Educational resources for self-learners
Linear Combinations, Span & Basis | Essence of Linear Algebra, Chapter 4
This lecture from 3Blue1Brown visually explains the core concepts of linear combinations, span, and basis in the context of vectors and geometry. It's part of a highly acclaimed series that builds intuition for linear algebra, making it ideal for students with a school math background interested in programming, product design, and computational thinking.
Astro Boy (2009)
An animated film set in Metro City, where a grieving scientist creates a robot boy with incredible powers. The movie implicitly showcases advanced calculus, physics, and spatial reasoning, relevant to robotics, city design, and the application of mathematical modeling and geometry in a futuristic context.
Math and Movies (Animation at Pixar) - Numberphile
Discover how mathematical modeling, vectors, and the geometry of curves are used in 3D animation at Pixar. This video explains the math behind creating smooth character movements, connecting abstract concepts to real-world applications in programming and product design.
Coordinate Free Proofs: Centroid of a Triangle
This recitation video from MIT OpenCourseWare's Multivariable Calculus course demonstrates how to use vectors for coordinate-free proofs, specifically focusing on proving the centroid of a triangle. This session will enhance your understanding of vector applications in geometry.
Hidden Figures
The incredible untold true story of Katherine Johnson, Dorothy Vaughan, and Mary Jackson—brilliant African-American women working at NASA who were the brains behind one of the greatest operations in history: the launch of astronaut John Glenn into orbit. This film showcases mathematical modeling, numerical methods, and geometry of space in a real-world context, perfect for those interested in programming, startups, psychology, and product design.
Lex Fridman Podcast #472: Terence Tao – Hardest Problems in Mathematics, Physics & the Future of AI
Dive into a profound conversation with mathematician Terence Tao on the Lex Fridman Podcast. This episode explores mathematical modeling through the lens of Navier-Stokes equations, the geometry of space in general relativity, and numerical methods in the context of AI-assisted theorem proving. It also delves into the nature of mathematical discovery, problem-solving strategies, and the intersection of mathematics with programming, AI, physics, and philosophy. Perfect for those interested in the foundational and applied aspects of advanced mathematics, and its relevance to technology, startups, psychology, and product design.
Lex Fridman Podcast #472: Terence Tao – Hardest Problems in Mathematics, Physics & the Future of AI
Dive into a profound conversation with mathematician Terence Tao on the Lex Fridman Podcast. This episode explores mathematical modeling through the lens of Navier-Stokes equations, the geometry of space in general relativity, and numerical methods in the context of AI-assisted theorem proving. It also delves into the nature of mathematical discovery, problem-solving strategies, and the intersection of mathematics with programming, AI, physics, and philosophy. Perfect for those interested in the foundational and applied aspects of advanced mathematics, and its relevance to technology, startups, psychology, and product design.
3D Vectors – Introduction to 3D Vectors, Dot Product and Cross Product
This lecture covers 3D vectors, including their representation and visualization, dot product, and cross product. It includes basic vector operations (addition, subtraction) and explains geometric interpretations. Provides clear worked examples geared to high school and early college students, perfect for those with a school math background. Suits students interested in practical, visual applications (such as in product design, computer graphics, or startup prototyping).
Flatland: The Movie
FLATLAND: THE MOVIE is an award-winning animated film inspired by Edwin A. Abbott's classic 1884 novel, “Flatland.” Set in a world of only two dimensions inhabited by sentient geometric shapes, the story follows Arthur Square (Martin Sheen) and his ever-curious granddaughter Hex (Kristen Bell). When a mysterious visitor arrives from Spaceland (Michael York), Arthur and Hex must come to terms with the truth of the third dimension, risking dire consequences from the evil Circles that have ruled Flatland for a thousand years.
The HISTORY of MATHEMATICS. Documentary
A comprehensive documentary exploring the evolution of mathematics from ancient civilizations to modern times, highlighting contributions and impacts on various fields.
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