Progress on linear algebra

It has been almost a year now since the linear algebra book is “almost finished.” I don’t have any real, legitimate excuse for this delay. The first seven chapters are now done, and have been thoroughly edited and finalized. What is taking forever is finishing the applications chapters, which I’m being super slow at. The only thing I can say in my defense is that there are A LOT of applications of linear algebra, and writing about even a small part of them takes a lot of time.

Okay, so what’s coming?

  • The applications chapter covers topics in cryptography, error correcting codes, network coding, Fourier analysis, as well as the standard topics of least-squares fitting and solving equations.
  • I’ve decided to cut the section on linear programming (the simplex method). Despite trying very hard to make the material interesting and concise, I wasn’t able to. It’s just a boring-as-hell topic, so I don’t see the point of including it in the book. The text is almost done though, so I’ll probably release it as a free PDF for students who have to do this in their class.
  • I added a new chapter on probability theory, Markov chains, and quantum mechanics. This will be optional reading, but I think I managed to fit all the important things (Dirac notation, postulates of QM, quantum gates, examples, etc.) to make a decent introduction to the subject.

The final version of the book will be around 450 pages, which is kind of chunky. Not cool, but I think it’s good to include the chapter on probability theory and QM, even though they are not “core” for a linear algebra class. What do y’all think? Should I include prob. theory and QM or cut it to make the book shorter by 60 pages (reply in the comments or by email)?

The other good news™ is my friend agreed to prepare exercises and problems for the book, which means the first edition (v1.0) will be very solid and complete. Estimated time of release is circa February 1st. Dear readers, I apologize for the massive delays. Hang in there, LA is coming!

The school of the future

It has been a long time since I last wrote something, but I haven’t been idle altogether. I’ve been planning what to do next for the books, calculating my move, so to say. It’s slowly starting to become clearer. Given my background as linux sysadmin and tutor, it only makes sense if the revolution looks to me like an open source software stack for schools. Read on to find the general strategy. Listen to this good tune if you’re missing an accompanying soundtrack; here is some more tunes in case the blog post ends up long.

I’m going to write a toolbox for every school out there to print their own textbooks and other educational material.

The best-in-class existing exercise framework is already available as open source and can be hosted on the school’s server (or virtual on AWS for $40/mo), but since we’re going to have a “school server,” wouldn’t we want to run some other stuff on there too?

I’m thinking:

  • printable exercises sheets for doing in class
  • printable problems to give as homework
  • printable exams (different version for each student)
  • print affordable textbooks (using POD service like

I’m happy for all the kids with iPods and computers at home, but not every school has the budget for computers, so let’s try to keep the costs to at most $20 per class for the week. A few good laser printers could keep the school running with students learning from top notch material, at the cost of a few thousand dollars per month. Toner and paper.

Okay, but where are you going to get the content.

There’s plenty of OER out there, but there could be more and it could be made more easily accessible.

Content framework

Here I must confess, I will be biased, because as a django person, I see the world through my own prism. A very good way for presenting structured content exists already, as free software. That’s the best place to start. Everything else on the content management side, and exporting printable PDFs I can script myself. The main content pipeline will be something like .md --> .tex --> .pdf; the softcover/polytexnic toolchain is very good at this.


The key is to make it easy for teachers to browse, use, and contribute content. The graph structure (and possible common core math categorization) will help the browsing, the .toPDF() methods will make the content immediately usable, and the only real problem remaining is the user experience that entices teachers to contribute content. That’s the biggie. But it can be done.

Software requirement specification

Given a collection of content items (paragraphs of text, entire sections of book, exercises, or problems), the system allows teachers to assemble custom “playlists” which consists of a sequence of content items with a `.toPDF` method.

No way I’m going to let them run the high schools. We’re taking over that business too now.

Aren’t big publishers better?

The market forces will prevail. What is better for a cash-strapped school, to order some crusty mainstream algebra textbook, that may or may not be standard-compliant, but sure is long and talks to students as retards, or to demand the printing of one copy of the best free book on the subject, for 1/10 of the cost.

How will you make money?

Nothing changes really. Minireference continues to sell university-level textbooks; we just make the high school material and the toolchain free. As for the potential loss of business due to high schools printing on their own instead of buying textbooks from me, I’d call that a win overall.

Books as tools for scaling knowledge

A great quote from Richard Hamming from his talk You and your research. It highlights the importance of the “information distillation” that books play.

