The Mathematics of Love

With Valentine’s Day around the corner, the whole of humanity is looking for answers on how to be truly happy in love, right?  And, certainly everyone is thinking of using the most powerful tool ever devised for answering life’s most difficult questions:

Mathematics, of course

Thanks to Hannah Fry’s TED talk posted today, we learn that Mathematics actually has a lot to say about optimizing your chances of finding love.  I’ve always been a big fan of hers, following her on Twitter (@FryRsquared), but this was an especially interesting talk.

In honor of Valentine’s day, check out the “Mathematics of Love”


Get “Things” for Free (An Excellent To-Do list app)

2014-11-21_9-33-48Before I moved all my action items to Trello, the “Things” app was my favorite To-Do list for getting things done (‪#‎GTD‬). It’s free this week if you want to try it out. I think they have separate apps for iPhone and iPad, so if you have both you might go ahead and get it now to try out later.

Remember, if you get a free app, it’s yours for good, even if they raise the price again later. So you could get it this week, then delete, but re-install it anytime in the future for free.

Apple is giving App Store customers something to be thankful for as its offering Things as its free App of the Week.


Connect the Dots Like a Numerical Analyst

I have to say, teaching Numerical Analysis is one of the highlights of my job. Granted, my primary responsibility at Wayland is the Virtual Campus Director, and I will never teach Numerical Analysis online. Nevertheless, I LOVE it. In fact, the course banner that I use in Blackboard reinforces that fact to my students every time they log in:

Just as a for instance, I was able to get them to “solve” the age-old Connect-the-Dot problem. What is that, you ask? Well, simple: We all know, from the time we are toddlers, how to complete a Connect the Dot worksheet:

BUT, what is the mathematical solution? After all, math majors should look at the connect-the-dot worksheet and wonder, “What’s the equation of the solution?”

So today, as an introduction to using splines for interpolation, we derived the simple formulas for a piecewise linear interpolant:

Given a set of n+1 points with coordinates {(x_j, y_j)}_{j=0}^n, we can uniquely describe the piecewise linear function S(x) where S(x_i)=y_i for all i=0, 1, ldots, n, as follows:

S(x)=Big{ S_j(x),   xin[x_j,x_{j+1}]   , for j=0, 1, ldots, n-1

where S_j(x)=a_j x+b_j,

a_j = displaystyle frac{y_{j+1}-y_j}{x_{j+1}-x_j},

And b_j = y_j - a_j x_j for j=0, 1, ldots, n-1

At least, that’s the solution I told them in class today.  The truth is that’s not correct.  In fact, this will only “solve” the limited case where you always move left to right and never go back the other way.  What we really need is a parametric approach.  Given the initial data set above, we assign a parameter t in mathbb{R} to each point, say t=j for the point (x_j, y_j).  Then we have the following solution to the Connect-the-Dot problem:

Given a set of n+1 points with coordinates {(x_j, y_j)}_{j=0}^n, we can uniquely describe the piecewise linear parametric function bar{S}(t) where bar{S}(j)=(x_j,y_j) for all j=0, 1, ldots, n-1, as follows:

bar{S}(t) = Big{ biglangle S_{j,x}(t), S_{j,y}(t) bigrangle, for j=0, 1, ldots, n-1

where S_{j,x}(t)=a_{j,x} t+b_{j,x} and S_{j,y}(t)=a_{j,y} t+b_{j,y}

a_{j,x} = x_{j+1}-x_j and a_{j,y} = y_{j+1}-y_j

b_{j,x} = x_j - a_{j,x} t and b_{j,y} = y_j - a_{j,y} t for j=0, 1, ldots, n-1

That’s better, don’t you think?  From there we launched into a derivation of linear system approach to interpolation by natural cubic splines.  Then I ran out of time before finishing the derivation, which lead to the instagram post below…

That moment when class is over but you haven’t finished the proof… #mathteacherproblems

A photo posted by Scott Franklin (@splineguy) on


The Importance of Your Worldview

This week, I have the privilege and honor to lead the discussion in the Faith and Science course at Wayland.  The topic of discussion will be the importance of your worldview.  We start with a discussion on the 19th century masterpiece, “Flatland: A Romance of Many Dimensions” by Edwin A. Abbot.

Then we’ll discuss a couple of readings:

Are Scientists Biased by Their Worldview

The Importance of Worldview

Slides for guided discussion:

9 Essential Settings for the Teacher’s iPad

When using your iPad to teach, particularly in the one-iPad classroom, you can run into a few frustrations with the technology. In spite of all the exciting new features you bring to the classroom with the iPad, there are also some headaches that come along with it.

Here are some of the settings that our teachers have discovered and implemented to help to alleviate many of those frustrations.

1. Use Side Switch to Lock Rotation

Tap the Settings icon on your home screen and go to the General tab. You can configure the side switch to either “Lock Rotation” or “Mute.” It is recommended that you change the default from “Mute” to “Lock Rotation.” This way you can switch from portrait to landscape mode when you move from one app to another, but while in the app, you can quickly lock the orientation.

Continue reading 9 Essential Settings for the Teacher’s iPad

18 Basic Tips and Tricks for the Teacher’s iPad

The best thing you can do to familiarize yourself with the iPad is just to play with it.  You’ve got to be willing to explore by tapping, pinching, and swiping away.  One of the core design principles at Apple has been that their systems should be intuitive.  As you learn some of the basic interactions, you simply need to explore these common icons and gestures in different apps. Below are some the most basic tips and tricks that help teachers (and most general users, as well) to navigate their iPad.

1. Launching and closing apps

When you are on the Home Screen, you can simply tap on an app’s icon to launch the app on the device.  Once an app is launched, all you need to do to exit the app is click the home button at the bottom of your device: Apps don’t completely close down when you move to the home screen.  They also don’t “run” in the background unless you have Background App Refresh enabled for the app.  An app will save its state and you can return to the app later. To completely close an app, double tap the home button and then swipe across to find the app you want to close.  To close the app, swipe the app up and away.


Continue reading 18 Basic Tips and Tricks for the Teacher’s iPad