Tag Archives: mathematics

October 24, 2011, 7:30 am

Math Monday: TV Lawyers Solve NP-Complete Problem (part 2)

This is the second installment of a two-part article from guest blogger Ed Aboufadel. Thanks again, Ed, for contributing.

In Part I, we learned of an instance of the NP-complete problem subset-sum [1] that was solved by three lawyers on an episode of the USA Network show Suits [2]. The problem was to go through a set of deposits made to five banks in Liechtenstein and find a subset of deposits, where the total of the deposits was $152,375,242.18. Described as “simple mathematics” by one of the lawyers, the team solved the problem in a relatively short length of time. They couldn’t use a quick approximation algorithm for subset-sum, since they needed the sum to be exactly equal to their target amount. So, were they just lucky, smarter than the rest of us, or did they do something practically impossible?

Consider the following “back of the envelope” calculations. First,…

October 17, 2011, 7:30 am

Math Monday: TV Lawyers Solve NP-Complete Problem (part 1)

By Robert Talbert

For the next couple of weeks, Math Monday here at the blog will feature a guest blogger. Ed Aboufadel is Professor of Mathematics and chair of the Mathematics Department at Grand Valley State University, where I work. He’ll be writing a two-part series on a neat appearance of an NP-complete problem on network TV, adding yet another data point that mathematics is indeed everywhere. Thanks in advance, Ed!

On the new USA-network TV series Suits [1], Harvey Specter is a senior partner at the law firm of Pearson Hardman, and Mike Ross is his new associate. Mike never went to law school, but he combines a photographic, elephantine memory with near-genius intelligence to fake it well. Harvey is in on the deception, but none of the other partners know. During the eighth episode of the first season of Suits (broadcast August 11, 2011), Harvey and Mike, working with Louis Litt, a…

October 11, 2011, 7:30 am

Is dependence on technology the real threat?

By Robert Talbert

I came across this Seymour Papert quote over the weekend, the best part of which is below. In context, Papert is speaking about effecting real change in the content of school mathematics, and he focuses particularly on the teaching of fractions:

One theory [among educators about why we should teach fractions in school] was that manipulating fractions was actually closer to what people needed back before there were calculators. So a lot of school math was useful once upon a time, but we now have calculators and so we don’t need it. But people say that surely we don’t want to be dependent on the calculator. To which I say, Look at this thing, these eyeglasses, that make a dramatic difference to my life and the life of everybody who reads or looks at any tiny detail. Once upon a time we would have been crippled, severely handicapped. Now we’ve got these and we don’t need to go …

September 28, 2011, 4:00 am

Midweek recap, 09.28.2011

By Robert Talbert

Good stuff from the internet this past week:

John Golden (Mathhombre) shares an #edchat conversation about mathematical misconceptions of all sorts.
Maria Andersen (Teaching College Math) emphasizes a point you can’t make strongly enough: Failure is a NORMAL part of learning.
Ben Deaton (jbdeaton.com) has a great article of advice for surviving your first year of graduate school.
ProfHacker is starting a sweet-looking series of articles about using the command line interface. Talk about a lost art.
On the technical/math/crypto side, Bruce Schneier (Schneier on Security) describes three emerging cyber threats. None of them have to do with hackers squatting over a computer in their dorm rooms or parents’ basement.
Danny Caballero (Think Like a Physicist) follows up a post featured on last week’s midweek recap by announcing (somewhat reluctantly) that they’ve gone with…

September 21, 2011, 9:00 am

Midweek recap, 9.21.2011

By Robert Talbert

Interesting stuff from elsewhere on the web this week:

Danny Caballero, who does really interesting research on physics education at UC-Boulder, has just started up his own blog. Every post on it so far has been excellent, but his article “Which computational tool should we teach?” in particular is a great analysis of three major computational software tools from the standpoint of teaching physics students computational modeling.
John D. Cook examines the question, what point on the Earth’s surface is farthest from its center? Hint: The answer involves trigonometry and is not Mount Everest.
Dave Richeson looks at an interesting probability rule (of thumb).
My GVSU colleague David Coffey considers the role of remuneration in the motivation of teachers.
Profhacker introduces us to Codeacademy, a sort of Khan Academy for computer science. On a related note, my afternoon just …

September 19, 2011, 8:00 am

Math Monday: What is casting out nines?

