Epic Circles
Explore fascinating mathematical concepts like Pappus chains and circle inversion in this engaging video featuring Simon Pampena's insights on the beauty and complexity of circular geometry.
The Distance Between Numbers
Explore an unexpected property of number sequences with mathematician Tom Crawford, delving into a fascinating mathematical concept that challenges intuition about distances between numbers.
The Yellowstone Permutation
Explore the fascinating Yellowstone Permutation sequence, its connection to geysers, and its mathematical properties with Neil Sloane, founder of the OEIS.
Cow-culus and Elegant Geometry
Explore two solutions to a geometric problem involving an injured cow, comparing a complex approach with an elegant one. Discover the beauty of mathematical problem-solving with Zvezdelina Stankova.
The Notorious Question Six - Cracked by Induction
Explore the infamous Question Six from the 1988 Math Olympiad, solved using induction. Zvezdelina Stankova breaks down this challenging problem, offering insights into advanced mathematical reasoning.
Epic Induction
Explore mathematical induction with Zvezdelina Stankova in this engaging video. Learn problem-solving techniques and gain insights into this powerful proof method through captivating examples and explanations.
Primes and Primitive Sets - An Erdős Conjecture Is Cracked
Explore the fascinating world of prime numbers and primitive sets as mathematician Jared Duker Lichtman discusses the recent proof of a long-standing Erdős conjecture in number theory.
Euler's Formula
Explore fascinating aspects of Euler's Formula with mathematician Tom Crawford, uncovering its beauty and significance in mathematics through engaging explanations and visual demonstrations.
Why Is This 15-Puzzle Impossible? - Numberphile
Professor Steven Bradlow explains the mathematical impossibility of solving certain configurations of the classic 15-puzzle, exploring permutations, invariants, and the fascinating properties of this seemingly simple game.
Complex Analysis - Examples of Complex Integrals
Explore practical applications of complex integration theorems through challenging examples, enhancing your understanding of advanced mathematical concepts.
Complex Analysis - Complex Residues
Explore the residue theorem and learn to compute complex contour integrals around singular points, culminating in the integral of f(z)=1/z.
Complex Analysis - Integrals in the Complex Plane
Explore contour integration in complex analysis, covering theorems, continuous deformation, and integration around singularities for a deeper understanding of complex functions.
Complex Analysis - Analytic Functions Solve Laplace's Equation
Explore how analytic complex functions' real and imaginary parts solve Laplace's equation, introducing harmonic functions in this in-depth mathematical analysis.
Complex Analysis - Analytic Functions and Cauchy-Riemann Conditions
Explore analytic complex functions and learn to test for analyticity using Cauchy-Riemann conditions in this comprehensive mathematical exploration.
Complex Analysis - Roots of Unity and Rational Powers of Z
Explore complex logarithms and exponentials to compute fractional powers of complex numbers, including nth roots of unity and special cases like the square root of i.
Complex Analysis - Functions of a Complex Variable, f(z)
Explore complex functions including monomials, exponentials, and trigonometric functions. Learn about Taylor series and important identities in complex analysis.
Numerical Integration of Chaotic Dynamics - Uncertainty Propagation & Vectorized Integration
Explore chaos and uncertainty propagation in dynamical systems through numerical integration. Learn efficient vectorization techniques in Python and MATLAB for faster computations.
Coding a Fourth-Order Runge-Kutta Integrator in Python and Matlab
Learn to implement a 4th-order Runge-Kutta integrator in Python and Matlab, and apply it to simulate the chaotic Lorenz 1963 system. Gain practical coding skills for numerical integration.
Runge-Kutta Integrator Overview - All Purpose Numerical Integration of Differential Equations
Comprehensive introduction to Runge-Kutta schemes for numerical integration of differential equations, covering RK2 and RK4 methods with intuitive explanations and visual representations.
Numerical Integration of ODEs with Forward Euler and Backward Euler in Python and Matlab
Explore Forward and Backward Euler integration methods for ODEs using Python and Matlab. Compare stability, error, and implementation on a spring-mass-damper system with analytic solutions.
Deriving Forward Euler and Backward-Implicit Euler Integration Schemes for Differential Equations
Explore Forward and Backward Euler integration methods for ODEs, including derivations, error sources, and stability analysis. Gain insights into numerical integration techniques for solving differential equations.