Trefethen & Bau & MATLAB & Julia, Lecture 3: Norms

Here are the MATLAB and julia notebooks. The big issue this time around was graphics. This topic dramatically illustrates the advantages on both sides of the commercial/open source fence. On the MATLAB side, it’s perfectly clear what you should do. There are many options that have been well constructed, and it’s all under a relatively consistent umbrella. There are things to learn and options to choose, but it’s clear what functions you will be using to make, say, a scatter plot, and a lot of similarity across commands.

Trefethen & Bau & MATLAB & Julia, Lecture 2

Here are the matlab and julia notebooks. Two things stood out this time. First, consider the following snippet. u = [ 4; -1; 2+2im ] v = [ -1; 1im; 1 ] println("dot(u,v) gives ", dot(u,v)) println("u'*v gives ",u'*v) The result is dot(u,v) gives -2 - 3im u'*v gives Complex{Int64}[-2 - 3im] Unlike in MATLAB, a scalar is not the same thing as a 1-by-1 matrix. This has consequences.

Trefethen & Bau, Lecture 1

Have a look at the MATLAB and Julia versions of the notebooks for this lecture. The first disappointment in Julia comes right at the start: no magic command in Julia! Why not? I love demonstrating with magic square matrices: They are instantly familiar or at least understandable to any level of mathematician. They have integer entries and thus display compactly. You can demonstrate sum, transpose, and diag naturally. And getting the “antidiagonal” sum is a nice exercise.

Trefethen & Bau, via MATLAB and Julia

This semester I’m teaching MATH 612, which is numerical linear and nonlinear algebra for grad students. Linear algebra dominates the course, and for that I’m following the now classic textbook by Trefethen & Bau. This book has real meaning to me because I learned the subject from Nick Trefethen at Cornell, just a year or two before the book was written. It’s when numerical analysis became an appealing subject to me.

Data science? Data science!

I just received a copy of SIAM News on a dead tree. It features a piece by Chris Johnson and Hans de Sterck about “Data Science: What Is It and How Is It Taught?” As usual in these articles, I find the specifics more interesting than the generalities of a panel discussion. I really liked this bit about the new program in Computational Modeling and Data Analytics at Virginia Tech:

A retrospective look at college math

I recommend the post What I Wish I Had Learned More About in College Mathematics, written by Sabrina Schmidt, a former math undergrad at Vassar who now works as a data manager. My favorite quote: I wish that I had been introduced earlier and more often to applications, as they would have provided me with a better idea of potential areas of specialization after graduation. She goes on to mention PageRank (which I usually cover in my numerical computation courses) as an application of linear algebra, and e-commerce as an application of number theory.

Flipping experiences

In June I attended a MathWorks faculty research summit in Boston. The idea was to bring together academics and industry reps. As one of the very few non-engineers, it didn’t give me much fodder for research. But there was a parallel session for educators with a couple of crossover sessions. I spoke in one of those about what I have learned from flipping the classroom in my numerical computation course. You can view the slides online.

Promotion system

In keeping with my post on how grades in a course affect student motivation, I’ve been pondering alternatives to the classic mean-them-and-mean-it model. All of my family members have spent time studying karate. (I’m a brown belt, FYI, which is like an A.B.D.) One thing I’ve always liked about the dojos I’ve known is how the belt promotion system works. It’s what I would now call a mastery based learning concept.

Grades and motivation

Grading is weird in so many ways. In the U.S. system, we report a “letter” grade that is basically an integer from 0 to 10 or so. This value appears on the student’s transcript without comment or context, which is an inherently meaningless way to present any data. But the raw value itself isn’t well defined anyway. When I give a student a C+ in calculus, does it mean that she mastered about 75% of the major topics in the course?

Making continuous assessment work

I’ve come to think that in math at least, continuous learning and assessment may be more important even than http://www.crlt.umich.edu/tstrategies/tsal. The traditional model of chunking assessments into weekly or monthly batches encourages the cram-and-dump style of “learning.” Since students are allowed to delay work on assignments that are crucial to their understanding of incoming material, it’s impossible for them to build that understanding in real time. Instead they copy and hope to parse later, when assessment is demanded.