Matrix Calculus in Data Science & ML Online Course

Matrix Calculus in Data Science & ML Online Course

This course builds a strong foundation in matrix calculus and optimization, essential for data science and machine learning. You’ll begin with core concepts such as vector and matrix derivatives, linear and quadratic forms, chain rules, and determinants, reinforced through exercises like least squares and Gaussian methods. The course then advances into optimization, covering gradient descent, multi-dimensional derivative tests, and Newton’s method with hands-on practice. You’ll also learn to set up your Anaconda environment and work with tools like NumPy, SciPy, and TensorFlow. Alongside technical skills, the course provides guidance on effective learning strategies and course sequencing. By the end, you’ll transition from theory to real-world applications, equipping yourself with the mathematical and computational tools needed to excel in data science and machine learning.

Who should take this Course?

This course is ideal for aspiring data scientists, machine learning practitioners, and students seeking to strengthen their mathematical foundation. It suits developers and professionals aiming to understand the calculus behind ML algorithms and optimization techniques. Beginners with basic math knowledge can benefit from structured explanations and practical exercises, while advanced learners can refine their skills in gradient descent, Newton’s method, and optimization. Anyone wanting to bridge the gap between theory and application in data science and ML will find this course highly valuable.

Course Outline 

Introduction

• Introduction and Outline
• How to succeed in this course
• Where to get the code

Matrix and Vector Derivatives

• Derivatives - Section Introduction
• Linear Form
• Quadratic Form (pt 1)
• Quadratic Form (pt 2)
• Exercise: Quadratic
• Exercise: Least Squares
• Exercise: Gaussian
• Chain Rule
• Chain Rule in Matrix Form
• Chain Rule Generalized
• Exercise: Quadratic with Constraints
• Left and Right Inverse as Optimization Problems
• Derivative of Determinant
• Derivatives - Section Summary
• Suggestion Box

Optimization Techniques

• Optimization - Section Introduction
• Second Derivative Test in Multiple Dimensions
• Gradient Descent (One Dimension)
• Gradient Descent (Multiple Dimensions)
• Newton's Method (One Dimension)
• Newton's Method (Multiple Dimensions)
• Exercise: Newton's Method for Least Squares
• Exercise: Code Preparation
• Gradient Descent and Newton's Method in Python
• Optimization - Section Summary

Setting Up Your Environment (Appendix/FAQ by Student Request)

• Anaconda Environment Setup
• How to install Numpy, Scipy, Matplotlib, Pandas, IPython, Theano, and TensorFlow

Effective Learning Strategies (Appendix/FAQ by Student Request)

• Can YouTube Teach Me Calculus? (Optional)
• Is this for Beginners or Experts? Academic or Practical? Fast or slow-paced?
• What order should I take your courses in? (part 1)
• What order should I take your courses in? (part 2)

Appendix / FAQ Finale

• What is the Appendix?
• BONUS