Linear algebra final push

Last week was a watershed moment for the linear algebra book. My editor finished her final pass of edits to the text and passed the ball back to me for the final touches. All the remaining tasks have been placed in a Trello board and now all I have to do is act on them to finally get the job finished.

It’s difficult to describe in words what a relief finishing this book will be for me. This book has been my life for the past four years. Here is a time lapse video that shows two-years-worth of commits in two minutes.

I want to thank all the readers who have supported me throughout the years. Thanks for all the feedback and suggestions, which made the book better. A big thank you to all the gumroad readers for your financial support and your patience—I’ve been “finishing up” the applications chapters for three years, yet not a single reader has threatened to come and break my legs because of the delays. Y’all are awesome!



Request for feedback

In parallel with the edits of the linear algebra book, I’ve also been working on a new look for the book covers.

Which version do you prefer and why? You can reply via the comments below or send me an email.

Improving the math chapter

The goal for the NO BULLSHIT guide to MATH & PHYSICS was to make a concise textbook that teaches university-level calculus and mechanics in a nice “combined package.” The math fundamentals chapter grew out of the need to introduce the prerequisite material that many students often lack. I didn’t want to be like “y’all should remember this math from high school,” because if you don’t remember the material such comments would not be very helpful. A review of high school math would be more helpful.

Over time, I kept adding and improving the introductory math material in Chapter 1 until it reached the point that it’s a pretty solid little intro to high school math. I was very proud of the fast paced flow of explanations which manages to cover a lot of material (70% of high school math topics) in less than one hundred pages. Many readers also praised this chapter, saying how useful they found it as a review of high school math topics.

Recently I’ve been hearing from several readers who say the intro chapter sucks, and the book sucks, and by extension I suck. If it was one or two reviewers I could have dismissed this feedback, but now I realize there is a clear and consistent message in the readers’ feedback: Chapter 1 sucks as a first contact with math. My effort to “cover” all the high school topics in a fast-paced narrative like in the free mechanics and linear algebra tutorials is probably the worst thing to do for absolute beginners. I can totally understand why a reader who is not familiar at all with sets, algebra, and functions will have a rough time in the opening pages of the book. In the words of a reader, the book “goes from 0 to 60 in the blink of an eye,” which might be a good thing for a sports car, but not for a math book. It doesn’t help that I say “anyone can learn math from this book, regardless of their mathematical background” in the marketing copy. I need to do something to fix Chapter 1, and soon.

So what am I going to do about it, then? Write, of course—what else can a writer do? I’m going to prioritize the basicmath project and write the best sequence of introductory math lessons that ever existed! I’ll then use these explanations to beef up  Chapter 1 to make it a solid foundation. I think adding 20–40 more pages will be enough, so the book won’t get that much thicker. It’s not just about adding though, I think Chapter 1 could use better organization, flow, and clarity of explanations.

Interestingly, the basicmath project overlaps well with my planned social media campaigns that will push the message “learn math; math is useful,” as well as the math lessons by email. February is gonna be very mathematical!

Math for lawyers

A reader recently suggested I should write more articles that introduce math specifically for different audiences. Math for doctors (although I’d hope they already know math!), math for artists, math for musicians, etc. I like this idea.

In the spirit of procrastination and given the three other tasks I have to do in currently open tabs, I’m going to now dedicate the next hour to writing a sample post that introduces math to people with a “legal mind.” Don’t worry, dear readers—it just takes an hour to write a blog post. Reading it will only take three minutes.


Yes. I’ve said the dirty word. Everyone’s dreaded topic. So factual and unforgiving—you’re either good at math or you’re not. Okay. No, no, no. We’re not going with the usual narrative today. Let’s deconstruct this thing that is math, and see what it’s made of. Perhaps it’s not so bad.


Axioms and rules

Math is very ordered. It’s a bit like the French system (civil-law). All of math can be summarized as basic axioms on which everything else is built. Think of math as a set of rules that people have found to be generally useful in the past two thousand years. Like, send a spacecraft-to-mars useful. Once you know the dozen or so rules for working with numbers and expressions, and the dozen definitions and observations about geometry, you’ll have access to some of the “best stuff” that human intellect has to offer. I guess what I’m trying to say is that A) math is not that hard to learn because there is a finite set of basic rules to learn, and B) once a reader learns the basics, the reader is granted a nonexclusive, royalty-free, perpetual, irrevocable, transferable, worldwide license, to make, use, enjoy, benefit from, teach, share, offer for sale, sell, reproduce, include in, distribute, modify, adapt, prepare derivative works of, display, perform, and otherwise exploit math.


