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.
Lecture 16 | Graphs I | Computer Science 106B, Programming Abstractions
This lecture from Stanford University's CS106B provides a comprehensive introduction to Graph Theory. You'll learn basic definitions like vertices, edges, paths, and cycles, explore different types of graphs (directed, undirected, weighted), and understand the conceptual development and applications of graph traversal algorithms like Breadth-First Search (BFS) and Depth-First Search (DFS). The lecture also covers trees and their properties, and demonstrates applications in computer networks and real-world scenarios, making it highly relevant for programming, startups, psychology, and product design.
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.
Algorithms Course - Graph Theory Tutorial from a Google Engineer
A comprehensive tutorial on Graph Theory algorithms, including DFS, BFS, shortest path algorithms, and more, with practical examples and Java source code. Presented by a Google Engineer on freeCodeCamp.org.
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.
Podcast: Not So Standard Deviations - 93 - df and dat
Hilary and Roger discuss Moka pots, follow up on the creative curve, name their data frames, discuss prediction vs. forecasting, and data science in military and intelligence applications. This episode touches upon mathematical optimization concepts within data science, relevant to programming, startups, and product design.
Math Academy: Optimizing student learning with Alex Smith and Justin Skycak (Ep 42)
This episode features two directors from Math Academy, an AI-powered online learning platform. The discussion covers how knowledge graphs (relevant to graph theory) are used to personalize and optimize math learning, practical instructional strategies, and Bloom's 2 sigma problem. The conversation blends education, data science, and cognition, providing insights that are valuable for students interested in the intersection of math, psychology, and product design.
Lec 6 | MIT 6.042J Mathematics for Computer Science, Fall 2010
Lecture 6: Graph Theory and Coloring Instructor: Tom Leighton. This lecture covers basic definitions (vertices, edges, paths, cycles), types of graphs (directed, undirected, weighted), conceptual traversal algorithms (BFS, DFS), introduces trees and their properties, and discusses applications in scheduling, optimization, and networks.
Lecture 5 | Convex Optimization I (Stanford)
Professor Stephen Boyd, of the Stanford University Electrical Engineering department, lectures on the different problems that are included within convex optimization for the course, Convex Optimization I (EE 364A). Convex Optimization I concentrates on recognizing and solving convex optimization problems that arise in engineering. Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering.
Numerical Methods: Series and Sequences
This PDF document from MIT OpenCourseWare's "Introduction to Numerical Analysis" course covers the fundamental concepts of series and sequences, which are essential for understanding numerical methods. It delves into the theoretical underpinnings necessary for applying these methods in programming and scientific computation.
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