There seem to be two pieces of technology that all mathematicians and other technical professionals use, regardless of how technophobic they might be: email, and . There are ways to typeset mathematical expressions out there that have a more shallow learning curve, but when it comes to flexibility, extendability, and just the sheer aesthetic quality of the result, has no rival. Plus, it’s free and runs on every computing platform in existence. It even runs on WordPress.com blogs (as you can see here) and just made its entry into Google Documents in miniature form as Google Docs’ equation editor. is not going anywhere anytime soon, and in fact it seems to be showing up in more and more places as the typesetting system of choice.

But gets a bad rap as too complicated for normal people to use. It seems to be something people learn only in graduate school, with few undergraduates — and even fewer high school students — ever seeing it, much less using it. There is a grain of truth there; is not a WYSIWYG word processor, and the near-programming aspect of using can overwhelm users used to pointing-and-clicking for everything.

But I think that the benefits of using outweigh the costs, and undergraduates and high school students can, and ought to, learn how to use as fluently as they use a word processor for other courses. A couple of years ago, I put together a series of twelve screencasts for use in our sophomore “transition-to-proof” class on learning . I put these screencasts online, but mainly they were only advertised to my students and colleagues. Now, however, I’d like to throw these out there for everyone to use.

All twelve of these are done on a Windows system running MiKTeX and the free IDE known as TeXNicCenter. This provides students with as close to a point/click interface to as you could expect to get. Within that context, there are two basic intro videos:

- LaTeX Basics, part 1 (6:39), and
- LaTeX Basics, part 2 (11:53).

These two videos are enough to learn how works and will allow you to make a simple file with uncomplicated math and text in it. The remaining 10 videos follow from these two. Some are prerequisites for the others — and those prereqs are stated explicitly at the beginning of any video that has them — but if you watch them in the following order there will be no dependency problems:

- Superscripts, subscripts, Greek, and special functions
- Roots, fractions, and $\displaystyle$
- Delimiters
- Tables and equation arrays
- Lists
- Text formatting
- Document formatting
- Packages and macros
- Errors and debugging
- Maple and LaTeX

Some of these are pretty long, but all totalled (including the two “basics” videos) this is less than two hours of viewing.

When I’ve used these in class, I give students some printed instructions on how to download and configure MiKTeX and TeXNicCenter, and then I have them watch these videos out of class. They are instructed to work along with the videos. I give them about a week to do so. Within that week, if there’s a problem set or something else in the class that could be done with , I’ll offer extra credit to students to do so, to incentivize their learning the system. After the end of that week, I will insist that all major assignments have to be done in , or else the assignment gets a grade of “0”.

Students have sometimes struggled to get up the learning curve, but if they’re allowed and encouraged to help each other, everyone eventually gets to the point where they are quite fluent writing up homework and so on. Students have even elected to use on assignments in other courses, even non-math courses.

I’m going to use these videos in linear algebra this semester (our transition-to-proof course is now defunct) and I’ll be making up a new screencast on MATLAB and . Later, probably during the summer, I’ve been thinking about redoing the entire video series; I now have better screencasting tools than I used to have, and I’d like to keep all the videos under 10 minutes so they can go on YouTube.

So feel free to use these (attributing authorship to me is appreciated but not required), and if you have suggestions or comments, please email them or leave them below.

Thanks for the great blog about LaTeX resources. I don’t teach math but I have designed LaTeX lessons in the past for my college level Linux students who have found the language to be very interesting.

I like to tell my students that this was the original markup language way before HTML was ever invented. Also, that knowing all about it might be their ticket to Geekdom.:-)

I don’t know if you’ve used this before with your students, but Kile is a great IDE for for Linux. That might be the one piece of Linux software that I really miss and wish that there were some OS X equivalent to it. (I think it’s possible to run Kile in OS X with a great deal of hacking.) All the stuff I did in the videos with TeXNicCenter on Windows could easily be substituted by Kile on Linux.

This really rocks! Thanks, Robert. Your reference to the defunct transition to proofs course does make me digress into that subject but I don’t know if you have a past thread on that so I will just broach it here, and please redirect me if so. I have never taken a proof-based course but would like to ask the question about the creativity element. If undergraduate proofs can be compiled via some algorithmic means that can be learned through repetition then I don’t see a need to fear them. But if coming up with a proof, as on an exam, involving things never before seen (for me) and that would require creativity (cleverness, genius, the math gene, etc.) then I am very justified in fearing for my very academic life. It is not at all clear to me as to what is acceptable as a proof – certain deductive steps involving axioms or previously established theorems, definitions, etc. that can be laid out as one learns in high school geometry. But all too often as I go through steps in proofs, stuff appears to be pulled out of the air as sheer serendipidy or trial and error, and now that can be learned algorithmically and incorporated into one’s proof techniques tool bag for future application perhaps. I still do not think that this can be successfully pursued by typical people, rather that one must have “the knack” of which I am most jealous and lacking. However, if it can be learned, at least enough to get through abtract algebra, analysis, and advanced calculus then maybe I will attempt it. Advice?

There is a fine line, with proofs, between the algorithmic and the creative. There are certain well-defined methods for setting up certain kinds of proofs; for example you can prove an implication by assuming the hypothesis and working to the conclusion, or try to prove the contrapositive, or try to prove by contradiction. But once the framework is established there is a certain sense of being on your own. I do think you can learn this sort of creativity, just as regular kids in high school take jazz band and learn how to improvise. I have some philosophy on that, but I think it basically boils down to (1) reading a lot of people’s proofs and seeing how they do things, (2) trying concrete examples of the thing you’re trying to prove and then try to construct a proof that captures the essence of the concrete solutions, and (3) develop a high tolerance for dead ends, because those happen a lot — much more often than the finished product in a textbook would let on.

This goes into the incubator file for more blog posts!

Also, to clarify, we don’t teach that course any longer because we decided students needed to learn proofs in several different settings versus one class. So we split the content up across Discrete Mathematics (where there’s a lot of induction proofs and so on) and Linear Algebra (where there’s a lot of proofs of equivalences and existence/uniqueness) for the “training phase” and then really hitting proofs hard in the senior-level Algebra, Analysis, and Geometry courses.

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Thanks for the amazing resource! Your video tutorials are really informative, short and to the point.

One notable omission is citations and references in Latex. I hope you will find time to do a tutorial on that too!