Overview

Coursera Plus Monthly Sale: All Certificates & Courses 40% Off!

Grab it

This course is designed to introduce you to the powerful world of Matrix Calculus, specifically focusing on its application in Data Science and Machine Learning. By the end of the course, you will gain a strong foundation in the essential calculus concepts, such as matrix and vector derivatives, optimization techniques, and their real-world applications in machine learning models. You'll also learn to navigate the complexities of data-driven algorithms through a deep understanding of matrix calculus. The journey begins with an introduction to the course, outlining key topics and offering strategies for success. You’ll be provided with practical guidance on accessing essential course code, allowing you to engage with real-world exercises. The first main section delves into matrix and vector derivatives, covering fundamental concepts like linear forms, quadratic forms, and chain rules. Each section includes hands-on exercises to solidify your understanding of these topics and their applications, such as solving least squares and Gaussian distribution problems. The second part of the course dives deep into optimization techniques, crucial for refining machine learning models. You will explore second derivative tests, gradient descent, and Newton's method, both in one and multiple dimensions. These methods will be demonstrated with Python code to show how optimization strategies are implemented in practice. By applying these techniques in various exercises, you will develop the skills needed to optimize machine learning algorithms efficiently. This course is ideal for those with a basic understanding of calculus and linear algebra who are looking to enhance their skills in the context of data science and machine learning. It is perfect for data scientists, machine learning enthusiasts, and researchers who want to learn the mathematical foundation behind the algorithms driving modern data-driven technologies.

Syllabus

Introduction

In this module, we will introduce you to the course structure, providing an overview of the topics and objectives. We will also offer guidance on how to succeed in the course and demonstrate where to find the essential code for the hands-on exercises.

Matrix and Vector Derivatives

In this section, we will explore derivatives in matrix calculus, starting with fundamental concepts like linear and quadratic forms. You will apply the chain rule and work through practical exercises, including least squares and Gaussian problems.

Optimization Techniques

In this module, we will delve into optimization techniques, covering methods like gradient descent and Newton’s method. We will also focus on practical coding exercises to implement these techniques and apply them to real data science problems.

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

In this section, we will guide you through setting up the Anaconda environment and installing necessary libraries for matrix calculus, ensuring you are fully prepared for the coding exercises in the course.

Effective Learning Strategies (Appendix/FAQ by Student Request)

In this module, we will discuss strategies for learning calculus effectively, evaluate the course’s fit for various learners, and recommend the optimal order for taking the courses to maximize understanding and progression.

Appendix / FAQ Finale

In this final section, we will explain the purpose of the appendix and provide bonus content, offering additional resources and insights to support your learning beyond the course material.