My calculus class hit optimization problems this week — or it might be better to say the class got hit by optimization problems. These are tough problems because of all their many moving parts, especially the fact that one of those parts is to build the model you plan to optimize. Most of my students have had calculus in high school, but too many calculus courses in high school as well as college focus almost primarily on algorithms for computation and spend little to no time with how to create a model in the first place. Classes that are so structured are doing massive harm to students in a number of ways, but that’s for another post or two.
Careful study of worked-out examples is an essential part of understanding optimization problems (though not the only part, and this alone isn’t sufficient). The textbook has a few of these. The professor can provide more, but class time really …
It’s been a little quiet on the screencasting front lately, but in the next couple of weeks my colleague teaching Calculus III will be hitting material for which I volunteered to provide some content: namely, using MATLAB to visualize some of the surfaces and solids used in multiple integration. Yesterday, I finished two of these. The first on is on polar coordinates and polar function plotting in MATLAB:
And the second one is on cylindrical coordinates and plotting two-variable functions in cylindrical coordinates:
MATLAB doesn’t provide a built-in function for plotting in cylindrical coordinates. Instead — and this is either ingenious or annoying depending on how you look at it — to plot something in cylindrical coordinates, you generate all the points you need in cylindrical coordinates and then use the pol2cart function to convert them en masse to cartesian coordinate…
So we started back to classes this past week, and getting ready has demanded much of my time and blogging capabilities. But I did get some new screencasts done. I finished the series of screencasts I was making for our calculus students to prepare for Mastery Exams, a series of short untimed quizzes over precalculus material that students have to pass with a 100% score. But then I turned around and did some more for my two sections of calculus on functions. There were three of them. The first one covers what a function is, and how we can work with them as formulas:
The second one continues with functions as graphs, tables, and verbal descriptions:
And this third one is all on domain and range:
The reason I made these was because we were doing the first section of the Stewart calculus book in one day of class. If you know this book, you realize this is impossible be…
By my count, this past week I produced and posted 22 different screencasts to YouTube! Almost all of those are short instructional videos for our calculus students taking Mastery Exams on precalculus material. But I did make two more MATLAB-oriented screencasts, like last week. These focus on creating contour plots in MATLAB.
Here’s Part 1:
And Part 2:
I found this topic really interesting and fun to screencast about. Contour plots are so useful and simple to understand — anybody who’s ever hiked or camped has probably used one, in the form of a topographical map — and it was fun to explore the eight (!) different commands that MATLAB has for producing them, each command producing a map that fits a different kind of need. There may be even more commands for contour maps that I’m missing.
I probably won’t match this week’s output next week, as I’ll be on the road in …
Sometimes when I read or hear discussions of innovation or change in teaching mathematics or other STEM disciplines, whether it’s me or somebody else doing the discussing, inevitably there’s the following response:
What do we need all that change for? After all, calculus [or whatever] hasn’t changed that much in 400 years, has it?
I’m not a historian of mathematics, so I can’t say how much calculus has or hasn’t changed since the times of Newton and Leibniz or even Euler. But I can say that the context in which calculus is situated has changed – utterly. And it’s those changes that surround calculus that are forcing the teaching of calculus (any many other STEM subjects) to change –radically.
I’ve just started on a binge of screencast-making that will probably continue throughout the fall. Some of these screencasts will support one of my colleagues who is teaching Calculus III this semester; this is our first attempt at making the course MATLAB-centric, and most of the students are alums of the MATLAB course from the spring. So those screencasts will be on topics where MATLAB can be used in multivariable calculus. Other screencasts will be for my two sections of calculus and will focus both on technology training and on additional calculus examples that we don’t have time for in class. Still others will be just random topics that I would like to contribute for the greater good.
Here are the first two. It’s a two-part series on plotting two-variable functions in MATLAB. Each is about 10 minutes long.
Part of the reason I’m doing all this, too, is to force myself …
I was having a conversation recently with a colleague who might be teaching a section of our intro programming course this fall. In sharing my experiences about teaching programming from the MATLAB course, I mentioned that the thing that is really hard about teaching programming is that students often lack a conceptual framework for what they’re learning. That is, they lack a mental structure into which they can place the topics and concepts they’re learning and then see those ideas in their proper place and relationship to each other. Expert learners — like some students who are taking an intro programming course but have been coding since they were 6 years old — have this framework, and the course is a breeze. Others, possibly a large majority of…
Wolfram, Inc. has just rolled out its newest creation: Wolfram|Alpha Widgets. These are small “apps” that execute a single W|A query using user input, without actually loading the W|A website. In just the last few days since W|A widgets have been around, hundreds of them have been made, from widgets that find anagrams to widgets that calculate comparative economic data between two states to widgets that take derivatives. Each widget also comes with the option to customize, share among social media applications (21 different services are represented), or embedded in popular blogging and wiki services such as WordPress and Mediawiki. (Sadly, there’s no WordPress.com embedding yet.) Take a look through the gallery at what’s been done.
What’s really exciting here is that you don’t need any programming knowledge to create a widget. You start with a basic W|A query, then highlight the…
Yesterday at the ASEE conference, I attended mostly sessions run by the Liberal Education Division. Today I gravitated toward the Mathematics Division, which is sort of an MAA-within-the-ASEE. In fact, I recognized several faces from past MAA meetings. I would like to say that the outcome of attending these talks has been all positive. Unfortunately it’s not. I should probably explain.
The general impression from the talks I attended is that the discussions, arguments, and crises that the engineering math community is dealing with are exactly the ones that the college mathematics community in general, and the MAA in particular, were having — in 1995. Back then, mathematics instructors were asking questions such as:
Now that there’s relatively inexpensive technology that will do things like plot graphs and take derivatives, what are we supposed to teach now?
I’ve made it to the end of another semester. Classes ended on Friday, and we have final exams this coming week. It’s been a long and full semester, as you can see by the relative lack of posting going on here since around October. How did things go?
Well, first of all I had a record course load this time around — four different courses, one of which was the MATLAB course that was brand new and outside my main discipline; plus an independent study that was more like an undergraduate research project, and so it required almost as much prep time from me as a regular course.
The Functions and Models class (formerly known as Pre-calculus) has been one of my favorites to teach here, and this class was no exception. We do precalculus a bit differently here, focusing on using functions as data modeling …
I am a mathematician and educator with interests in cryptology, computer science, and STEM education. I am affiliated with the Mathematics Department at Grand Valley State University in Allendale, Michigan. The views here are my own and are not necessarily shared by GVSU.
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