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Over the accomplished four years I’ve been autograph a book, A Programmer’s Introduction to Mathematics. It teaches accession with programming ability and acquaintance how to appoint with mathematics. I can accomplish this ambition abundantly because of the absolute overlap in the agreeable and means of cerebration amid algebraic and programming. Despite that, there is no bland arch from one apple to the other—a arch that explains the alien genitalia and focuses on the important concepts, while leveraging programming to authenticate applications.



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Until now. If you’re a programmer who wants to absolutely grok math, this book is for you.

In this commodity I’ll explain how I wrote and self-published the book.

Having accounting abstruse blog accessories for eight years, the autograph action acquainted natural. I wrote about a third of the book aural a few months afterwards starting, and I was 100% blessed with the content—though not the style, cf. “Editing.”



I could accept kept writing, but I knew I had to constrain myself to article that could fit in a reasonable-sized book. I aimed for 300 pages (final book is about 375 pages of content), but by the time I accomplished that I bare to cut some content, I had already accounting about 100 pages.

This aboriginal 100 pages covered the three capacity “Polynomials,” “Sets,” and “Graphs.” I capital capacity on calculus, beeline algebra, optimization, probability, accumulation theory, circuitous numbers, and cogwheel equations. But polynomials, sets, and graphs are the easiest capacity content-wise. These added capacity would be necessarily longer. I capital to accumulate anniversary affiliate to ~50 pages. Including all the capacity would beforehand the book aloft 500 pages. I additionally didn’t appetite it to be too close (I could charge beeline algebra into 50 pages, if I leave out the account that absolutely makes my book account reading; spiral that!).

This action of acid out absolute chapters, and whittling anniversary actual affiliate to its amount while still accouterment advantageous high-level insights, accepted to be the best arduous allotment of writing.

This resulted in audacious omissions. The book has a affiliate on calculus, but omits integration. Instead, the calculus affiliate focuses primarily on derivatives and Taylor series. This fits abundantly with my claimed experience — Taylor alternation are added applicative to algebraic (and the affectionate of algebraic that shows up in programming) than accretion bizarre integrals. Taylor alternation additionally had use in afterwards capacity for optimization, big-O notation, and physics.

Cutting affiliation was a advised choice. The accepted appearance of approximation is what I appetite the clairvoyant to internalize, and already that’s done acquirements why affiliation makes faculty is abundant easier. I acquainted this way about best capacity I omitted. Already you accept a able compassionate of sets and the basal analogue about combinatorics, the boilerplate book on detached anticipation is added digestible. Perhaps that is ambitious thinking, but I had to accomplish compromises about or I’d never accomplishment the book.

Instead of aggravating to charge every accountable in the book, or assumption the best topics, I chose capacity that accumulate capital abilities and patterns, which I could additionally authenticate with code. Then, with abounding contest to go out and analyze algebraic aloft the book, the clairvoyant will body the cerebral abilities to apprentice whatever algebraic affair they desire.

I had to do some added analysis for the book. While graphs and eigenvalues are readily in my brain, added capacity I had abstruse and continued forgotten. Abstract geometry was one (specifically how to compute in the abstract plane), I had to accredit to a few physics books about the archetypal way they present algebraic models for waves, and I accept I did accretion a newer and added complete compassionate of the amount definitions of multivariable calculus.

As I echo in the book, every time you re-learn a subject, you accretion new and advantageous insights.

The absolute book was typeset in LaTeX.

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I was able to jump into the autograph afterwards cerebration too abundant about formatting because I started with a copy/pasted book arrangement from Overleaf. I concluded up alteration that arrangement absolutely a bit (for some reason, it alloyed serif and sans-serif text?), mostly simplifying it, configuring cipher samples, exercise lists (using the exercise package), and assumption environments. If you ask me later, I will appropriately upload these structural TeX files so they can be reused, but be acquainted I’m not a TeX expert, so it’s apparently bigger to alpha from a template.

I stored all my files on Dropbox. In 2014, that fabricated faculty for me, as I was aloof starting to use git in earnest. If I were to do it afresh today, I’d do it in git on principle, but there were no aloft drawbacks to autumn on Dropbox.

Each affiliate is in a altered file, and no TeX book is best than about 3k lines. At 80 chars per line, the absolute book is about absolutely 20k curve (including all TeX annotations in the affiliate files, like basis markers and figures).

I wrote the book in vim, and acclimated latexmk to automate accumulation (more details).

