\(\LaTeX\) and Selected Topics in Mathematics

If you’re unfamiliar with  \(\LaTeX\), it’s the system I use to create the slides and tests in our courses. It’s also used to enter mathematical expressions on this site (and many others).

By request I’ll be running some tutorials in \(\LaTeX\) on Mondays after school (usually these will be held in my classroom, but for the first week it’ll be in 122). It would be useful to know if you’re writing a math-heavy extended essay (in mathematics or one of the sciences, for example), and would also be useful for your mathematical exploration.

After we’ve finished looking at  \(\LaTeX\), we can look at some additional topics in mathematics, with topics selected based on interest (these could include things that typically fall outside the scope of the IB Mathematics courses, like linear algebra, logic, set theory, abstract algebra, or analysis).

If you’re interested in getting started with  \(\LaTeX\), I recommend that you install a full version of  \(\LaTeX\) on your computer—I’ve added instructions for installation here.

What is NACLO?

NACLO is the North American Computational Linguistics Olympiad, and this organization runs an annual contest that offers an opportunity for you to challenge your logical and critical thinking skills, and no particular knowledge of linguistics (or a second language) is required. A sample of the sorts of questions you might see can be found here. Try them, they’re fun!

This year the Canadian Linguistics Organization (OLCLO) will become an independent organization, and will be running the contest on January 25th.

If you’re interested in participating, or learning more about the contest, talk to Irene, Henry, or Yuheng (members of the Linguistics Club) for more information.

Why Study Numbers?

Here’s a link to a recent article about mathematics research. Why do we need to know about prime numbers? Do you know of any important current applications of prime numbers? How would you feel knowing that you were working on solving a problem that may well have no application in your lifetime?

Feel free to share your thoughts below!

Is Calculus Worth It?

Recently there has been some debate in the media (particularly in the US) concerning the merits of learning what could be called higher mathematics (algebra, calculus, etc.) in school.

One book that suggests otherwise—The Math Myth by Andrew Hacker—has provoked an interesting debate. Here are two discussions of that book, one critical and the other in defence of the book’s claims.

What do you think?

Fractals and GeoGebra

Have you downloaded GeoGebra yet? You can download the desktop version from GeoGebra.org, and you can also find versions for your phone or tablet. There’s also a version that runs in a web browser.

One of the nice features of GeoGebra is that you can create an account with GeoGebra, and then that will allow you to access saved files on any of your devices.

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For example, I can create files on my laptop, save them, and then open those files on my iPad.

Once you’ve got GeoGebra installed, check out this file which creates a fractal. Fractal patterns are generated by analysing  sequences of complex numbers. Year 12 students will hear more about this soon!

Mathematics in Action

One relatively recent branch of mathematics that you may encounter at university is called graph theory. This branch of mathematics has nothing to do with bar graphs, pie charts, etc., but is instead concerned with the study of graphical networks (graphs), which look like “connect-the-dots” puzzles—the dots are called vertices, and the lines connecting them are called edges.

One pioneer in the field of graph theory is Bill Tutte, and you can read an article about him and his role in the Second World War here.

GeoGebra 5 Released (3D!)

If you’ve got a desktop or laptop Mac, GeoGebra 5 is now available in the Mac App Store. (A Windows version should be available soon too).

GeoGebra 5 adds 3D graphing capabilities. Earlier in the course we had looked at a question that had a geometric interpretation. Have a look at the new version of GeoGebra and see if you can produce a visual representation of the problem we had solved.