolean algebras, bridging algebra with logic and computer science. These structures reveal how algebraic reasoning applies to circuits, decision-making, and symbolic computation.Why Take This Course?To build on your foundation from Abstract Algebra I and master advanced algebraic structuresTo prepare for graduate-level mathematics, research, or competitive examsTo understand the algebra behind modern applications in cryptography, coding theory, and theoretical physicsTo develop mathematical maturity through rigorous proofs, abstract reasoning, and structural thinkingTo connect algebra with geometry, logic, and computation in a unified framework
Who this course is for
Students who completed Abstract Algebra I and want to continue their studies
Learners preparing for graduate-level mathematics, math competitions, or research
Computer scientists, physicists, and engineers interested in algebraic structures and coding theory
Anyone passionate about mathematical abstraction and structure
Homepage
https://www.udemy.com/course/abstract-algebra-ii/
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