At the end of the book, I accomplished I capital an index, and I went through the absolute book aloof hunting for places to put basis markers. LaTeX will body an basis for you automatically, but you accept to acquaint it absolutely what area to index, and what chat refers to that location. This formed out absolutely accurately for some things; for example, I indexed the area area I ascertain anniversary bit of new notation. It was additionally a slog.

Finally, at the actual end I did accession canyon over the book application chktex with some slight agreement to acquaint it to avoid cipher listings, texttt, etc. I abstruse a few new things about TeX aback accomplishing this, but it apparently wouldn’t accept dead me to skip that step.

The awning art is an aboriginal 1900’s painting by Piet Mondrian. I did the awning alignment and blueprint application Sketch. One discharge is that Sketch doesn’t consign pdfs in a way that you can accept a resolution (it acclimated 72ppi by default), so I had to use a altered apparatus (ImageMagick catechumen CLI) to acclimatize the resolution.

During writing, I apprehend anniversary affiliate abstract almost three times. Afterwards autograph the accomplished book, I apprehend it awning to awning twice.

I fabricated abounding awkward mistakes, and I anchored the ones I found, but I bet there are still mistakes in the book. If you acquisition any, abide an absurdity at pimbook.org.

During aboriginal edits I rewrote ample portions of anniversary chapter. I struggled to accomplish the appropriate the clip and body for the aboriginal few chapters. I capital the book to accept a ramp. The beforehand capacity should be attainable to anyone without—as I put it agilely insensitively—a anxiety of fractions. The ambition of those capacity is to acquaint notation, to wean readers assimilate cultural expectations like autograph bottomward examples, to lay out basal definitions and affidavit techniques, and to get accomplished that assured allotment of account algebraic area your eyes coat over attractive at a formula.

In accession to proofing the book myself, I beatific it out to basically anyone who would ask for it via commitment list. I trolled Hacker News posts area programmers griped about algebraic and slipped in an advertisement, and abounding of them contacted me via email and some provided advantageous feedback. I additionally gave aboriginal asperous drafts to any of my accompany who capital to booty a look, and abounding provided acceptable feedback.

However, one audacious blank was a thorough, paid abstruse analysis of the algebraic and programs. I struggled to acquisition accession who would accomplish to reviewing added than one chapter. I anticipate in allotment it was because accompany and colleagues didn’t appetite to alpha a business accord and be on the angle for a accord or article (I would never end a accord over this!). Finally, I got in blow with an old acquaintance from my time in the Budapest Semesters in Mathematics who agreed to analysis two capacity that I was decidedly anxious about. If I did it again, I’d assignment harder to acquisition assorted abstruse reviewers and get bigger advantage in that regard.

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A few canicule afterwards publication, it was already bright that I should accept spent added time editing. I had somehow skipped my final spell analysis on the Sets chapter, and an aboriginal clairvoyant submitted a cardinal of typo corrections. Rats.

But about a ages afore my ultimate advertisement date, I was aloof beat by all the editing. I acquainted that I was ultimately OK publishing it with some accessory imperfections, and that I was appreciative of it in its accepted state. And that was how I absitively I was done editing.

Over the years I formed on the book, I had discussed a book accord with a few publishers, including O’Reilly. What I took abroad from those conversations was that the added assignment of alive with a publisher, and the added deadlines, wasn’t account the benefit.

The action was article like “$5k beforehand paid now, again 10–15% royalties on sales afterwards those royalties pay aback the $5k advance.” What I’d get in acknowledgment was a archetype editor, the brand, the press and administration channels, and the advertising.

There were a few catches. Best non-academic publishers won’t let the columnist abode in LaTeX (and for algebraic book there is artlessly no added way), so I was told assorted times I’d accept to catechumen my absolute 150 folio abstract into Chat or OpenOffice format.

If that abandoned wasn’t a accord breaker, some publishers told me that I was on my own for award abstruse reviewers. Couple this with my adversity affair a borderline (see “Timing”), and I acquainted the administrator would add added accent than support. I additionally knew in the aback of my arch that they’d force me to change the appearance of my book in a cardinal of ways, and that added some uncertainty.

I had congenital up an admirers from my blog, with a commitment account of 1,000 bodies (closer to 2,000 by publication), so I acquainted I had a cast and appropriate distribution. I was assured I could typeset the book professionally enough. The alteration wouldn’t be perfect, but I could alive with that.

Most importantly, I knew about on-demand publishers like CreateSpace, aback (disclaimer) I had formed at CreateSpace allotment time as an undergraduate. CreateSpace (owned by Amazon) allows you to upload a book autogenous as a pdf and a cover, and “publish” instantly. Again whenever accession orders the book on Amazon, they book it and abode it that day. That covers distribution. I can assurance up for Google Ads and agenda promotional talks and interviews. I can’t print, store, and abode books to customers, abounding stop. So CreateSpace was capital in my choice.

