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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Online Course

Algebraic Number Theory

Master advanced number theory concepts, from Diophantine equations to field extensions, exploring algebraic structures, class groups, and L-functions while building expertise in computational methods and proofs.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

NPTEL;  IIT Kanpur

Modern Algebra

Explore fundamental concepts and advanced topics in modern algebra through a comprehensive series of lectures by Prof. Manindra Agrawal, covering key principles and applications.

• YouTube
• 14 hours
• On-Demand
• Free Video

Michael Penn

Abstract Algebra - Ring Homomorphisms

Explore ring homomorphisms in abstract algebra, including definitions, examples, and key properties like multiplicative behavior and kernels.

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

Michael Penn

Abstract Algebra - Units and Zero Divisors of a Ring

Explore units and zero divisors in Zn and 2x2 real matrices, classifying elements and proving key properties in abstract algebra.

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

ICTP Mathematics

Abstract Algebra

Master fundamental algebraic structures including groups, rings, and fields through comprehensive lectures by Lothar Göttsche at ICTP Mathematics.

• YouTube
• 1 day 6 hours 15 minutes
• On-Demand
• Free Video