No bullshit linear algebra v2 release

The NO BULLSHIT guide to LINEAR ALGEBRA is finally ready. After two years of writing and two years of editing, the book is now complete! Thanks to all the feedback from readers and the amazing attention to detail of my editor Sandy Gordon, the first print release is very polished.

No bullshit guide to linear algebra product shot

Can I see a preview?

I’ve posted an extended preview of the book here (160 pages, PDF) so you can get a feel of what’s included. I tried to make the preview useful on its own: rather than showing only a few pages from the introduction, I’ve included the definitions from all the sections, which are the most important part of the book.

If you’re not interested in reading a whole book, but just want to see the graphical representation of all the linear algebra topics, I encourage you to check the concept maps here. If you’re looking for a quick refresher on linear algebra concepts, you can check the four-page linear algebra summary here.

 

Why should I learn linear algebra?

Linear algebra is the foundation of science and engineering. Knowledge of linear algebra is a prerequisite for studying statistics, machine learning, computer graphics, signal processing, chemistry, economics, and quantum mechanics. Indeed, linear algebra offers a powerful toolbox for modelling the real world. All areas of advanced science and engineering make use of linear algebra models in one way or another. So essentially, you need to learn linear algebra if you want to do science.

 

Why do I need this book?

There are many great books about linear algebra that exist out there[1,2,3]. The NO BULLSHIT guide to LINEAR ALGEBRA is special because of the concise, conversational tone it is written in, the prerequisites material it includes, and the numerous exciting applications of linear algebra it discusses. This book is the result of  years of private tutoring, which makes the narrative feel much more like a conversation with a friend rather than a stuffy lecture. I know from experience that many adults don’t remember basic math topics like algebra, functions, and equations, so the book includes a comprehensive review chapter (Chapter 1) to make sure everyone is on board with the fundamentals.

The “main course” of the book (Chapters 2 through 6) consists of all the standard material covered in linear algebra courses with lots of examples, exercises, and practice problems with solutions.

The book concludes with three “dessert” chapters that discuss applications of linear algebra. We start with applications to chemistry, economics, electrical engineering, graph theory, numerical optimization, cryptography, and signal processing (Chapter 7). Next we followup with a chapter on probability theory, Markov chains, and an exploration of Google’s PageRank algorithm (Chapter 8). The book concludes with a chapter that introduces the fundamental ideas of quantum mechanics and quantum computing (Chapter 9). Many of the topics covered in chapters 7, 8, and 9 are considered “advanced” or “graduate level,” but readers of the book who’ve gained a solid grasp of linear algebra concepts will be able to learn about these exciting applications with no problem at all.

 

Where can I buy this book?

It depends on what you want. The eBook version costs $29 and is a pretty sweet deal since it comes with all future updates. But if you really want to learn the material, you should get the softcover print version, which is much better for focused learning, and costs about the same: \$39 – 20% off = \$31. If money isn’t a constraint for you right now, you should get the hardcover, which is printed on larger paper and has a construction that will last for decades.

Regardless of your choice of medium, you’ll be getting the same high quality book that will introduce you to the wonderful subject of linear algebra in the least intimidating way possible.

The textbook business

This is a followup on my previous post about the challenges of open educational resources (OER) production and adoption. I’ve come to the conclusion that the key aspect holding back the “OER dream” is not the lack of collaboration tools or the ability for teachers to discover material, but the quality of the content. You can’t write a textbook by committee. It’s as simple as that!

I wish collectives of qualified authors/teachers could come together to create the free textbooks and other educational material, but it seems human nature doesn’t work this way, and it’s very difficult for multiple authors to “sync” their thoughts together and come up with a coherent narrative for book-length projects.

The key to the production of quality educational content is to set the right incentives for knowledgeable authors to write. I’m thinking graduate students writing tutorials, blog posts, HOWTOs, books, and generally living from the proceeds of their work. Rather than wishful thinking about “collaborative projects” where multiple authors come together to write a book, why don’t we focus on single-author textbooks? Rather than a “commons” approach where nobody owns the project, let’s have a single author “own” the project and make them personally involved with its success. I believe the monetary incentives will be enough to make the author invest the time needed to make the book/project/resource a success.

It’s possible to replicate, and generalize the business model I used with the MATH&PHYS, and LA books with experts in other fields: chemistry, biology, economics, psychology, history, etc. If a young person (think an M.Sc. or a Ph.D. student) with practical and teaching experience in a particular subject writes books, I can guarantee the book will be a success.

 

Business model

The beautify of the matter is we don’t need to invent anything new. We’ll use a very traditional business model, where we sell products to make cash. The authors will make a significant profit from each copy of the book sold, and will thus be incentivized to produce quality content that sells.

The publisher (Minireference Co.) will also make profits from the book sales and be able to fund software development, marketing efforts, author advances, and generally take care of the business overhead for running operations. The main innovation of this business model is that, rather than the publisher being in an exploitative relationship with the author, they are equal partners. Rather than authors making 10% royalties, at Minireference Co. authors earn 50% royalties. The publishers takes care of the boring stuff and allows the authors to focus on the hard task—writing, polishing, and curating the content. Equal partners, with parts of the proceeds.

The market(s)

The main audience for the textbooks will be students, but students in the broadest sense of the term. We’re talking advanced-level high school students,  university students, parents, and adult learners. By setting a price point for the products around $29 to $39, we’ll make sure the books are affordable for everyone, but also make enough money to sustain the authors so they can keep producing more books.

 

Okay, so where is the OER in all of this?

By now, my dear readers, you might be wondering if there is no case of “bate and switch” going on here. We started with the promise/mission to make open educational resources more accessible to students and adult learners around the world, and somehow we ended-up with a reaffirmation of a business plan to make money from selling books. Perhaps there is some of this going on, but you must agree that building stable organizations with individuals who earn a living by teaching is a step in the right direction.

The approach that I imagine for getting achieving the “OER dream” is to encourage authors to sell their university-level books, but contribute primary and high school material as OER. I think the “university for money, but high schools stuff for free” approach will work for two reasons. Some authors might start from an altruistic point of view, and want to do something good for society by releasing some introductory lessons for free. Other authors might be motivated by purely capitalistic incentives, since releasing the high school material for free is an excellent way to promote their work.

 

Focus, focus, focus

There’s only a limited things one person can do in their lifetime so it’s important to focus on the things that make sense, and which have potential for growth and high impact. I’ve invested the past 5+ years of my life in the math textbook business so I think it’s important to continue that project instead of changing priorities or working on other projects.

The beauty of this idea is that it doesn’t require any miracles, breakthroughs, or external funding. All it takes is an evolution of the project I have currently going on, so I can work with more authors. Life always tends to make things more complicated over time, so starting with a simple plan, and keeping the focus is generally a good way forward. Vamolos; ándale!

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.

MATH

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.

Cases

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 bit.ly as a URL shortener, you can put an entire problem solution as a URL: http://bit.ly/distxrcis.

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.