Mathematical Proofs Courses and Certifications

Mathologer

Sex and Marriage Theorems

Explore mathematical theorems on stable marriages and debunk sex statistics myths. Discover how mathematicians can earn Nobel-like recognition through innovative problem-solving.

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

Ryan O'Donnell

The SDP Relaxation for Max-Cut - Lecture 19b of CS Theory Toolkit

Explore SDP relaxation for Max-Cut, transforming a quadratic program into a semidefinite program solvable by the Ellipsoid Algorithm. Part of CMU's graduate-level CS Theory Toolkit course.

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

Insights into Mathematics

Isosceles Triangles in Hyperbolic Geometry - Universal Hyperbolic Geometry - NJ Wildberger

Explore isosceles triangles in hyperbolic geometry, including special formulas, midpoint construction, and related theorems. Gain insights through proofs, exercises, and applications of the cross law.

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

Insights into Mathematics

Polyhedra and Euler's Formula - Algebraic Topology

Explore Platonic solids, Euler's formula, and spherical geometry in this engaging lecture on algebraic topology, featuring proofs and insights into fundamental mathematical concepts.

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

Insights into Mathematics

The Spread Law in Universal Hyperbolic Geometry - Universal Hyperbolic Geometry

Explores the Spread law in universal hyperbolic geometry, including its definition, relation to Euclidean geometry, proof, and implications. Covers key concepts like quadrance, spread duality, and quadrea.

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

Insights into Mathematics

Pythagoras' Theorem in Universal Hyperbolic Geometry

Explore the hyperbolic version of Pythagoras' theorem, its importance in geometry, and the concept of quadrance. Learn about planar coordinates, formulas, and proofs in Universal Hyperbolic Geometry.

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

Insights into Mathematics

Apollonius and Polarity Revisited - Universal Hyperbolic Geometry

Explores Apollonius' polarity in hyperbolic geometry, focusing on null points, quadrangles, and the relationship between poles and polars. Includes explicit formulas and computational examples.

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

Insights into Mathematics

The Realm of Natural Numbers - Data Structures in Mathematics

Explore natural numbers through multisets, examining addition, union, and intersection operations. Discover unique properties, including a new distributive law that forms the basis for tropical calculus.

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

Insights into Mathematics

Rational Trigonometry, Generalized Triangle Geometry and Four-Fold Incenter Symmetry

Explores rational trigonometry and generalized triangle geometry, introducing quadrances, spreads, and chromogeometry. Discusses Euler lines, incenters, and various triangle centers, culminating in a novel result on colored incenters.

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

Insights into Mathematics

Complex Numbers and Algebra - Math History - NJ Wildberger

Explore complex numbers' history, applications in cubic equations, and geometric representations. Delve into the Fundamental Theorem of Algebra and its proofs by d'Alembert and Gauss.

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

Insights into Mathematics

The Area of a Triangle and Archimedes' Formula - Famous Math Problems

Novel approach to calculating triangle area using rational trigonometry, avoiding unnecessary irrationalities in Heron's formula. Presents a clearer solution based on Pythagoras' theorem and Triple quad formula, with practical applications.

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

Institute for Advanced Study

A Gentle Approach to Crystalline Cohomology - Jacob Lurie

Explore crystalline cohomology and the de Rham-Witt complex in algebraic geometry, with insights on alternative constructions and applications in positive characteristic fields.

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

Institute for Advanced Study

Eisenstein Series and the Cubic Moment for PGL(2) - Paul Nelson

Explore Eisenstein series, cubic moments for PGL(2), and their applications in number theory. Gain insights into spectral expansions, hypergeometric functions, and improved bounds.

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

Institute for Advanced Study

Singularity Formation for Reduced Models of Fluid Equations - Mimi Dai

Explore singularity formation in reduced fluid equation models, focusing on electron magnetohydrodynamics and its connection to Euler equations. Gain insights into nonlinear dynamics and finite-time singularities.

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

Society for Industrial and Applied Mathematics

Matrix Equations and Model Reduction - Lecture 4

Explore matrix equations and model reduction techniques, focusing on SR method, high multiplicity, and theoretical background with renowned expert Peter Benner.

• YouTube
• 1 hour 38 minutes
• On-Demand
• Free Video