Educational resources for self-learners
Convex Optimization I, Lecture 1: Introduction and Convex Optimization Overview
Dive into the conceptual foundations of optimization with Professor Stephen Boyd from Stanford University. This lecture covers linear programming (including the Simplex Method as a case study), introduces convex sets and functions, explores the core concepts of convex optimization, and provides an introduction to gradient descent—all crucial for understanding machine learning, product design, and business applications.
Euler's Numerical Method for y'=f(x,y)
A lecture on the fundamental numerical solution for ordinary differential equations, covering Euler's method and its generalizations.
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.
Liz Fearon: Co-producing mathematics with the public
This episode explores how mathematical models are built collaboratively with the public, focusing on their impact on public health, policy, and design. It is highly relevant for understanding the practical applications of mathematical modeling in areas like programming, startups, psychology, and product design.
mathispower4u
A YouTube channel offering clear and concise explanations of various mathematical concepts, including differential equations.
Scraping Bits Podcast #102: Learning Mathematics Like an Athlete
This episode features mathematician and educator Justin Skycak, who discusses how to approach learning mathematics like an athlete. It covers mindset, habit formation, motivation, and "first principles" thinking, connecting mathematical learning to goal-setting, gamification, and progress tracking. This discussion is highly relevant for students interested in programming, startups, psychology, and product design, as it explores how mathematical thinking applies to real-world problem-solving and personal growth.
3.1: Introduction to Systems of ODEs
An academic article introducing systems of ordinary differential equations (ODEs), covering their structure, applications, and conversion of higher-order ODEs to first-order systems. From Mathematics LibreTexts.
L5.0 Gradient Descent -- Lecture Overview
A full-length lecture providing an overview of Gradient Descent, its intuition, mechanism, and properties, with applications in neural networks and machine learning. Presented by Sebastian Raschka.
Modeling Climate Change | MIT Computational Thinking (Spring 2021)
This lecture from MIT's Computational Thinking course explores mathematical modeling through the lens of climate change. You'll learn about computational methods, optimization, and policy implications, using the Julia programming language. This is highly relevant for students interested in programming, startups, and understanding complex systems.
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