Mathematics For Machine Learning And Ai I : Essentials

Linear Algebra, Calculus, Optimization for Machine Learning and AI Fundamentals

What you'll learn

Understand and apply key concepts in linear algebra, including vector operations, subspaces, and eigenvalues.

Learn the foundations of calculus and multivariable calculus needed for machine learning models.

Master probability theory, Bayes’ theorem, and statistical tools like MLE and hypothesis testing.

Apply essential optimization techniques such as gradient descent, KKT conditions, and linear programming in Python.

Requirements

Basic high school-level algebra and geometry knowledge is helpful but not required.

A willingness to learn mathematical concepts with practical relevance to AI and data science.

Description

This course is designed to give you a complete mathematical foundation for understanding and applying machine learning and AI methods in practice. Whether you're preparing for advanced ML courses or working on real-world projects, this course ensures you understand the math that powers it all — without needing a degree in mathematics.We start with linear algebra — vectors, subspaces, eigenvalues, and orthogonality — and explain how they’re used in ML algorithms. You’ll not only learn the theory but also see hands-on applications in Python and MATLAB, especially for eigenvalues and orthogonalization.Then we move into calculus and multivariable calculus: functions, derivatives, partial derivatives, Hessians, and Lagrange multipliers. These are essential for understanding how models learn and optimize.Next comes probability and statistics: foundational probability concepts, distributions, Bayes' theorem, hypothesis testing, and MLE — everything you need for probabilistic reasoning in AI systems.Finally, we go into optimization: gradient descent, RMSProp, AdaGrad, KKT conditions, and linear programming. You'll understand how models are trained, constrained, and improved over time.The content is clear, structured, and applied. You'll learn both the mathematical logic and how it's implemented in code. No prior programming or ML knowledge is assumed — just a desire to learn.By the end of this course, you’ll be confident in your math skills and ready to move forward in your machine learning and AI journey.

Overview

Section 1: Introduction

Lecture 1 Introduction

Section 2: Python Programming (Optional)

Lecture 2 What is Python?

Lecture 3 Anaconda & Jupyter & Visual Studio Code

Lecture 4 Google Colab

Lecture 5 Environment Setup

Lecture 6 Python Syntax & Basic Operations

Lecture 7 Data Structures: Lists, Tuples, Sets

Lecture 8 Control Structures & Looping

Lecture 9 Functions & Basic Functional Programming

Lecture 10 Intermediate Functions

Lecture 11 Dictionaries and Advanced Data Structures

Lecture 12 Exception Handling & Robust Code

Lecture 13 Modules, Packages & Importing Libraries

Lecture 14 File Handling

Lecture 15 Basic Object-Oriented Programming (OOP)

Section 3: Linear Algebra Essentials

Lecture 16 Introduction to Vectors and Vector Operations - Mathematics

Lecture 17 Introduction to Vectors and Vector Operations - Practice

Lecture 18 Vector Spaces and Subspaces

Lecture 19 Eigenvalues and Eigenvectors - Theory

Lecture 20 Orthogonality and Orthogonalization - Practice

Section 4: Calculus for Machine Learning

Lecture 21 Derivatives and Differentiation Rules

Section 5: Multivariable Calculus

Lecture 22 Partial Derivatives

Lecture 23 Gradients and Directional Derivatives

Lecture 24 Chain Rule for Multivariable Functions

Lecture 25 Hessian Matrices

Lecture 26 Multiple Integrals

Lecture 27 Vector-Valued Functions

Lecture 28 Lagrange Multipliers

Section 6: Optimization Theory

Lecture 29 Gradient Descent

Lecture 30 RMSProp

Lecture 31 AdaGrad

Lecture 32 AdaGrad Python Implementation

Lecture 33 Karush-Kuhn-Tucker (KKT) Conditions

Aspiring data scientists, machine learning engineers, or AI enthusiasts who want a solid foundation in math.,Students in engineering, computer science, or related fields preparing for advanced ML courses.,Professionals looking to refresh or deepen their understanding of core math concepts used in AI.