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

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 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 Online Course

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 Online Course

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 Online Course

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

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 Online Course

Insights into Mathematics

Isometry Groups of the Projective Line - Rational Geometry Math Foundations

Exploring finite field geometry: isometries, rotations, and reflections on the projective line, revealing connections to relativistic geometry and offering a new perspective on Euclidean concepts.

• YouTube
• 35 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

Ptolemy's Theorem and Generalizations - Rational Geometry Math Foundations

Explores Ptolemy's theorem in rational geometry, extending it to finite fields and relativistic planar geometry. Demonstrates how classical results can yield broader insights when formulated without infinite processes.

• YouTube
• 46 minutes
• On-Demand
• Free Online Course

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 Online Course

Insights into Mathematics

An Informal Introduction to Abstract Algebra

Informal introduction to abstract algebra, covering fields, rings, and vector spaces. Explores key concepts and examples, from basic number systems to advanced constructions, providing essential background for algebraic topology.

• YouTube
• 49 minutes
• On-Demand
• Free Online Course

TheIACR

Cryptanalysis 2

Explore cryptanalysis techniques, focusing on discrete logarithm problems in finite fields. Learn about L notation, historical developments, and computational complexity.

• YouTube
• 52 minutes
• On-Demand
• Free Online Course

Insights into Mathematics

How to Construct the True Complex Numbers I - Famous Math Problems

Exploring the construction of true complex numbers using field theory and linear algebra, challenging traditional approaches and introducing novel concepts for a modern understanding.

• YouTube
• 37 minutes
• On-Demand
• Free Online Course

Ryan O'Donnell

Polynomials

Explore polynomials, from formal definitions to applications in finite fields, interpolation, and error-correcting codes for noisy communication channels.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

Valentin Blomer - The Polynomial Method for Point Counting and Exponential Sums, Lecture III

Explore advanced techniques for counting points on curves over finite fields and estimating exponential sums using auxiliary polynomials and character sums.

• YouTube
• 45 minutes
• On-Demand
• Free Online Course