Combinatorics
Explore fundamental concepts of combinatorics, including ordered sequences, permutations, and probability, with applications to real-world scenarios like poker hands.
Basics of Discrete Mathematics
Explore set theory, relations, functions, counting principles, and propositional logic in this comprehensive introduction to discrete mathematics, essential for computer science and AI.
Stanford Lecture - Don Knuth - Twintrees, Baxter Permutations, and Floorplans (2022)
Explore the fascinating connections between twintrees, Baxter permutations, and floorplans in this lecture by renowned computer scientist Donald Knuth, revealing unexpected relationships in mathematics and computer science.
Hamiltonian Paths in Antiquity - Stanford Lecture 2016
Explore the ancient origins of Hamiltonian paths with Donald Knuth, tracing their history from Graeco-Roman times through Sanskrit and Arabic documents, and their modern relevance in computer science.
Twintrees, Baxter Permutations, and Floorplans in Computer Science - Lecture 2022
Explore the fascinating connections between twintrees, Baxter permutations, and floorplans in this lecture by renowned computer scientist Don Knuth, revealing unexpected relationships in mathematics and data structures.
Introduction to Statistical Mechanics
This is an introductory course in classical and quantum statistical mechanics which deals with the principle of ensembles, Classical, Fermi and Bose ideal gases, Pauli paramagnestim, Debye and Einstein’s theory of specific heat and the 1D Ising model.
Algebra 1
Foundational PG level course in Algebra, suitable for M.Sc and first-year Ph.D. students in Mathematics. Learn Permutations. Group Axioms. Order and Conjugacy. Subgroups. Problem solving. Group Actions. Cosets. Group Homomorphisms. Normal subgroups. Quti…
Probability
Explore probability concepts, from basic principles to advanced topics like mutually exclusive events and binomial coefficients, enhancing your statistical analysis skills.
The Bunkbed Conjecture Debunked - A Counterexample with 7222 Vertices
Explore a groundbreaking development in probabilistic graph theory in this 15-minute video by Dr. Trefor Bazett. Learn about the recent disproval of the famous bunkbed conjecture, featuring a surprising counterexample with 7,222 vertices. Delve into the…
Sharp Estimates for Gowers Norms on Discrete Cubes
Explore sharp estimates for Gowers norms on discrete cubes in this 57-minute lecture by Vjekoslav Kovač from the Hausdorff Center for Mathematics. Delve into optimal dimensionless estimates between Gowers U^k norms and l^p norms for functions supported o…
Isoperimetric and Poincaré Inequalities on the Hamming Cube
Explore isoperimetric inequalities on the Hamming cube near and at the critical exponent 1/2, as well as closely related L1 Poincaré inequalities in this one-hour lecture. Delve into joint research conducted with P. Durcik and P. Ivanisvili, focusing on…
Combinatorial Inequalities and Combinatorial Interpretations - Part III
Explore the intricacies of combinatorial inequalities and interpretations in this third installment of a seminar series presented by Igor Pak at the Institute for Advanced Study. Delve into inequalities for linear extensions of finite posets, beginning w…
A Very Special Knight's Tour
Explore a unique knight's tour on a chessboard, uncovering mathematical patterns and strategies for this classic problem in combinatorial game theory.
Random Graphs and Nonlinear Spectral Gaps
Explore discrete Poincaré inequalities in regular expander graphs, long-range expansion properties, and their implications for Banach space-valued functions, with improved estimates for Poincaré constants.
Approximate Polymorphisms in Boolean Functions
Explore approximate polymorphisms in theoretical computer science, focusing on stability results for functions satisfying certain properties and their implications.
Decoupling Identities and Oriented Matroids and Beyond
Explore advanced mathematical concepts in decoupling identities and oriented matroids, delving into their applications and extensions in physics and beyond.
The Ramsey Numbers - New Results and New Perspectives
Explore fundamental Ramsey numbers in combinatorics, recent advancements, and connections to high-dimensional random variable geometry with Julian Sahasrabudhe.
Analytic Insights into the Zig-Zag Product and Its Friends - Part II
Explore advanced analysis of graph operators using full spectrum and analytic techniques. Gain insights into Zig-Zag product, derandomized squaring, and their optimal bounds through finite free probability and analytic combinatorics.
Double Factorial: Introduction to the Alternate Factorial
Explore the double factorial (!!), its unique properties, and applications in graph theory. Discover how this alternate factorial notation skips every other number while respecting parity.
Counting Probabilities with Combinatorics and the Factorial
Master combinatorics and factorial concepts in probability. Learn to count event occurrences, analyze sampling methods, and apply formulas for various probability scenarios, including coin flips and poker hands.
The Longest Mathematical Proof Ever: Exploring Schur Number Five
Dive into the world's longest mathematical proof, exploring Schur number five and its 2-petabyte size. Uncover propositional logic, SAT solvers, and proof verification in this fascinating journey.