Abstract Algebra Courses and Certifications

Wrath of Math

Cool Examples of Quotient Groups in Abstract Algebra

Explore fascinating examples of quotient groups in abstract algebra, including finite order elements, commutators, and group centers. Gain insights into factor groups and their properties.

• YouTube
• 15 minutes
• On-Demand
• Free Video

Kimberly Brehm

Abstract Algebra

1 review

Comprehensive introduction to abstract algebra, covering symmetries, groups, isomorphisms, and more. Follows Gallian's text with accompanying slide decks for in-depth understanding.

• YouTube
• 2 hours 30 minutes
• On-Demand
• Free Video

Abstract Algebra - Polynomial Rings

Explora el álgebra abstracta con enfoque en anillos polinomiales, algoritmo de división, polinomios irreducibles y criterio de Eisenstein.

• YouTube
• 2 hours 30 minutes
• On-Demand
• Free Video

Abstract Algebra Integral Domains

Explore advanced concepts in integral domains, including fractions, primes, factorization, and various domain types. Gain deep insights into abstract algebra principles and their applications.

• YouTube
• 4 hours 30 minutes
• On-Demand
• Free Video

Insights into Mathematics

Rethinking Roots of Unity in Complex Algebra - Math Foundations 218

Explores complex roots of unity, challenging traditional views and highlighting logical difficulties in their definition and existence, emphasizing rational parametrization and algebraic approaches over infinite processes.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Insights into Mathematics

Fundamental Theorem of Algebra Reexamined - Math Foundations 217

Reexamines the Fundamental Theorem of Algebra, proposing new formulations based on rational complex arithmetic and quadrance, avoiding assumptions about continuity and real/complex numbers.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Insights into Mathematics

The Fundamental Dream of Algebra - Math Foundations 216

Challenging the Fundamental Theorem of Algebra, this video explores its flaws and proposes new thinking in mathematics, connecting to broader issues in the field.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Insights into Mathematics

Commutative Groups: Isomorphisms, Homomorphisms, Cosets and Quotient Groups - Lecture 3

Explore commutative groups, isomorphisms, homomorphisms, cosets, and quotient groups. Learn the fundamental structure theorem and its applications in understanding group theory concepts.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Insights into Mathematics

Bases and Dimension for Integral Linear Spaces - Math Foundations 222

Explores algorithm for finding simplified bases of integral linear spaces, adapting Gaussian elimination to work with integral combinations. Introduces key concepts in abstract algebra through practical computation.

• YouTube
• 45 minutes
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

Quadratic Forms, Milnor K-Theory, and Arithmetic - 2021

Explore quadratic forms theory, Milnor K-theory, and arithmetic through the Hasse-Minkowski theorem, quadratic reciprocity law, and Siegel mass formula with experimental mathematics.

• YouTube
• 17 hours 6 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

A Natural Language Formalization of Perfectoid Rings in Naproche

Explore the formalization of perfectoid rings using natural language in Naproche, bridging advanced mathematics with computational logic.

• YouTube
• 40 minutes
• On-Demand
• Free Video

BIMSA

A Categorification of the Ring of Integer-Valued Polynomials

Explore Khovanov's groundbreaking categorification of integer-valued polynomial rings in this advanced mathematical lecture from BIMSA's conference series.

• YouTube
• 1 hour 48 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Monomial Identities in the Weyl Algebra - A Combinatorial and Computational Approach

Delve into advanced algebraic concepts exploring monomial identities in Weyl algebra, covering operational characterizations, lattice path invariants, and rook theory applications in characteristic 0 fields.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Math Sorcerer

9 Hours of Mathematical Proofs for Self Study - Topology, Analysis, Complex Variables, Abstract Algebra, Number Theory, and Advanced Calculus

Dive into comprehensive mathematical proofs spanning topology, analysis, complex variables, abstract algebra, number theory, and advanced calculus for intensive self-study.

• YouTube
• 8 hours 10 minutes
• On-Demand
• Free Video

Insights into Mathematics

Linear Spaces and Spans I - Abstract Algebra Math Foundations 219

Introduction to linear spaces and spans, generalizing natural numbers with addition to form spans of multisets. Explores fundamental concepts in abstract algebra and linear algebra.

• YouTube
• 24 minutes
• On-Demand
• Free Video