In this day of practically infinite knowledge, we need orientation to find our way. Let me tell you what infinite knowledge is. Since from the time of Newton to now, we have come close to doubling knowledge every 17 years, more or less. And we cope with that, essentially, by specialization. In the next 340 years at that rate, there will be 20 doublings, i.e. a million, and there will be a million fields of specialty for every one field now. It isn’t going to happen. The present growth of knowledge will choke itself off until we get different tools. I believe that books which try to digest, coordinate, get rid of the duplication, get rid of the less fruitful methods and present the underlying ideas clearly of what we know now, will be the things the future generations will value.

Digital vs. print and the future of books

I’m reading an interesting paper by M. Julee Tanner that compares the cognitive aspect of digital vs. print delivery for book-length material. In summary, the printed book is not dead!

I’ve always thought the print medium (especially typeset by LaTeX) is far superior for learning and comprehension, but I figured this was my “old timer” ways (I’m 32). It seems I’m not the only one though:

Despite decades of work by computer and e-reader engineers and designers to improve the optics, display, and ease of navigation of virtual texts, readers still have a general preference for the print presentation, especially when it comes to longer, more challenging material.

The author states many good things print books have going for them, but the most interesting to me is the following quote:

[…] the greatest difference in metacognitive strategy was also found among the users of e-readers, in their reluctance to review previously read passages by virtually turning back pages. It seems that the perceived unwieldiness of screen-tapping to turn pages did negatively impact comprehension of expository texts on the e-reader platform (Margolin et al., 2013).
Since monitoring one’s understanding while reading, reviewing previously read material if necessary, underlining, and taking marginal notes are so vital to the comprehension of more challenging texts, it is important for students and educators to know how applicable these metacognitive strategies are to virtual texts.

Indeed, think about it—if you’re reading a complicated passage in a math book, wouldn’t you want to flip back and look at the equation which you saw five pages ago? In a printed book you could do that (you could in fact leave you finger on that spread and conveniently flip between the two pages). In a PDF read on the computer, it’s also somewhat passible to flip back (though a bit imprecisely), but on an eBook reader it’s not easy to do.

Learning math/physics (or other cognitively demanding material) from an eBook reader feels a bit like I’m placed in front of a slide deck: information comes, then it’s quickly taken away, leaving me in a disorganized state of mind.

Here’s the full reference: Tanner, M. J. (2014). Digital vs. print: Reading comprehension and the future of the book. SJSU School of Information Student Research Journal, 4(2).

Internet propaganda

TL;DR: The fight on the Internet is not just about True vs False, but also True vs Noise.

I’m reading this article about Internet propaganda in China, and I can’t help but wonder how much of this exists in the West. How many PR firms employ armies of paid commenters ready to intervene and vote up (or down) any content item? How many politicians employ the services of these PR firms?

I find it very interesting to dissect the tools of the System—to try to deconstruct the methods which the powers that be use to control the People. There seems to be three forces at play for any issue X. Voices in support of X, voices in opposition to X, and noise. Assuming X is something the people want, people-opposing forces (which we’ll call the System for simplicity), have at least two options to silence the X discussion:

  1. Pay shills to post opinions against X.
  2. Produce noise to drown out the X discussion altogether.

In totalitarian regimes (think Russia), official police and secret police act to suppress the supporters of X, while in “open societies” (the West) corporate media control (which is a mix of options 1. and 2. above) are used to suppress X.

It seems China’s regime is siding with the Western approach for their Internet censorship. Here’s a quote from the above article:

It’s not clear the degree to which paid comments influence the conversation the way Communist Party members hope they do. Xiaolan says the paid commenters could be adding noise to the conversation simply to drown out normal people’s desire to converse online.

The noise strategy reminds me of the “jammer towers” (заглушителни станции) that I’ve seen in Bulgaria during the communist days. The idea was to isolate the Bulgarian people from FM transmissions from neighbouring Greece and Turkey. I’m guessing they were going for FM and/or TV, because I know AM radio is more difficult to block.

Could it be that the whole education system is intentionally dysfunctional? An informed and educated citizenry would be much harder to indoctrinate and control. No. Surely this is a crazy idea to imagine science education is intentionally restricted to a small group of people, who are indoctrinated with the “you’ll get a big paycheque”-mentality in school, and forced to join the System immediately upon graduation to repay their student debt. In any case it’s worth checking. If science textbooks were made intentionally inaccessible by the system, then making more accessible science and technology textbooks will lead to more politically active citizens, armed with metis. Let’s see.

