Why are for example infinitesimal methods not “rigorous”? Merely answering “because they are not careful” obviously accomplishes nothing. But then of course they would be obligated to prove that the two definitions are synonymous, which they never seem to realise.įor instance, people generally assume that “rigour” means something along the lines of “very careful reasoning.” This certainly takes care of (2) very well, but it completely fails (1). I do, however, know of plenty of definitions satisfying one or the other, which leads me to suspect that people rely one one definition for the one purpose and another definition for the other. I do not know of any definition of “rigour” satisfying both of these conditions. Since no one ever argues for this, it must apparently be evident already from the definition why this is so. It is always taken for granted as a virtual truism that a “rigorous” proof is better than a “non-rigorous” one. It must make it clear why being “rigorous” is desirable. Whether something is “rigorous” or not is supposed to be an objective, straightforward question, rather like telling whether a shirt is red or blue.Ģ. It must entail a clear-cut way of telling “rigorous” from “non-rigorous” methods. Judging by the way people use the term, the definition of “rigorous,” what ever it is, must, it seems, fulfil two key conditions:ġ. And I very much doubt that all those zealous advocates of “rigorous” mathematics do either. All rights reserved.Some people would insist that the kinds of proofs I give in my calculus textbook are “not rigorous.” What does this even mean? They are not what exactly? What is the definition of “rigorous”? I do not know any credible definition of this term. The Aperiodical © 2023 Peter Rowlett, Katie Steckles and Christian Lawson-Perfect. I also like the Hoffman text, which isn’t mentioned at the AIM site. If done as an ebook, it could also include links to many fabulous ideas in the blogs I follow.Ĭrowell may do enough of what I wanted (better than I could have, perhaps) that I can forget this thought, and go back to writing poetry in my spare time. I have two reasons: none of the textbooks are in the order I want, and none gave enough historical connection. I am, perhaps foolishly, also thinking about writing a(n open source) calculus textbook. I think it would make a great way for them to understand calculus better. It’s very readable, and his approach, both the infinitesimal, with discrete examples, and the historical connections, is very different from what they’ve seen so far. I think I’ll share the Crowell with my Calc I on their last day of class tomorrow. Tags: Benjamin Crowell, calculus, github, Matt Boelkins, open textbook, Open Textbook Initiative, open-source, Oppikirjamaraton, Project Gutenberg, textbook, Wikibooks About the authorĢ Responses to “Help a dude write an open-source calculus textbook (or use one of the many great ones already available)” There’s also, of course, the Wikibooks project’s maths section, and Project Gutenberg’s fantastic collection of lovingly reset out-of-copyright maths textbooks, mentioned here way back in April. The American Institute of Mathematics has an Open Textbook Initiative which maintains a list of approved texts, and Rob Beezer keeps his own list of material at the site for his (reputedly very good) First Course in Linear Algebra. There’s actually a lot of work being done to create and collate open course material for maths. Finally, there’s the Oppikirjamaraton, which produced a Finnish high school maths textbook in a weekend. Benjamin Crowell’s Calculus is also on GitHub and looks a lot more like a commercial textbook than other open textbooks, which tend not to elaborate on the default LaTeX style. Matt’s doing things in a more rigorous manner – his textbook is currently available on request, and will only be more easily available once it’s been tested. Matt Boelkins has been quietly plugging away at his Open Calculus for about a year. This is by no means the first open source calculus textbook, or even the first one called Open Calculus. It looks like a hobby project more than something serious. All the LaTeX source code is available in a repository at GitHub, so anyone with a working knowledge of version control can clone it and start adding material. He’s only a few pages in so far, so there’s plenty to do. He’s writing an open source calculus text, based at, which is aimed at students in their first semester of study. Posted Decemin NewsĪ chap called Dixon Crews has posted to reddit’s maths section asking for help with a writing project. You're reading: News Help a dude write an open-source calculus textbook (or use one of the many great ones already available)īy Christian Lawson-Perfect. Help a dude write an open-source calculus textbook (or use one of the many great ones already available) | The Aperiodical The Aperiodical
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