Mathematics for AI
Master the essential mathematics for AI engineering. Learn linear algebra, calculus, statistics, probability, and optimisation with practical Python implementations and real AI applications.
Created by Baljeet Dogra
Course Overview
A comprehensive 6-week course covering all essential mathematics for AI engineering. Learn through practical Python implementations and see how each concept applies to real AI systems.
AI-Focused Mathematics
Every mathematical concept is taught with direct applications to AI. Understand why each topic matters for machine learning and deep learning.
Python Implementation
Learn mathematics through code. Use NumPy, SciPy, and Matplotlib to implement and visualize mathematical concepts.
Practical Projects
Build 12+ projects including gradient descent from scratch, PCA implementation, neural network math, and statistical analysis tools.
No Advanced Math Required
Perfect for those with basic high school math. We build from fundamentals and explain everything in the context of AI applications.
Visual Learning
Use visualizations and interactive examples to understand complex mathematical concepts. See gradients, transformations, and distributions in action.
Real AI Applications
See how linear algebra powers neural networks, how calculus enables gradient descent, and how statistics drives model evaluation.
6-Week Curriculum
A structured 6-week program covering linear algebra, calculus, statistics, probability, optimization, and information theory. Each week includes hands-on projects.
Week 1: Linear Algebra Fundamentals
Module 1: Vectors and Vector Operations
Vector addition, scalar multiplication, dot product, cross product, vector norms, unit vectors. Applications in embeddings and feature vectors.
Project:
Build a similarity calculator using vector dot products
Module 2: Matrices and Matrix Operations
Matrix addition, multiplication, transpose, inverse, determinant, rank. Matrix representations of data and transformations.
Project:
Implement matrix operations for image transformations
Module 3: Eigenvalues, Eigenvectors, and SVD
Eigenvalue decomposition, singular value decomposition (SVD), principal component analysis (PCA). Applications in dimensionality reduction.
Project:
Implement PCA from scratch using SVD
Week 2: Calculus for Optimization
Module 4: Derivatives and Gradients
Partial derivatives, gradients, chain rule, Jacobian matrix. Understanding how neural networks compute gradients.
Project:
Compute gradients manually for a simple neural network
Module 5: Optimization Basics
Local minima, global minima, convex functions, gradient descent, learning rates. The math behind training neural networks.
Project:
Implement gradient descent from scratch to minimize a function
Module 6: Advanced Optimization
Momentum, Adam optimizer, second-order methods, Hessian matrix. Understanding modern optimization algorithms.
Project:
Compare different optimization algorithms on a loss function
Week 3: Statistics for AI
Module 7: Descriptive Statistics
Mean, median, mode, variance, standard deviation, skewness, kurtosis. Understanding data distributions.
Project:
Build a statistical analysis tool for datasets
Module 8: Inferential Statistics
Hypothesis testing, confidence intervals, p-values, t-tests, ANOVA. Statistical significance in model evaluation.
Project:
Perform hypothesis testing on model performance metrics
Module 9: Regression Analysis
Linear regression, least squares, R-squared, residual analysis. The mathematics behind regression models.
Project:
Implement linear regression from scratch using least squares
Week 4: Probability Theory
Module 10: Probability Fundamentals
Probability axioms, conditional probability, Bayes' theorem, independence. Foundation for Bayesian methods.
Project:
Build a Bayesian spam classifier
Module 11: Probability Distributions
Normal, binomial, Poisson, exponential distributions. Understanding data distributions and their properties.
Project:
Simulate and visualize different probability distributions
Module 12: Maximum Likelihood Estimation
Likelihood functions, log-likelihood, MLE, parameter estimation. How models learn from data.
Project:
Estimate distribution parameters using MLE
Week 5: Advanced Mathematical Concepts
Module 13: Information Theory
Entropy, mutual information, KL divergence, cross-entropy loss. Understanding information in machine learning.
Project:
Calculate entropy and information gain for decision trees
Module 14: Convex Optimization
Convex sets, convex functions, Lagrange multipliers, constrained optimization. Optimization theory for ML.
Project:
Solve constrained optimization problems
Module 15: Numerical Methods
Numerical differentiation, integration, root finding, numerical stability. Practical computation in AI.
Project:
Implement numerical methods for solving equations
Week 6: AI Applications & Capstone
Module 16: Mathematics of Neural Networks
Forward propagation, backpropagation, activation functions, loss functions. Complete mathematical understanding of neural networks.
Project:
Build a neural network from scratch using only NumPy
Module 17: Mathematics of Machine Learning
Bias-variance tradeoff, regularization mathematics, cross-validation theory, model selection criteria.
Project:
Analyze bias-variance tradeoff mathematically
Module 18: Capstone Project
Build a complete machine learning model from scratch using only mathematical foundations. Implement all components manually.
Capstone:
Complete ML Pipeline: Data Analysis → Feature Engineering → Model Training → Evaluation
Technical Requirements
Everything you need to get started with Mathematics for AI.
Prerequisites
- Python 3.8 or higher
- Basic Python programming knowledge
- High school level mathematics (algebra, basic calculus helpful but not required)
- Willingness to learn mathematical concepts
Required Libraries
pip install numpy
pip install scipy
pip install matplotlib
pip install pandas
pip install sympy
All libraries covered in course
Ready to Master Mathematics for AI?
Join the Mathematics for AI course and build a strong mathematical foundation for AI engineering. Understand the math behind every AI algorithm.
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