Books vs Apps

I just read (actually the computer read it to me) a Business Insider interview with Jeff Bezos in which he talks about book pricing. Specifically, the conversation seems to be about eBooks, but the conversation seems to cover books in general—as a medium.

The most important thing to observe is that books don’t just compete against books. Books compete against people reading blogs and news articles and playing video games and watching TV and going to see movies. Books are the competitive set for leisure time. It takes many hours to read a book. It’s a big commitment. If you narrow your field of view and only think about books competing against books, you make really bad decisions. What we really have to do, if we want a healthy culture of long-form reading, is to make books more accessible.

Part of that is making them less expensive. Books, in my view, are too expensive. Thirty dollars for a book is too expensive. If I’m only competing against other $30 books, then you don’t get there. If you realize that you’re really competing against Candy Crush and everything else, then you start to say, “Gosh, maybe we should really work on reducing friction on long-form reading.” –J.B.

Good point. I never thought of it this way. Books, taken down from their high-horse position as the vehicle of intellectual thought, are forced to deliver the same entertainment-per-dollar value to the consumer.

But that’s a very mechanistic and anti-intellectual way of looking at things, don’t you think? Who said books are for entertainment? Who said delivering the feeling of “information buzz,” commonly associated with news articles and feed-based apps, is the universal goal of all media?

Aren’t books valuable precisely because they are different from the torrent of superficial-level information that is the Internet. Isn’t the main point of a book to summarize and distill information (which is plentiful and free) into a high-value package that earns the reader’s attention, not for it’s entertainment value, but for its quality of insight?

If you ask me, we should optimize for value-per-page (or value-per-unit-of-attention if you prefer) not compete on price with other media. The price of a book should be proportional to the value it brings to the reader. The Internet is an amazing tool that allows anyone to access gigabytes of information on any subject in the click of a button. This abundance of information is actually a problem for readers, as they have to separate the wheat from the chaff. This is where knowledgeable authors come in, whose curation and distillation of ideas brings order to the chaos. When we buy books, we don’t buy ideas, we buy the synthesis of ideas.

In the internet era, almost all of the tools for reading have been reducing the friction of short-form reading. The internet is perfect for delivering three paragraphs to your smartphone. The Kindle is trying to reduce friction for reading a whole book. It’s working. […] We’re making books easier to get, more affordable, more accessible. You are getting more reading. Mostly things have gotten better, and we live in a world where I hope things continue to get better. Surely making reading more affordable is not going to make authors less money. Making reading more affordable is going to make authors more money. –J.B.

Hm. That’s a big step in terms of logic. Bezos’ claim is that lower prices will lead to more readers, which in turn will lead to more revenue for authors. It’s a question of two rates: if the authors’ margins decrease at a rate higher than the rate at which their readership increases, the new publishing paradigm will be a net loss for authors’ bottom line.

Overall, I will qualify the Interview as an advanced-level PR effort to dismiss this summer’s battle between Amazon and Hachette over contol of book pricing, which in turn is tied to the existence of non-amazon sales channels. Amazon’s CEO used this interview as a platform to reiterate the same talking points—that Amazon is out, fighting for better prices on behalf of readers. This is a convenient position when you’re in the business of competing on distribution through economies of scale, and your business model is based on offering the lowest price based on the distributor discount offered by manufacturers and publishers. It’s a neat business model, which attracts customers in troves. It works. Good job. But pretending amazon is doing all this on behalf of the customer is a bit intellectually dishonest. The price on amazon is 10–15% cheaper than anywhere else so that Amazon can maintain and increase its market share, and not some sort of act of robynhoodism.

Survive the exams special

I know many students are currently worried about their upcoming CALCULUS and MECHANICS exams. Are you one of them? If so, don’t worry. Chill. Forget about reading your thick textbooks–I have a better option for you! I wrote a math textbook based on 15 years of tutoring experience.


