TENSOR CALCULUS for Deep Learning

Master the mathematics behind modern AI without getting lost in theory.

Most deep learning books either skip the math or bury you in abstract theory. Tensor Calculus for Deep Learning bridges that gap, giving you exactly the mathematical tools you need to understand, build, and debug real machine learning models.

Whether you're a student, engineer, or self-taught practitioner, this book takes you from core linear algebra and multivariable calculus to the tensor operations that power neural networks step by step, with clarity and purpose.

You will learn how gradients flow through networks, how backpropagation really works, and how optimization algorithms shape model performance, all through the lens of tensor calculus.

What you will learn:

How vectors, matrices, and tensors connect in deep learning
The multivariable chain rule and its role in backpropagation
Gradient descent, optimization methods, and loss functions
Tensor operations including contraction, broadcasting, and einsum
The mathematics behind neural networks, CNNs, RNNs, and transformers
How automatic differentiation engines work
Advanced topics including manifolds and natural gradients

Why this book is different:

Practical focus: only the math that actually shows up in machine learning
Step-by-step solutions with no skipped reasoning
Worked examples for every major concept
Complete answers for all exercises
Built around real-world frameworks like PyTorch and JAX
Who this book is for:

College students in data science, AI, or engineering
Machine learning practitioners who want deeper understanding
Self-taught programmers transitioning into AI
Anyone who wants to read research papers with confidence

If deep learning has ever felt like a black box, this book will give you the mathematical clarity to understand what is really happening inside.