Last Minute Lecture

Vectors, Dot Products, and the Mathematics Behind Machine Learning | Chapter 2 of Why Machines Learn Chapter 2, “We Are All Just Numbers Here…,” from Why Machines Learn: The Elegant Math Behind Modern AI dives into the mathematical foundations that make learning algorithms possible. Moving from 19th-century discoveries in vector algebra to the modern perceptron, the chapter explains why linear algebra is the language of machine learning. This post expands on the video’s core ideas and provides an accessible walkthrough of the geometry, notation, and logic that help machines interpret the world as numbers. For a deeper guided explanation, be sure to watch the chapter summary above. Supporting the Last Minute Lecture channel helps us keep producing accessible academic breakdowns for complex textbooks. From Quaternions to Vectors: The Birth of Modern AI Mathematics Anil Ananthaswamy begins by tracing the story of William Rowan Hamilton, whose work on quaternions introduced c...

Units, Vectors & Problem Solving Explained: University Physics Chapter 1 Chapter 1 of University Physics establishes the mathematical foundations necessary for tackling physics problems with confidence. In this summary, we cover how physical quantities are measured in SI units and converted algebraically, how to maintain precision using significant figures and scientific notation, and how to apply the ISEE strategy for problem solving. We also introduce vectors—graphical addition, component resolution, and vector algebra—which underpin mechanics, electromagnetism, and modern physics. Standards of Measurement and Unit Conversion The International System of Units (SI) provides a standardized framework for expressing physical quantities such as length (meter), mass (kilogram), and time (second). Unlike the British system, SI units are defined by fundamental constants, ensuring consistency across experiments. Treating units algebraically allows you to convert between units smoo...