Mathematics for Machine Learning: Multivariate Calculus

Welcome to Module 1! This module provides a comprehensive overview of the basics of calculus, including functions, rise over run, definition of derivatives, product rule, and chain rule. Learners will gain a strong foundation in differentiation and understanding the gradient of a function.

Module 2 delves into multivariate calculus, covering differentiation with respect to multiple variables, the Jacobian, and the Hessian. Participants will develop the skills to calculate Jacobians and Hessians, essential for understanding and working with multivariate functions.

Module 3 explores the multivariate chain rule and its applications in simple neural networks. Participants will gain insights into backpropagation and its role in training neural networks, providing a practical understanding of the multivariate chain rule in the context of machine learning.

Module 4 introduces Taylor series and linearization, focusing on building approximate functions and developing power series. Participants will learn to apply the Taylor series to approximate functions, visualize Taylor series, and understand its significance in machine learning applications.

Module 5 provides an introduction to optimization, covering gradient descent, constrained optimization, Newton-Raphson, and Lagrange multipliers. Learners will gain practical skills in optimizing algorithms and understanding the importance of optimization in machine learning.

Module 6 delves into regression, covering simple linear regression, non-linear least squares, and fitting distribution data. Participants will gain practical insights into regression analysis, equipping them with the skills to apply regression techniques in machine learning models.