By Robert Talbert

http://www.flickr.com/photos/artnoose/

Last week in this post, I asked for requests for math topics you’d like to read about. One person wrote in and asked:

Why don’t you enlighten us about the name “Casting Out Nines?” I learned a system in grade school with the same name –it was a way of checking multiplication and long division answers. Long before calculators.

A review please?

OK then. Casting out nines is an old-fashioned method of checking for errors in basic arithmetic problems (addition and subtraction too, not just multiplication and division). Here’s how it works, using addition as an example.

Let’s suppose I’m trying to add 32189 to 87011. I get a sum of 119200. But did I make a mistake? Do the following to check:

Take the first number, 32189, and remove — “cast out” — any 9′s…

September 15, 2011, 8:52 pm

Using clickers for peer review of proofs

By Robert Talbert

http://www.flickr.com/photos/unav/

Right now I’m teaching a course called Communicating in Mathematics, which serves two purposes. First, it’s a transitional course for students heading from the freshman calculus sequence into more theoretical upper-level math courses. We learn about logic, how to formulate and test mathematical conjectures, and we spend a lot of time learning how to write correct mathematical proofs. And therein is the second purpose: The course is also labelled as a “Supplemental Writing Skills” course at Grand Valley, which means that a large portion of the class, and of the course grade, is based on writing. (Here are the specifics.) It’s a sort of second-semester, discipline-specific composition class. (Students at GVSU have to have two of these SWS courses, each in different…

September 7, 2011, 7:30 am

Midweek recap, 9.7.2011

By Robert Talbert

From around the interwebs this past week:

John Cook shares Python code used to slice open a Menger sponge.
OxDE talks about antiparallelograms and asks some questions about tiling the plane with them.
360 asks the important questions, such as Why can’t people on Glee do math right? There’s more than one right answer to that question, I think.
Alasdair McAndrew takes a detailed look at alternatives to MATLAB, including Octave, Scilab, and Freemat. Sadly, his preferred alternative isn’t 100% OS X friendly, but that’s not his fault.
My GVSU colleague John Golden looks at different ways to annotate PDF’s using a Bamboo tablet.
On Slashdot, a report that Google is shuttering 10 of its projects. Most of these are marginal at best, with the notable exception of Google Notebooks, which does seem to get used by a nontrivial number of people.
Finally, at Mark Guzdial’s Computing…

May 26, 2011, 8:01 pm

Any questions about this video?

By Robert Talbert

As part of preparing for our impending move from Indy to Grand Rapids, my family and I have made a couple of visits to the area. These by necessity combine business with pleasure, since our three kids (ages 2, 5, and 7) don’t handle extended amounts of business well. On the last visit, we spent some time at the Grand Rapids Childrens Museum, the second floor of which is full of stuff that could occupy children — and mathematicians — for hours. This “exhibit” was, for me, one of the most evocative. Have a look:

Spinning table from Robert Talbert on Vimeo.

I asked this on Twitter a few days ago, but I’ll repost it here: In the spirit of Dan Meyer’s Any Questions? meme, what questions come to mind as you watch this? Particularly math, physics, etc. questions.

One other thing — just after I wrapped up the video on this, someone put one of the little discs rolling on the turntable…

May 10, 2011, 7:42 am

Understanding "understanding"

By Robert Talbert

This past Saturday, I was grading a batch of tests that weren’t looking so great at the time, and I tweeted:

I do ask these two questions a lot in my classes, and despite what I tweeted, I will probably continue to do so. Sometimes when I do this, I get questions, and sometimes only silence. When it’s silence, I am often skeptical, but I am willing to let students have their end of the responsibility of seeking help when they need it and handling the consequences if they don’t.

But in many cases, such as with this particular test, the absence of questions leads to unresolved issues with learning, which compound themselves when a new topic is connected to the old one, compounded further when the next topic is reached, and so on. Unresolved questions are like an invasive species entering an ecosystem. Pretty soon, it becomes impossible even to ask or answer questions about the material…