Math has a lot of common-law aspects to it too. Theorems (big results) and lemmas (little results) are like cases that mathematicians have proved. A proof is a bit like a trial, where the mathematician tries to convince the jury (usually consisting of fellow mathematicians) that some new mathematical fact is true. Unlike a real-world courthouse that depends on a judge’s judgment at some point \(t\) in time, a mathematical proof is always on trial. If the mathematician’s proof is solid and can be followed to the basic axioms, it’s very unlikely it will ever turn out to be wrong, so it’s common for mathematicians to simply cite theorems as if they were “ruled upon” case law.


The pitch

So here we are talking about math as if it’s some cool new thing, but we all know that math is difficult to learn and probably not that useful in every day life. Yes, perhaps it is so, but the point remains that certain math—let’s call it the useful part—has been around for thousands of years and hasn’t been proven wrong. Basic math is well understood, highly useful, and totally empowering.

Do you want to be part of this math thing? If so, check out the books.


Linear algebra problem sets progress

I’ve been working on the problem sets for the linear algebra book non-stop for the past month. It’s a lot of work, but also very rewarding. I’m going through online resources and looking for inspiration by reading exams and books to find illustrative exercises and challenging problems. This leads to a lot of  learning and reviewing of ideas along the way…

Finalizing 50 pages of problems and solutions is not an easy task, luckily I have good coffee to temporarily boost me, and more importantly access to the SymPy live shell. In combination with TeXShop, writing up more than one solution per hour becomes possible.  Check this screenshot if you want to see the author at work . Using as a URL shortener, you can put an entire problem solution as a URL:

So far I am yet to find a useful linear algebra problem that I haven’t covered in the book. I’m pretty happy about this because when writing a textbook from scratch you never know what topics you might miss. I’m only using the formulas from the book, and able to handle most problem types… Linear algebra? we got you covered!

Call for student assistance: are you taking a linear algebra class this term? Do you want to solve all the exercises and problems in the book as “extra practice” for your final exam? Get in touch with me ASAP (my_first_name at minireference dot com), and I’ll send you the PDF of the entire problem sets. It might take you up to a week to go through all of them, but by the end of it you’ll be able to handle even the toughest  linear algebra final.

Linear algebra v2 beta release

The No bullshit guide to linear algebra files on gumroad were updated. The book is now v2 beta 2, and scheduled for release in early January 2017.

If you’re taking a linear algebra class this term, or need to know linear algebra for a more advanced class, this will be the best money you spend this semester.



Math is power. Specifically, the ability to use math models to describe real-world phenomenon and predict the future is a powerful general tool to add to you toolbox. Linear algebra has applications to many fields. In general, understanding basic math, and specifically functions of the form \(f(x)=y\) like \(x,x^2,x^3,x^n,e^x,\ln(x),\sin(x),\cos(x),\tan(x),\ldots\) opens many doors for mathematical modelling.

Linear algebra is the study of linear transformations, or vector functions of the form \(T(\vec{v}) = \vec{w}\). The linear transformations take vectors \(\vec{v}\) as inputs and produce vectors \(\vec{w}\) as outputs.  Many real-world phenomena in computer science, physics, chemistry, biology, and many other fields can be modeled as vector quantities, so linear algebra has countless applications. Linear algebra is the vector extension to your math modelling toolbox.



Everyone knows that math is useful, but people much rather leave the learning of math to other people, rather than learn math themselves. Most people imagine learning math is a difficult task, like carrying big bags of potatoes up a steep hill. Surely, such hard work is not for everyone, and we should delegate all the potato-carrying to experts in the field (mathematicians, scientists, and engineers). This way of thinking gave us a modern world where only a small portion of the world is math literate. Everyone else lives in ignorance and fear of all things mathematical.

It doesn’t need to be this way. Everyone can learn math—even advanced math like linear algebra—if they follow a structured approach. Each section in the No bullshit guide to linear algebra follows the same recipe:

  • Motivation to trick readers into wanting to learn about the topic
  • Definitions of all quantities and variables relevant to the topic
  • Formulas: all the essential formulas associated with the topic are given
  • Examples that show how to use the formulas in different scenarios
  • Explanations about how the formulas are derived and how to understand them
  • Discussion about how the connections between this topic and other
  • Exercises to test your understanding of the concept
  • Links to web resources for further reading

This structure allows to get all the important information across in the shortest amount of time. The reader is free to skim through superficially, or dig in an read all the explanations. The exercises help both students and self-learners test there understanding of the material.



The No bullshit guide to linear algebra is a short textbook that covers all the standard topics of university-level linear algebra, and also discusses applications like machine learning, computer graphics, probability theory, and quantum mechanics.

You can buy the eBook bundle here ($29, includes all future updates). The book is currently being edited, so it’s likely to see some further improvements to the chapters on applications, but the main material (that which will be on a an exam) is absolutely solid now.

@Students: get in touch with me if you’d like to be a “test subject” for the new  problem sets. I wrote 50+ pages of new problems and solutions for the book, and I could use your help to double-check the answers.