CreateSpace additionally gives abundant bigger royalties, about 40% of the account amount for a paperback. Self-publishing additionally gave me the adaptability of allotment a area to advertise the ebook. A acquaintance of abundance appear a book application Gumroad, and they seemed appealing good, accouterment about 95% royalties on sales. The ebook was artlessly a pdf download.

Along with the book I had associated programs, some of which were actual long, with the important $.25 assuming up in the book itself. So I bare a website and a GitHub athenaeum to acquiesce readers to see the abounding code.

I fabricated a simple website in Hugo, which was accessible and pleasant. Although, best of the assignment was in addition out how to accomplish a one-page site, admitting best tutorials and templates are for blogs.

The book cipher was accounting in Python 3.x, and artlessly it has a abounding analysis apartment with Travis CI and Coveralls active adjoin the cipher athenaeum to ensure it stays healthy. I accept already accustomed one cull appeal for a adaptation abhorrence I overlooked.

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I wrote the aboriginal capacity at a time aback I had been competent in Python, but I hadn’t acclimated it professionally. By the time I accomplished the aboriginal draft, I absitively I should go aback and carbon all the aboriginal Python cipher so it accommodated to bigger engineering practices docstrings, added modular organization, connected analysis framework, etc. I would accept admired to use added avant-garde Python appearance like dataclasses and blazon hints, but I acquainted they were too new and ability accept befuddled off some readers who are either acclimated to Python 2 or new to Python entirely. Blazon hints in accurate add a lot of noise.

I additionally wrote an alternate decision in d3 for the eigenvalues chapter, which is hosted on the book’s website.

I formed on this book for four years. During that time, I accomplished a PhD thesis, got married, confused beyond the US, and switched jobs twice.

Periods of time during which I absolutely absent steam. I got bored, or hit a bank aggravating to adjudge what capacity to awning or what applications to use. I went out and fabricated new friends, best up new hobbies like bedrock aggressive and ability cocktails, played video games, went aback to blogging, and formed on accidental ancillary projects.

I like to acquaint myself I could accept accomplished the book in a year if I formed on it abounding time. But to be honest, I anticipate the book angry out bigger with the wait. I abode bigger software now, and I accept a stronger compassionate of the industry aback I’ve been out of alum school. And my autograph appearance always improves.

I listed the book at $35 for the album and $20 for the ebook. (i.e., $20 or pay what you appetite aloft that) The royalties formed out to about $15-$18 per sale. I originally anticipation I should account the book for cheaper, but I undersell myself and so I looked about at what added books were affairs for, absurd to myself what I anticipation was a fair price, and added $10.

Initial sales accept been great. I set a baseline for myself that if I couldn’t advertise a thousand copies of the book, again I would accede it an base failure. At the time of this autograph I’ve awash added than 2,500 copies, with about 60% of that actuality paperback, and the majority of the sales advancing from the US. Added importantly, antecedent accession has been heartwarmingly positive. I can’t delay to see how bodies feel afterwards they’ve apprehend the accomplished book.

Many association accept been allurement for a architecture of the ebook that is accordant with Kindles (epub or mobi format). They appetite to resize argument and such. Sadly, I don’t apperceive of any acceptable way to do this that is amount able for me and still produces a book with the affection I expect. In particular, every website I looked that that showed how to put algebraic formulas in epub/mobi produced after-effects that looked awful. And you accept to manually carbon all the account formulas so that they fit aural the accepted anatomy factor. Six inches bare margins is absolutely baby for equations! I’m abiding there is a way to architect it, but I don’t accept the time to do it myself. I’d abundant rather be autograph accession book.

Two barter accept asked for “refunds” so far accompanying to the ebook format, and I’ve gotten a scattering of odds-and-ends requests for added $.25 of chump account and accessibility. A few bodies accept asked if it will be accessible in added languages (Spanish and Chinese, so far). I’m added than blessed to abode chump apropos it if it’s not too abundant work, but a aloft adventure like a adaptation will apparently not appear for a little while.

Finally, I’m starting to adapt a alternation of talks and interviews to advance the book. I can allocution about acquirements algebraic as a software engineer, about air-conditioned algebraic being on its own, or alike about the action of self-publishing with all the nitty-gritty typesetting.

If you appetite to coordinate, amuse email meat book@jeremykun.com.

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Last Updated: December 15th, 2018 by admin
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