College Math Teaching

December 16, 2015

And I deducted points for a “Merry Christmas” math joke

Filed under: pedagogy, recreational mathematics — Tags: , — collegemathteaching @ 11:12 pm

From a student’s final exam in my “Life Contingencies” class (and no, I have no actuarial mathematics training…more on that later)

The student completely ignored the domain considerations for the log function and therefore lost points.

OK, not really. But it makes a better meme to say that.

October 3, 2014

There are semesters and classes like this

Filed under: editorial — Tags: , — collegemathteaching @ 1:46 pm

This semester: I am ok with the classes that I have to teach. No, my students aren’t perfect, but neither am I.

This semester is what I signed up for when I took the job here.

But there ARE semesters when one ends up with…well…a class full of people who have already failed once and have a low probability of success and…

it is a bit like this:

August 26, 2014

How some mathematical definitions are made

I love what Brad Osgood says at 47:37.

The context: one is showing that the Fourier transform of the convolution of two functions is the product of the Fourier transforms (very similar to what happens in the Laplace transform); that is $\mathcal{F}(f*g) = F(s)G(s)$ where $f*g = \int^{\infty}_{-\infty} f(x-t)g(t) dt$

August 6, 2014

Where “j” comes from

I laughed at what was said from 30:30 to 31:05 or so:

If you are wondering why your engineering students want to use $j = \sqrt{-1}$ is is because, in electrical engineering, $i$ usually stands for “current”.

Though many of you know this, this lesson also gives an excellent reason to use the complex form of the Fourier series; e. g. if $f$ is piece wise smooth and has period 1, write $f(x) = \Sigma^{k = \infty}_{k=-\infty}c_k e^{i 2k\pi x}$ (usual abuse of the equals sign) rather than writing it out in sines and cosines. of course, $\overline{c_{-k}} = c_k$ if $f$ is real valued.

How is this easier? Well, when you give a demonstration as to what the coefficients have to be (assuming that the series exists to begin with, the orthogonality condition is very easy to deal with. Calculate: $c_m= \int^1_0 e^{i 2k\pi t}e^{i 2m\pi x} dx$ for when $k \ne m$. There is nothing to it; easy integral. Of course, one has to demonstrate the validity of $e^{ix} = cos(x) + isin(x)$ and show that the usual differentiation rules work ahead of time, but you need to do that only once.

July 30, 2014

Differential equations mentioned in National Review

Filed under: differential equations, media — Tags: , — collegemathteaching @ 10:29 pm

[…]One part insecure hipsterism, one part unwarranted condescension, the two defining characteristics of self-professed nerds are (a) the belief that one can discover all of the secrets of human experience through differential equations and (b) the unlovely tendency to presume themselves to be smarter than everybody else in the world. Prominent examples include […]

(emphasis mine).

Oh noes! I love differential equations! 🙂

Yeah, I am just having fun with the quote; I couldn’t resist mentioning an article in the popular press that mentions differential equations. I am not sure that I’ll teach the chapter on “all the secrets of human experience” in my upcoming differential equations class though.

July 27, 2014

This is SO me during summer break…

Filed under: academia, editorial — Tags: , , — collegemathteaching @ 10:14 pm

(click for larger)

It is a minor miracle that I publish at all during the “social media” era. 🙂

March 5, 2014

Before they get to college…

Filed under: editorial — Tags: , , — collegemathteaching @ 4:16 pm

March 2, 2014

Ironic….

Filed under: editorial — Tags: , — collegemathteaching @ 6:01 pm

This is a whine so be forewarned:

Today and tomorrow, I have some “recruitment” duties. Today, I’ll make some calls to some of the better students that have been admitted to our mathematics program. Yes, I volunteered ….to call the more promising ones. I refuse to call the “20 on the ACT ones” as these never make it as math majors, at least here (we have the data).

Tomorrow: I have to work a “admitted student visit day” (meet with parents and prospective students) and to meet with a candidate for one of our two open tenure track positions.

So, I am going to spend the next couple of days trying to talk people into coming here….when, to be blunt, I’d leave if I had opportunities elsewhere!

Ok, I might not be saying this if I hadn’t have just come in from shoveling snow for the thousandth time this winter; I never wanted to live in the frigging Yukon!!! It is MARCH, for crying out loud!!!!!

Ok, to be fair, our University has done a great job keeping the parking lots, sidewalks clear this winter, and it wasn’t easy to do. I can honestly say that.

August 12, 2013

2. What is with the $\sqrt{2}$ ???
Note: I’d prefer $|\Psi> = p(|"live cat">) + (1-p)(|"dead cat">)$ where $0 \le p \le 1$