Finite Fields Courses and Certifications

Principles of Digital Communication II

Advanced coding techniques for approaching Shannon limit in AWGN channels. Covers block codes, convolutional codes, trellis representations, turbo codes, LDPC codes, and bandwidth-limited coding.

• MIT OpenCourseWare
• On-Demand
• Free Online Course

Simons Institute

A Polynomial Bogolyubov Type Result for the Special Linear Group

Explores a polynomial density result for the special linear group over finite fields, using hyper-contractive estimates derived from 2-to-2 games research.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Insights into Mathematics

Infinitesimal Calculus with Finite Fields - Famous Math Problems

Explore infinitesimal calculus in finite fields through the semi-cubical parabola over F_7, challenging traditional real number analysis and emphasizing polynumbers and de Casteljau Bezier curves.

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

NPTEL-NOC IITM

Existence Theorem for Finite Fields

Explore the existence theorem for finite fields, proving their existence for every prime power order.

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

NPTEL-NOC IITM

Subfields of a Finite Field

Explore the concept of subfields within finite fields, understanding their properties and significance in abstract algebra and number theory.

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

Fields Institute

Towards the Classification of MVSPs over Finite Fields

Explore the classification of MVSPs over finite fields in this mathematical talk by Lucas Reis, delving into advanced algebraic concepts and their applications.

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

Wolfram

Finite Fields and Their Applications

Explore new Mathematica 13.3 features for finite field computations, including arithmetic, mappings, and polynomials. Learn about upcoming linear algebra and equation solving capabilities.

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

Centre de recherches mathématiques - CRM

Tensor Rank and Bias of Multilinear Forms Over Finite Fields

Explorez les liens entre le rang tensoriel et le biais des formes multilinéaires sur les corps finis dans cette conférence mathématique approfondie.

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

NPTEL;  IIT Madras

Coding Theory

This course provides an introduction to traditional and modern coding theory. Topics covered include linear block codes, cyclic codes (BCH and RS codes), convolutional codes, turbo codes and low-density parity-check (LDPC) codes.

• YouTube
• 1 day 13 hours
• On-Demand
• Free Video

Galois Theory

This course is an attempt to present the theory in such alight, and in a manner suitable for undergraduate and graduate students as well as researchers.

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

Discrete Mathematics for CS

Master essential discrete mathematics concepts from proofs and combinatorics to graph theory, number theory, and algebra, with practical applications in computer science and cryptography.

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

IMSC;  NPTEL

Algebra - II

Explore advanced algebraic concepts including Galois theory, category theory, and multilinear algebra. Ideal for graduate-level mathematics students seeking in-depth understanding of abstract structures.

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

Chennai Mathematical Institute;  NPTEL

Introduction To Rings And Fields

Explore abstract algebra with rings and fields, covering key concepts like ideals, domains, and field extensions. Ideal for math students seeking a deeper understanding of algebraic structures.

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

Simons Institute

Randomness in Number Theory

Explore randomness in number theory, covering topics like finite fields, graphs, quantum gates, and the Riemann Hypothesis with Princeton's Peter Sarnak.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Insights into Mathematics

Differential Geometry With Finite Fields - Differential Geometry

Exploring differential geometry in finite fields, introducing arithmetic in prime fields, polynomial operations, and tangent conics to cubics. Highlights unique patterns and combinatorial structures in finite calculus.

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