Polynomial Rings Courses and Certifications

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
• On-Demand
• Free Video

Michael Penn

Abstract Algebra - Polynomial Rings

Explore polynomial rings, their properties, and key theorems, including the proof that R[x] is an integral domain when R is one.

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

Fields Institute

Symmetric Group Fixed Quotients of Polynomial Rings and Stanley-Reisner Rings

Explore the mathematical properties of symmetric group fixed quotients in polynomial and Stanley-Reisner rings in this advanced algebraic topology presentation.

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

Institute for Advanced Study

Tropical Ideals and Their Properties in Polynomial Rings

Delve into the mathematical foundations of tropical ideals, exploring their combinatorial properties, matroid representations, and connections to polynomial rings through advanced algebraic geometry concepts.

• YouTube
• 1 hour 8 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

Chennai Mathematical Institute;  NPTEL

Introduction to Galois Theory

Explore algebraic structures, field extensions, and Galois groups. Delve into fundamental theorems and applications like insolvability of quintics and cyclotomic extensions.

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

ICTP Mathematics

Algebraic Geometry - Lecture 3

Explore advanced concepts in algebraic geometry, focusing on complex mathematical theories and their applications in modern mathematics and theoretical physics.

• YouTube
• 1 hour 31 minutes
• On-Demand
• Free Video

Michael Penn

A Commutative Vertex Algebra

Explore the universal commutative vertex algebra with one generator, demonstrating how to give a polynomial ring vertex algebra structure through an in-depth mathematical analysis.

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

Michael Penn

The Vector Spaces for Vertex Algebras

Explore key vector spaces for vertex algebras: polynomial rings, exterior algebras with infinite variables, and universal enveloping algebra of the Virasoro Lie algebra. Gain essential understanding for advanced algebraic studies.

• YouTube
• 21 minutes
• 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

Simons Institute

Signatures, Commitments, Zero-Knowledge, and Applications

Explore lattice-based cryptography, focusing on polynomial rings, homomorphic encryption, and zero-knowledge proofs. Learn about theoretical foundations and practical applications in modern cryptographic systems.

• YouTube
• 1 hour 39 minutes
• On-Demand
• Free Video

Fields Institute

Computational Commutative Algebra and Computational Algebraic Geometry

Master computational methods in commutative algebra and algebraic geometry through 11 comprehensive lectures by Professor Mike Stillman at the Fields Institute.

• YouTube
• 1 day 3 hours 35 minutes
• On-Demand
• Free Video

TheIACR

One Shot Verifiable Encryption from Lattices

Explore lattice-based cryptography with a focus on one-shot verifiable encryption, covering zero-knowledge proofs, Ring-LWE encryption, and practical applications in this cutting-edge research presentation.

• YouTube
• 25 minutes
• On-Demand
• Conference Talk

IEEE

Implementing Conjunction Obfuscation under Entropic Ring LWE

Explore secure program obfuscation implementation for conjunction programs, addressing practicality challenges and achieving significant performance improvements in obfuscation and evaluation runtimes.

• YouTube
• 20 minutes
• On-Demand
• Conference Talk

Centre de recherches mathématiques - CRM

Free Resolutions of Powers of Square-Free Monomial Ideals

Explore free resolutions of square-free monomial ideals and their powers, focusing on combinatorial methods and discrete topology. Gain insights into this central problem in commutative algebra.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video