Steiner's Regions of Space Problem - Famous Math Problems
Exploration of Steiner's space division problem, analyzing how many regions n planes can create in space, with insights into the analogous 2D problem and mathematical reasoning.
How to Do CS Theory - Lecture 1b: Research Tips for Theoretical Computer Science
Insights and tips for aspiring theoretical computer science researchers, covering research methods, paper writing, presentation skills, and essential resources in the field.
The Decline of Rigour in Modern Mathematics - Real Numbers and Limits
Explores the decline of mathematical rigor, discussing Euclid's Elements, proof concepts, and problematic topics in modern mathematics. Examines reasons for this decline and its impact on mathematical foundations.
Find a Closed Form for This Intimidating Sequence
Explore a challenging sequence problem with creative problem-solving techniques and mathematical insights to find its closed form solution.
How to Create the Best Contest Problems
Insights on crafting engaging math contest problems from two expert educators. Learn techniques for designing challenging, creative, and thought-provoking mathematical puzzles.
Generalizing the Right Angle
Explore the concept of generalizing right angles, extending geometric principles beyond traditional 90-degree angles for a deeper understanding of mathematical relationships.
Problem Solving - Techniques from Number Theory
Explore key Number Theory concepts and techniques for solving math competition problems, with practical examples including a 1985 AIME question.
No Simple Groups of Order 66 or 144
Explore advanced group theory using Sylow's Theorems to prove the non-existence of simple groups with specific orders, demonstrating powerful algebraic techniques.
Real Analysis - The Fundamental Theorem of Calculus
Comprehensive proof of both parts of the Fundamental Theorem of Calculus, demonstrating the relationship between differentiation and integration in real analysis.
Step Up to STEM Summer Program Information Session 2021
Free summer program for underrepresented 9th graders in North Carolina, offering STEM and communication skills through real-world challenges. Includes campus living and enrichment activities in the Triangle area.
Vanessa Robins Interviewed by Elizabeth Bradley
Explore applied topology with Vanessa Robins as she discusses her career journey, research interests, and insights on granular materials, collaborations, and emerging areas in the field.
Larry Wasserman - Robust Topological Inference
Explore robust topological inference with Larry Wasserman, covering persistence, confidence bands, bootstrap methods, and optimal tuning for data analysis and statistical modeling.
The Invariant Subspace Problem: A Brief Overview of Recent Developments
Explore recent developments in the invariant subspace problem, covering history, proofs, reflexivity, and various techniques in operator theory and functional analysis.
On the MLC Conjecture by Misha Lyubich
Explore the MLC Conjecture with Misha Lyubich in this interactive lecture, offering insights into complex dynamics and opportunities for audience engagement.
Dmitri Burago: A Mozaic from Geometry, Dynamics, PDEs, and Maybe More
Explore unsolved problems and recent progress in geometry, dynamics, and PDEs through a mosaic of interconnected topics, featuring insights from collaborative research.
Oxford Calculus - Taylor's Theorem Explained with Examples and Derivation
Comprehensive explanation of Taylor's Theorem, including derivation and practical examples. Covers polynomial approximation of functions, Cauchy's Mean Value Theorem, and power series expansion, with interactive exercises and additional resources.
Computing with or Despite the Computer - IPAM at UCLA
Explore the interplay between manual, computer-assisted, and formally verified computations in number theory, examining challenges and opportunities in mathematical research.
On Ulam's Problem 19 and Related Problems - IPAM at UCLA
Explore uniqueness problems related to Ulam's Problem 19 from the Scottish book, presented by Dima Ryabogin at IPAM's Calculus of Variations workshop.
The 3 Differents
Explore the concept of "The 3 Differents" in mathematics with expert insights from C. POLINI of the University of Notre Dame, offering a deep dive into this intriguing topic.
Recent Advances on Variants of the F-Signature
Explore recent developments in F-signature variants, focusing on mathematical advancements and their implications in algebraic geometry and commutative algebra.
What Does "Same" Mean in Math? It Depends.
Explores the nuanced concept of "sameness" in mathematics, examining various contexts where equality and equivalence have different interpretations and implications.