This fall, I’m going back to school to study Robotics as a graduate student.

It’s been almost five years since I graduated from undergrad, so to prepare myself I created a list of study materials for review. I hope others might find this list of recommendations helpful.

There were two main areas I wanted to cover: mathematics review, and introduction to robotics concepts. The latter section might be useful for someone interested in robotics but not sure which areas they want to pursue.

Please comment if you have any questions!

General Math

How to Prove It by Velleman

Man, I wish I had read this book BEFORE undergrad. In this book, Velleman does three things:

• describes basic concepts in Logic
• gives common proof strategies, with plenty of examples
• dives into more set theory, defining functions, etc

He does all this assuming the reader is NOT a mathematician–in fact, he does an excellent job of explaining a mathematician’s thought process when trying to prove something.

I highly recommend this book if you feel uncomfortable reading and/or writing proofs, since it will make the following math books much more enjoyable to read!

Calculus

Barron’s College Review Series: Calculus

This book was my warm-up. It is very simple, and is focused more on computation than rigorous proofs. I think I got through it in a weekend, while completing most of the exercises. It does NOT include multivariate calculus.

Khan Academy: Calculus

Khan Academy lectures, while time-consuming, are a great reference if there is a specific concept that you’re struggling with. That said, I don’t recommend watching the whole series, but rather searching for a specific topic (say, “gradient”) when you want more information.

Probability and Statistics

Khan Academy: Probability and Statistics (combined with Combinatorial Probabilities cheat sheet)

I have to say: I always had problems getting combinatorics straight in my head, and watching these videos + completing the exercises really helped.

Introduction to Bayesian Statistics by Bolstad

This book is AMAZING. Bayesian statistics is extremely important to modern robotics, and this book provides an excellent introduction. Highly recommended!

Note that if you’re already comfortable with traditional probability, you can skip the Khan Academy altogether and skip straight to the Bolstad book.

Differential Equations

Elementary Differential Equations by Boyce and DiPrima

All-around excellent book. Probably my favorite, most-referenced textbook from undergrad.

Khan Academy: Differential Equations

Again, don’t watch the all the lectures, but use them as a reference when you want a simple, thoroughly-explained overview of a specific topic.

Linear Algebra

Linear Algebra by Hefferon (also available in print)

If you had to pick a single math topic to study before entering robotics, linear algebra would be it. This book is particularly good because it starts with solving systems of equations, defining spaces, and creating functions and maps between spaces–and only after this foundation is laid does it introduce matrices as a convenient form for dealing with these concepts.

Khan Academy: Linear Algebra

Again, don’t watch the all the lectures, but use them as a reference when you want a simple, thoroughly-explained overview of a specific topic.

Code

The Nature of Code

I’ve been programming since high school, so I didn’t really need much review in this area. However, The Nature of Code is an amazing book, it’s free!, and it includes online exercises in the Processing language, so I have to recommend it.

Also note that the Udacity CS-373 course includes programming exercises in Python.

Robotics

If you complete the following courses, you’ll get a high-level understanding of some of the most important concepts in robotics.

Udacity CS-373, Artificial Intelligence for Robotics

Topics include: Localization, Particle Filters, Kalman Filters, Search (including A* Search), PID control, and SLAM (simultaneous localization and mapping). If you understand these concepts, you can write software for a mobile robot! Even better, each section has multiple programming exercises in Python, so you really get practice with the topic.

If you want to dig deeper into some of the above topics, I recommend Sebastian’s book, Probabilistic Robotics

Udacity CS-271, Introduction to Artificial Intelligence

If you’re interested in Machine Learning, this is a great course. It’s not as slick as CS-373, but still worthwhile.