# What are some calculus, linear algebra and probability and statistics books you would recommend that focus on applications with minimum proofs?

I am a machine learning engineer and I decided I wanted to brush up on the topics relevant for machine learning:

• calculus
• linear algebra
• probability and statistics

I will be doing this in my free time, alongside my full-time job.

My college education entailed calculus (although I didn't do any multiple integrals, for example). I also had linear algebra and discrete mathematics. I had statistics, but not probability, although I did self-study probability, but I never did probability with calculus for example (like calculating the surface under a probability density function using an integral).

I want to emphasize that the books should be focused on applications and not proofs. Actually, the less theory oriented the book, the better. I don't mind going through a few crucial proofs, but that's it. I want to focus on the "mechanics". Maybe in a later pass through these topics I will find myself reading some more theory oriented books, but for now, my plan is to read application-oriented books with minimal or no focus on theory and try to solve as many exercises as I can.

Having said this, what are your recommendations for books on calculus, linear algebra and probability and statistics that focus on applications with minimum proofs?

• It would help if you could give us a better idea of which specific "mechanics" you're interested in. For example, a lot of linear algebra textbooks spend a lot of time (too much I think) talking about solving problems using row-reduction, a technique that's only really useful if you're solving problems with paper and pencil and therefore probably not very applicable to your interests Commented Sep 23, 2023 at 22:23
• @BenGrossmann my end goal would be to able to read machine learning papers (such as this one, for example) and be completely comfortable with the math in the sense that I read that math almost as easily as I read the words. While I was waiting for someone to answer here, I think a good (if not the best) idea would be to go through the relevant MIT OpenCourseware college courses. If you have any other suggestions, feel free to share. Commented Sep 24, 2023 at 10:36

As someone who had an engineering/operations research undergrad I think I get what you are looking for.

## Calculus

You mentioned you haven't done multivariate calculus. I think before you go any further in probability or linear algebra you should get a firm grounding in what would normally be called Calculus I, II, and III in a typical US college sequence for engineers and scientists.

For this, I highly recommend Thomas' Calculus: Early Transcendentals and enthusiastically reviewed here.

I used a much older version of this in my days, but the 13th edition and beyond were even better. It is very problem-solving focused vs proof focused, it has lots of exercises, half of which have answers in the back, and it has very good color diagrams.

This book will take you from single variable calculus (should be familiar to you) up through multivariate and vector calculus, ending neatly with the unification of the Fundamental Theorem of Calculus, Green's Theorem, Stokes' Theorem, and the Divergence Theorem:

The integral of a differential operator acting on a field over a region equals the sum of the field components appropriate to that operator over the boundary of the region.

The more advanced formulation of that (which you'll see in advanced courses) is the Generalized Stokes' Theorem or "Fundamental Theorem of Multivariate Calculus" -- it's stated in terms of differential forms so beyond the scope of Thomas' book.

## Linear Algebra

Here I'd highly recommend Jim Hefferon's book Linear Algebra, available free by the author here. It covers the core topics of linear algebra without getting overly abstract and formal. He has lots of problems and a (free!) solutions manual that details out every problem.

## Probability and Statistics

For a solid, calculus-based treatment of probability and statistics, I'd recommend Probability and Statistics for Engineering and the Sciences by Jay Devore.

It is very much focused on applications and problem solving vs rigorous mathematical statistics. I used this as a first course in prob and stats and it will set you up well to solve real-world probability and stats problems.

• I'd like to note that I did, in fact, have multivariable calculus. I am familiar with f(x, y, z) and multi-order derivaties. I just never had exposure to multiple integrals, for example. As for your suggestion, thank you very much. I think I can also go for the MIT OCW courses related to all of those topics. I think that's a great option as well. Commented Sep 25, 2023 at 7:20
• @Pointer_to_void yep MIT OCW is great as well. You asked for books so I suggested some ones that are aligned with your goals. All the best as you study these topics:) Commented Sep 25, 2023 at 7:43
• Annika, although this is far from my field I’ve heard the words “gradient descent” enough times to believe that OP might want a basic PDE reference as part of “calculus”. Do you have a recommendation in that direction? Commented Sep 25, 2023 at 10:02
• @EricNathanStucky -- I liked: amazon.com/Differential-Equations-Boundary-Value-Problems/dp/… Commented Sep 25, 2023 at 16:15