Visual Algebra YouTube lectures
Visual Algebra YouTube lectures
Chapter 0: Introduction and Preface (1 hr, 52 min).
- Lecture 0.1: What is Visual Algebra all about?
[YouTube (52:41) |
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- Lecture 0.2: Highlights of Visual Algebra
[YouTube (59:42) |
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Chapter 1: Groups, intuitively (3 hrs, 28 min).
Chapter 2: Examples of groups. (6 hrs, 58 min).
- Lecture 2.1: Complex numbers and matrices
[YouTube (33:26) |
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- Lecture 2.2: Cyclic groups
[YouTube (25:23) |
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- Lecture 2.3: Dihedral groups
[YouTube (20:52) |
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- Lecture 2.4: Abelian groups
[YouTube (33:03) |
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- Lecture 2.5: Groups of permutations
[YouTube (44:42) |
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- Lecture 2.6: The symmetric and alternating groups
[YouTube (52:57) |
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- Lecture 2.7: Dicyclic and diquaternion groups
[YouTube (38:42) |
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- Lecture 2.8: Semidihedral and semiabelian groups
[YouTube (31:54) |
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- Lecture 2.9: Semidirect products, intuitively
[YouTube (32:30) |
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- Lecture 2.10: Examples of semidirect products
[YouTube (45:13) |
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- Lecture 2.11: Groups of matrices
[YouTube (40:14) |
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- Lecture 2.12: Other finite groups
[YouTube (19:10) |
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Chapter 3: Group structure. (6 hrs, 34 min)
Chapter 4: Maps between groups (6 hrs, 27 min).
- Lecture 4.1: Homomorphisms
[YouTube (27:37) |
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- Lecture 4.2: Embeddings and quotients
[YouTube (29:05) |
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- Lecture 4.3: The fundamental homomorphism theorem
[YouTube (36:00) |
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- Lecture 4.4: Subgroups of quotient groups
[YouTube (41:08) |
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- Lecture 4.5: Quotients of quotient groups
[YouTube (27:35) |
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- Lecture 4.6: Subquotients
[YouTube (45:40) |
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- Lecture 4.7: Automorphisms
[YouTube (24:36) |
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- Lecture 4.8: Inner and outer automorphisms
[YouTube (45:28) |
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- Lecture 4.9: External products and holomorphs
[YouTube (29:09) |
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- Lecture 4.10: Internal products
[YouTube (52:44) |
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- Lecture 4.11: Homomorphisms in surprising locations
[YouTube (28:08) |
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Chapter 5: Actions of groups.
- Lecture 5.1: G-sets and actions graphs
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- Lecture 5.2: Five features of a group action
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- Lecture 5.3: Two theorems on orbits
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- Lecture 5.4: Examples of actions
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- Lecture 5.5: Actions of automorphisms
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- Lecture 5.6: Action equivalence
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- Lecture 5.7: Transitive actions
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- Lecture 5.8: Simply transitive actions
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- Lecture 5.9: Equivariance and G-set homomorphisms
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- Lecture 5.10: p-groups
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- Lecture 5.11: The first two Sylow theorems
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- Lecture 5.12: The third Sylow theorem and simple groups
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Below this point, I have not yet made the slides. They will be chopped of and polished versions of the full chapter slides available on my Visual Algebra webpage. I will make the slides and videos for Chapter 8 before returning to Chapters 6 and 7.
Chapter 6: Extensions of groups.
- Lecture 6.1: Finite abelian groups
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- Lecture 6.2: Finite nonabelian groups
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- Lecture 6.3: Extensions and short exact sequences
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- Lecture 6.4: Simple extensions and composition series
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- Lecture 6.5: Abelian extensions and solvable groups
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- Lecture 6.6: Central extensions and nilpotent groups
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- Lecture 6.7: Ascending and descending central series
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Chapter 7: Universal constructions.
- Lecture 7.1: Factoring maps between groups
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- Lecture 7.2: Universal and co-universal properties
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- Lecture 7.3: Direct products and direct sums
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- Lecture 7.4: Some basic category theory
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- Lecture 7.5: Initial, terminal, and zero objects
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- Lecture 7.6: Free groups
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- Lecture 7.7: Free objects
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- Lecture 7.8: Group presentations, formalized
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- Lecture 7.9: Free products
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- Lecture 7.10: Fiber products and coproducts
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Chapter 8: Rings.
- Lecture 8.1: Rings and their substructures
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- Lecture 8.2: Examples of rings
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- Lecture 8.3: Types of rings
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- Lecture 8.4: Ring homomorphisms
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- Lecture 8.5: Maximal ideals
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- Lecture 8.6: Finite fields
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- Lecture 8.7: Prime and primary ideals
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- Lecture 8.8: Radical ideals
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- Lecture 8.9: Rings of fractions
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Chapter 9: Domains.
- Lecture 9.1: Divisibility via ideals
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- Lecture 9.2: Primes and irreducibles
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- Lecture 9.3: PIDs and UFDs
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- Lecture 9.4: Euclidean domains
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- Lecture 9.5: Quadratic integer rings
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- Lecture 9.6: The splitting of primes and the class group
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- Lecture 9.7: Norm-Euclidean domains
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- Lecture 9.8: The Sunzi remainder theorem
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- Lecture 9.9: Polynomial rings
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- Lecture 9.10: Multivariate polynomial rings
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Chapter 10: Fields.
- Lecture 10.1: A history and overview of field theory
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- Lecture 10.2: Subfields and extension fields
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- Lecture 10.3: Algebraic extensions and splitting fields
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- Lecture 10.4: Minimal polynomials
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- Lecture 10.5: Field extensions and lifting theorems
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- Lecture 10.6: Cyclotomic extensions
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- Lecture 10.7: Ruler and compass constructions
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Chapter 11: Galois theory.
- Lecture 11.1: Field automorphisms and Galois groups
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- Lecture 11.2: Transitive groups
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- Lecture 11.3: Galois groups of cyclotomic extensions
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- Lecture 11.4: The Galois corrrespondence
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- Lecture 11.5: Actions of the Galois group
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- Lecture 11.6: Normal and separable extensions
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- Lecture 11.7: Solvability by radicals
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- Lecture 11.8: Galois groups as semidirect products
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- Lecture 11.9: Symmetric polynomials
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- Lecture 11.10: Galois groups of degree-4 polynomials
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- Lecture 11.11: Computing Galois groups by reduction mod p
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All work is licensed under the Creative Commons BY-NC-SA 4.0 License.