# Category Archives: Weekly features

April 11, 2014, 9:30 am

Spring, rising from the ashes. Or the mulch.

It was a busy week here at Casting Out Nines, with this post generating more comments than any other one I’ve ever had – and quite a lot of heat as well in the comment section. Let’s take a break from all that with some interesting stuff from around the interwebs:

I’ve been a big fan of the programming language Scratch – designed for kids to use – for a long time, and Mark Guzdial reports on the new ScratchJr project that aims to bring coding to kids of even younger ages. I’d be thrilled to have this publicly available by summertime so I can foist it upon my 10- and 8-year olds.

Lifehacker describes how being humble, kind, and calm will make your life easier. This is always good advice, especially for people in academia and doubly so this time of the …

April 4, 2014, 10:00 am

From around the interwebs this week:

Wired Campus reports on how taking notes by hand benefits recall. I’ve believed in this for years. One thing I’d have liked the article to mention is that “writing longhand” and using a computer are not mutually exclusive – I take almost all my notes from meetings, reading, and talks longhand on my iPad using Notability and a Boxwave stylus.

Software developer Jason Lewis has a well-thought-out post on computational literacy and learning math. From the article: “If we want kids to code, we must not only allow them to apply that knowledge whenever and wherever the opportunity arises, we must also train teachers to always and everywhere encourage the application of computational thinking (as well as programming) to whatever problem set presents itself as a viable candidate.” In other words, teach the teachers first.

A while back I…

March 21, 2014, 11:44 am

This is not what Spring looks like in Michigan at the moment.

Welcome to your weekly small-shiny-objects-from-the-web post:

Is banning PowerPoint slides the key to having meetings that are more informative, interactive, and community-driven? Well, it couldn’t hurt. I’d heard about US military command groups banning PowerPoint in meetings but the similar ban from physicists is new to me.

Some states are beginning to allow computer science classes to count toward the foreign language requirements for high school students. You might think that’s a boon for CS educators, but this post explains why maybe it isn’t such a great idea.

Good article at Wired on why punishing students for using electronic gadgets will only make things worse for them in the future. Better to design instruction that engages the…

March 7, 2014, 9:00 am

Here’s a picture of some tacos, for no real reason other than it might make you happy.

It’s been a busy week of blogging around here with the posts about the flipped calculus class. I’m taking a break from that series until next week, but in the meantime here are more items to read and discuss.

• If you read one thing from this list, read this article in which Evan Selinger and Andrew Phelps argue that colleges need to start acting like startup or face obsolescence. It’s a perplexing read. On the one hand, their thought that innovation is the correct lens through which to consider higher ed is compelling. On the other hand, I think their three pillars of startup-hood – density, shared resources, and nurturing communities – don’t always apply to successful colleges, and the focus on these has the…

February 28, 2014, 11:15 am

This week’s small shiny objects from around the interwebs:

John Cook has an interesting short article on the log semiring. Suitable for nontrivial examples in your next ring theory class.

Here’s a terrific short video that explains the Diffie-Hellman key exchange in terms of color mixing.

Here’s a longer video of John Baez talking about network theory, which we first mentioned a few weeks ago.

And here’s a video by Stephen Wolfram giving an introduction to the Wolfram Language. I’m curious to try this out.

Just in time for the NFL Draft season (OK, it’s still six weeks away, but whatever) here’s an interesting article on how the Dallas Cowboys used statistics and computers to revolutionize their approach to tracking and choosing players. Consider it an early prototype of Big Data.

February 14, 2014, 2:00 pm

Look! A small shiny object.

From the week that was, here is your random list of shiny objects from around the web.

January 31, 2014, 2:00 pm

### Technology

• I’m enrolled in Cathy Davidson’s higher education MOOC right now and she mentioned lynda.com in one of the lectures. It’s a massive repository of instructional videos on all kinds of technical subjects from programming languages to how to arrange the lighting for your video shoot. Costs money to subscribe but you can get some videos free.
• Evernote (one of my can’t-live-without apps) has made some nice updates to the iOS version. Android next please?

### Education

January 24, 2014, 8:03 am

Here are some items from around the web for your weekend enjoyment.

## Math

• Here’s a great post on Medium by Nik Custodio in which he explains Bitcoin like I’m five. I think the audience level here is rather older than five, but it’s still probably the best explanation of the problems that Bitcoin attempts to solve, and how it solves them, that I’ve seen. (I wasn’t sure whether to file this under “Math” or “Technology” because it’s a lot of both.)

## Education

• If you’ve ever been interested in standards-based grading, you won’t want to miss Kate Owens’ post An Adventure in Standards-Based Calculus where she lays out why, and bits about “how”, she intends to use SBG in her Calculus 2 course this semester. Don’t miss the link to George McNulty’s calc 2 syllabus at the end, which is a great example of how to use SBG in actual practice.
• Good report…

December 12, 2011, 7:45 am

# Columnar transpositions: Looking at the initial cycle

Welcome to Math Monday! Each Monday here at Casting Out Nines, we feature a mathematics-themed article. Today’s is a new installment in an ongoing virtual seminar on columnar transposition ciphers.

Let’s return to our ongoing look at the columnar transposition cipher. In the last article, we introduced the notion of cycles. A cycle can be thought of as a cluster of points which are moved around in a circular nature by a permutation. All permutations — including the permutation implemented by a columnar transposition cipher — break down into a product of disjoint cycles, and we can determine the order of a permutation (the smallest nonnegative power of the permutation that returns it to the identity) by finding the least common multiple of the lengths of the cycles in its disjoint cycle decomposition.

November 28, 2011, 7:45 am

# Cycles, and the cycle decomposition of a permutation

Last week’s installment on columnar transposition ciphers described a formula for the underlying permutation for a CTC. If we assume that the number of columns being used divides the length of the message, we get a nice, self-contained way of determining where the characters in the message go when enciphered. Now that we have the permutation fully specified, we’ll use it to learn a little about how the CTC permutation works — in particular, we’re going to learn about cycles in permutations and try to understand the cycle structure of a CTC.

First, what’s a cycle? Let’s go back to a simpler permutation to get the basic concept. Consider the bijective function $$p$$ that maps the set $$\{0,1,2,3,4, 5\}$$ onto itself by the rule
$$p(0) = 4 \quad p(1) = 5 \quad p(2) = 0 \quad p(3) = 3 \quad p(4) = 2 \quad p(5) = 1$$
If you look carefully at the numbers here, you’ll see that some of…

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