Mathematics for artificial intelligence: Foundation of linear algebra and probality

Mathematics is the heartbeat of Artificial Intelligence (AI). Every algorithm that predicts, classifies, generates, or optimizes is, at its core, a set of mathematical operations executed at high speed by a computer. While the modern AI revolution is often presented in terms of "neural networks," "deep learning," or "big data," the reality is that none of these technologies could exist without the solid mathematical foundations provided by Linear Algebra and Probability.
This book, Mathematics for Artificial Intelligence: Foundations of Linear Algebra and Probability, has been designed with a singular purpose: to equip undergraduate and postgraduate students, researchers, and professionals with the essential mathematical knowledge required to understand, develop, and innovate in AI, Machine Learning (ML), and Data Science (DS).
Unlike generic math textbooks, this book is not an abstract treatment of mathematical theory. Instead, it is a context-driven, application-oriented guide where every formula, theorem, and concept is directly linked to AI applications. Each chapter contains not only the theoretical explanations but also step-by-step worked examples, visual illustrations, Python implementations, and case studies showing how the mathematics is applied in real AI models.


Why This Book is Needed
The AI education landscape faces a persistent gap. Many students are introduced to machine learning or deep learning without fully understanding the mathematical machinery that powers these models. This results in a "black box" understanding: they can use libraries like TensorFlow, PyTorch, or scikit-learn, but they cannot explain why these models work, how to tune them effectively, or how to build new ones from scratch.
By focusing on Linear Algebra and Probability, this book addresses that gap. These two branches of mathematics are the twin pillars of AI:

• Linear Algebra powers vector representations, transformations, embeddings, convolution operations, dimensionality reduction, and deep learning computations.
• Probability enables reasoning under uncertainty, statistical inference, probabilistic models, Bayesian learning, and reinforcement learning.

By mastering these topics, readers will gain the ability to not just use AI tools but to innovate and optimize AI algorithms for specific problems.


Who This Book is For
This book has been designed for:

• Undergraduate Students of Computer Science, AI, Data Science, Electronics, and related fields who need a solid math foundation for later AI/ML courses.
• Postgraduate Students in AI, ML, and DS who wish to strengthen their theoretical foundations while working on advanced research or applied projects.
• Educators looking for a comprehensive, structured curriculum that bridges pure mathematics and AI applications.
• Professionals transitioning into AI/ML from other fields, who may not have touched mathematics for years but need a refresher with application focus.
• Researchers who want a ready reference for mathematical concepts used in developing novel AI algorithms.

How the Book is Structured
The book is divided into six parts, each logically building upon the previous one.