Ring Theory Courses and Certifications

Numberphile

Lord of the Commutative Rings

Dive into the fascinating world of mathematical rings and discover their fundamental properties and structures in this engaging exploration of abstract algebra.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

International Mathematical Union

Neena Gupta- The Zariski Cancellation Problem and Related Problems in Affine Algebraic Geometry

Explore Zariski Cancellation Problem and related topics in affine algebraic geometry, including Asanuma rings, affine fibration, epimorphism theorems, and notable examples from leading mathematicians.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

Michael Penn

How the Power Set Forms a Ring

Explore how the power set forms a ring in this mathematical demonstration, showcasing set theory principles and algebraic structures.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

BIMSA

On Low Rank Fusion Rings - Methods for Generation and Classification

Explore computational methods for generating and analyzing low-rank fusion rings, featuring a new website and Wolfram Language package for researchers in tensor categories and anyon theory.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Existentially Definable Henselian Valuations

Explore existential definability of henselian valuation rings within their fields of fractions, focusing on classification by residue field properties and key mathematical examples.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Diophantine Maps and Hilbert's Tenth Problem for Some Noncommutative Rings

Explore Diophantine maps and Hilbert's tenth problem in noncommutative rings, including twisted polynomial rings and their division ring variants.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Wolfram

Noncommutative Algebra and Its Applications

Explore Mathematica's new noncommutative algebra functionality, including polynomial transformations, Groebner bases, and computations with Weyl, Clifford, and Grassmann algebras.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Wolfram

Expanding Exponentials in Noncommutative Algebras

Explore advanced mathematical formulas for decomposing exponentials in noncommutative settings, featuring Wolfram Language implementations and applications to operator theory.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - More Ring Theory Examples

Explore advanced ring theory concepts, including ideals and homomorphisms in matrix and polynomial rings, with in-depth examples and proofs.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

Abstract Algebra

Explore fundamental concepts of abstract algebra, including groups, rings, fields, and vector spaces, with a focus on definitions, examples, and key theorems.

• YouTube
• 3 hours 30 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Reversible D-Dimensional CA Over the Ring ZM and Some Applications in Ergodic Theory

Explore cellular automata on $\mathbf{Z}_p$ and $\mathbf{Z}_m$, covering invertibility, ergodic properties, and entropy concepts. Delve into measure-theoretic and topological entropy for 1D linear CA and $\mathbb{Z}^2$-actions.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Harvard CMSA

Resolving the Photon Ring: Theory and Analysis Methods for Black Hole Imaging

Delve into the physics of photon rings around black holes, exploring interferometric imaging, strong lensing effects, and innovative methods for resolving these mysterious structures in M87* and SgrA*.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Pondicherry University;  CEC

Algebra

Comprehensive exploration of algebraic structures, group theory, and ring theory, providing a strong foundation for advanced mathematics and teaching careers.

• Swayam
• 15 weeks
• Self-Paced
• Free Online Course

Algebra 1: Foundations

Dive into the foundations of algebra, from set theory and logic to linear algebra concepts like vector spaces, matrices, and Jordan forms, building a solid mathematical framework.

• Swayam
• 12 weeks
• Self-Paced
• Free Online Course

IMSC;  NPTEL

Algebra - I

Comprehensive postgraduate-level algebra course covering groups, rings, modules, and their applications. Ideal for M.Sc and first-year PhD mathematics students seeking a strong foundation in abstract algebra.

• Swayam
• 12 weeks
• Self-Paced
• Free Online Course