Finite Fields Courses and Certifications

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

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

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

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

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

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

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

Simons Foundation

Doing Elementary Number Theory in Lean - Talk 2

Explore elementary number theory formalization in Lean through practical exercises covering rings, unique factorization domains, congruence, finite fields, and quadratic reciprocity.

• YouTube
• 1 hour 8 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

TheIACR

Private Multiplication over Finite Fields

Explore secure multiparty computation techniques for private multiplication in finite fields, focusing on cryptographic protocols and their applications.

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

Centre de recherches mathématiques - CRM

Point Counting over Finite Fields and the Cohomology of Moduli Spaces of Curves

Explore algebraic geometry through point counting over finite fields and cohomology of moduli spaces of curves, resolving longstanding questions and confirming Langlands program predictions.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Sharp Fourier Restriction Theory Over Finite Fields

Explore recent developments in sharp Fourier restriction theory over finite fields, examining the intersection of two key areas in mathematical research.

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

Centre International de Rencontres Mathématiques

Lang-Weil Type Bounds in Finite Difference Fields

Explore Lang-Weil type bounds in finite difference fields with Martin Hils, delving into advanced mathematical concepts and their applications.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Lower Bound on the Maximal Number of Rational Points on Curves over Finite Fields

Explore lower bounds on maximal rational points for curves over finite fields. Delve into strategies, Kzarnak Theory, and proofs in algebraic geometry.

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