Which Came First: Theory Or Application?

This is a question I've had for about a year now: Which came first, theory or application.
I know this is equivalent to asking "Which came first, the chicken or the egg?" However, it's still intriguing.

Last semester I took three of theory courses. This semester I'm taking two which are more application than theory, another which is more balanced (numerical methods), and a theory. My current problem is jumping back and forth between application and theory within the same context. It could just be mathematical immaturity, but I have to wonder if some people are just meant to silo themselves either into pure theory or pure application without spending too much time trying to bounce back and forth. Perhaps that's why many research projects take years.

So which came first, the chicken or the egg?

Google, Medicine, and The Expert

I was reading an interesting article this afternoon from the New York Times about patients Googling for health information. It's just more evidence that a little learning is a dangerous thing. I rather prefer Alexander Pope's verion: "People who know only a little do not understand how little they know and are therefore prone to error."

I really divide these people into two big camps. First, those well meaning, humble folks with an active curiosity and desire to learn. The second are the instant experts who think a few minutes on the Internet qualifies them to diagnose rare diseases or some such thing.

The former are really not a problem as with a little patience and preparation they can become useful allies once steered toward good sources of information. I'm one of them and usually apologize in advance for asking questions that are "probably obvious" out of my own curiosity and if I'm going to cite a source, I cite a source. None of this "I read it on the Internet" garbage.

The instant experts (read: instant idiots) are dangerous and annoying. Dangerous because they can now do something they couldn't before but don't have a good understanding of the consequences, much like the infamous blind axeman in a classroom, etc. Annoying because they can't resist butting into what should be the purview of the expert.

God save us from inquisitive idiots.

Another one bites the dust

That would be another finals season.

This one was in fact surprisingly relaxing. I had plenty of time to do other things, and completely wasted it. But they're all done now, so there's no going back.

Prepping for a Math Final

It's taken seven semesters, but I think I've finally figured it out. While it's a great thing, I wish I knew a while ago what I know now.

The basic process is like this:

1. Find during the semester another textbook in the area. Classic books in the area are usually a good choice.
2. The prof (or experience) should indicate what the spread of material is for the test.
3. Go through the other book, identify each relevant section, and work as many problems as possible from that book, using its examples and exposition.

If done right, this should result in you having retaught yourself the entire course in a week or two from a different but similar perspective.

The remaining problem is textbook selection. This is tougher. For my compex analysis course, we used Saff and Snieder's book and I prepped out of Churchill. It turns out Churchill is so cannonical that Saff and Snieder is in some sense equivilent to it. This turned out really well since the prof followed the book very closely and specified the problem areas in a fairly granular fashion. Ergo, Churchill became a source of problems more than alternative viewpoint.

On the other hand, for a course where the prof is more prone to do somewhere a bit off the beaten path with tests, it would probably be better to find a book which approaches the area in a different way than the origional so as to be more or less orthogonal in both approach and problems. Then working the other book is very much like relearning the entire course and may expose one to an additional perspective that may come in handy come test time. Having worked out of Royden for my second semester or reals, I would probably use Baby Rudin as my "orthogonal" text.

Heading into finals

Final exams . . . grrrr . . .

I have two thoughts. First, I have to do as well as possible. Second, I'm going to spend a fortunate on caffeine.

New Grading Scale Proposal

What are two seeming constants in the debates about education? Assessment and grade/gpa inflation. As a student I find the whole debate very deeply interesting for personal reasons. Intersting enough to put together the following rough sketch of what I would impliment if I got to pick how grades where assigned.

As a student, I want my grades to measure how capable I am with the material. Sadly, that's pretty hard to condense into one of five letters.

Thinking like an admissions officer, I would want grades to transparently reflect performance and provide a common measure across applicants from different backgrounds.

So what's wrong with the tried and true A-B-C-D-F system? For one, it condenses everything about performance into a single value thus hiding HUGE amounts of potentially useful information like class size, class difficulty, etc. Secondly, it's easy to inflate even in the face of all but the most draconian standards.

It is my belief we can alleviate the second by addressing the first.

Rather than a simple letter grade (or any other single number) the final report for a class should look like this:

• Raw Percentage
• Five number summary (min, Q4, Median, Q2, max) for the class
  
• Five number summary across all classes
• Class Size
• Some form of objective letter grade
• Subjective letter grade/Overall letter grade
• Prof's comments (?)
  

In short, include a basic set of summary statistics with the overall letter grade. The first four items allow anyone looking at the transcript to gage things like how well the student did relative to their peers in the class and against everyone who took the class (which should average out differences across sections). Not perfect, but being trapped in a harder than normal section will show up (as will easier than normal sections and grade inflation). The objective letter grade might be as simple as which quintile the student's raw score falls into, and the overall letter grade and perhaps some simple comment codes would help take into account things like effort, etc.