Math Behind LLM

About this course

Large Language Models (LLMs) like GPT, LLaMA, and Claude are transforming how we work with text and knowledge—but what makes them tick at a mathematical level? This course, Math Behind LLMs, is designed for developers, data scientists, and AI enthusiasts who want to understand the core mathematical principles powering today’s most advanced AI systems.

We start with the fundamentals of linear algebra (vectors, matrices, embeddings) and probability theory (Bayesian reasoning, distributions). Then we dive into the calculus of optimization—gradients, backpropagation, and loss functions that guide model training.

From there, we’ll unpack the Transformer architecture, focusing on the math of attention: dot products, softmax, normalization, and multi-head projections. You’ll also explore how concepts like matrix factorization, eigenvalues, and singular value decomposition connect to dimensionality reduction and embeddings.

By the end of the course, you’ll have a clear mathematical understanding of:

• How LLMs represent language in vector spaces
• Why attention mechanisms work so effectively
• The optimization math that enables training on billions of parameters
• The optimization math that enables training on billions of parameters
• The optimization math that enables training on billions of parameters

This is not just theory—you’ll work through examples, visualizations, and hands-on problem sets that bridge the gap between equations and working LLMs.

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