Emergence and Grokking in Simple Neural Architectures
Dive into emergence and grokking in simple neural architectures. Explore MLPs' remarkable behaviors, feature-learning kernel machines, and their implications for understanding modern deep learning phenomena.
Multiplication Methods in the 1500s - The Grounde of Arts by Robert Recorde
Explore a unique 16th-century multiplication method from Robert Recorde's popular arithmetic textbook. Discover its strengths, weaknesses, and validity through examples and proofs.
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.
Cohomology of Moduli Spaces of Curves
Dive into the cohomology of moduli spaces of curves with Hannah Larson. Explore tautological rings, compactifications, and the mysteries of non-tautological cohomology groups in algebraic geometry.
The Weil Conjectures and A1-homotopy Theory
Dive into the Weil Conjectures and A1-homotopy theory, exploring connections between algebraic topology and finite field equations in this mathematical colloquium.
Hidden Structures on de Rham Cohomology of P-adic Analytic Varieties
Dive into hidden structures on de Rham cohomology of p-adic analytic varieties. Explore Hodge filtration, Frobenius, and monodromy in this advanced mathematical colloquium.
Representations of Reductive Groups Over Local and Global Fields
Dive into Langlands' theory of reductive groups and their representations in number theory, exploring local and global fields and their connections to arithmetic and geometry.
Generalizations of the Bernstein Problem
Dive into Otis Chodosh's exploration of the Bernstein Problem's generalizations, examining minimal surface equations and their connections to higher dimensions.
A Descriptive Approach to Pointwise Ergodic Theorems
Dive into a descriptive approach to pointwise ergodic theorems, exploring their applications in dynamical systems, probability, and number theory.
The Ramanujan Conjecture for Modular Forms
Dive into the Ramanujan conjecture for modular forms, exploring its history and recent developments in a gentle overview suitable for all levels of mathematical background.
Counting Periodic Orbits of One-Dimensional Maps - Lecture 1
Dive into the fascinating world of periodic orbits in one-dimensional maps. Explore connections to number theory and thermodynamic formalism, starting with Milnor and Thurston's work on interval maps.
Counting Periodic Orbits of One-Dimensional Maps - Lecture 3
Delve into the mathematics of counting periodic orbits in one-dimensional maps. Explore connections to number theory, thermodynamic formalism, and the prime orbit theorem for hyperbolic systems.
Counting Periodic Orbits of One-Dimensional Maps - Lecture 2
Delve into the mathematics of counting periodic orbits in one-dimensional maps. Explore connections to number theory and thermodynamic formalism, focusing on interval and complex rational maps.
Number Theory
Comprehensive exploration of number theory, covering foundational concepts to advanced topics like quadratic reciprocity, integer partitions, and Ramanujan's congruences.
Problem Solving Techniques
Explore advanced problem-solving techniques including the Pigeonhole Principle, induction, symmetry, and number theory applications to enhance analytical skills.
The Dilogarithm
Explore the dilogarithm function, its properties, and interesting sum identities in this mathematical deep dive.
Number Theory
Explore fundamental concepts of number theory, including induction, divisibility, congruences, and prime numbers. Delve into advanced topics like quadratic reciprocity and Dirichlet's divisor problem.
Grade 9 Mathematics Unit 1 Relation
Comprehensive exploration of number systems, operations, and mathematical concepts for Ethiopian Grade 9 students, covering rational, irrational, and real numbers, radicals, and more.
Pi Hiding in Prime Regularities
Explore the fascinating connection between pi, primes, and complex numbers through animated explanations, uncovering hidden patterns and mathematical relationships in number theory.
Number Theory Full Course - A to Z
Comprehensive exploration of number theory, covering fundamental concepts, theorems, and applications. Ideal for learners seeking in-depth understanding of integer properties and advanced mathematical principles.
Why Was This Visual Proof Missed for 400 Years? - Fermat's Two Square Theorem
Explore a visual proof of Fermat's two square theorem, uncovering its 400-year history and the elegant 'windmill trick' that simplifies this complex mathematical concept.