    1. Review of math basics (equations, functions, geometry)
    2. Differential calculus ($\lim$, $f'(x)$, $\max/\min$)
    3. Integral calculus ($\int f(x)dx$, $\sum_i a_i$)
    4. Mechanics ($\vec{F}=m\vec{a}$, $a(t)=x”(t)$, $\vec{p}=m\vec{v}$, $\sum E_i= \sum E_f$, $x(t)=A\sin(\omega t+\phi)$ )

All this in a tiny book you can read in a week. Available in PDF or in print. Checkout the preview and the free tutorials[2,3,4]. has a crazy special on print books this weekend. You can order the No bullshit guide to math and physics for just $19 using coupon code WQT32 (expires Dec 3rd). I’ve also decreased the price of the PDF on gumroad to match the print price.

Trust me on this one, this will be the best twenty bucks you ever spent on your science education.

Book pricing for optimal growth

I had a meeting with a business mentor last week (a McGill professor who has started dozens of companies). He helped me realize the most important thing for the company right now is growth—not margins. The success of Minireference Co. depends on how many students read the book by the end of this year, and by the end of the next. We’ll work on the margins once we have scale.

Below are some observations about book pricing for optimal growth.

Amazon technique

Since I listed the book on, all the print book sales have gone to them (mostly .com but a bit of Why would you buy the book from for \$29 when you can get it from amazon for \$25? People are not stupid, even though I link to from the main site, they all go to amazon to check if it’s available and order from there.

To be honest, I think the print quality of the books from is superior to the book produced by amazon CreateSpace and IngramSpark. I think has been in the “print on demand” business for the longest of the three companies, so they know what they’re doing. The print quality of lulu books is very uniform and crisp, unlike the CreateSpace version which had some pages in darker ink and some in lighter. The main reason why I like is because their paper is thinner, which makes the 445pp book actually look much more approachable; we’re talking about a difference of 3-4 mm in overall thickness, but the psychological effects are important.

How can I communicate this difference to my readers? Maybe something like “I recommend you purchase the book through, because of the higher print quality and thinner paper” could do. Though is this better print quality worth the \$4 extra, which is really \$10 extra when combined with the shipping. I guess I should tell my readers the facts, and let them decide for themselves.

Ingram channel

The other new channel I’ve been working on is the “serious” distribution to bookstores via Ingram. Printing through IngramSpark makes the book available through all kinds of online distributors (e.g. and also makes the book available to order from the Ingram catalog, which is how most physical bookstores order their books.

The list price is \$29, and the printing cost are \$6.7, which means there is \$22.3 of “value” to split between me, Ingram, and the bookstore. There are two options for the wholesale discount I can offer 55% wholesale discount (bookstore margin: 35%-40%) or offer 40% wholesale discount (bookstore margin: 20%–30%).

If I provide a wholesale discount of 40% (a.k.a short discount or academic discount), the wholesale price is 17.40, which leaves me with 17.40-6.7 = \$10.7 of profit per book sold.

If instead I offer 55% (industry standard, a.k.a trade discount), the wholesale price will drop to \$13.05, which leaves me with 13.05-6.7 = \$6.35 gains per book sold.

After yesterday’s conversation with my mentor, I’m switching to the 55% discount. Give everyone a cut. We’ll jack-up the prices when everyone is hooked on the knowledge buzz that learning mathematics provides 😉 .

eBook pricing

In parallel to the print book distribution, there is the question of eBook pricing. Both the print book and the eBook version have been \$29. Historically, eBook sales have been very good to me, but ever since the book has appeared on the amazons, the eBook sales have slowed to a trickle. Why would you buy a eBook for \$29 if you can get the print book for \$25?

I’m thinking of dropping the eBook price to \$19. Hopefully this will make more sense for potential customers. Surely the years of effort invested to write the best calculus book there could be is worth a twenty…

Devaluating the book

The other consideration to keep in mind in the face of these price deviations from the old price of \$29 is the psychological effects of “perceived value” of the book. How could this be a good book if it’s just \$25? Mainstream university-level math and physics textbooks cost hundreds of dollars. Specifically, \$190 for precalculus, \$209 for calculus, and \$192 for physics. How can your book cost only a fraction of that and be of comparable quality? No way, I don’t believe it!

I had picked the price \$29 to be as low as possible (looking out for the student’s interest) while still making the book business profitable for me. As the price is dropping below \$29 due to discounts, the situation with the “this book looks suspiciously cheap” problem is getting worse. I might think about bringing the price up to \$39 for the 6th edition, to better communicate the value.

Take home message

There is a general lesson to learn here, which is advice I’ve heard from several successful entrepreneurs, but I never took seriously until now. Price your products for growth not profit. You might lose some money at first, but reaching a wider audience is worth much more than short term profits.