I’m not taking any math courses this semester, as I’ve already fulfilled the mathematics requirements for my Associate of Arts in Mathematics degree. I’m taking four other courses to fulfill the other requirements for the AA, as well as some of the UIS general education requirements. I miss taking math, but I suppose I’ll likely be able to do that again soon enough.

Today I received the official transcript copies I’d ordered from JCCC. I had each institution I’ve attended mail transcripts directly to UIS, but I also had them send some to me, so that I can include the still-sealed envelopes with my application. I’ve had trouble in the past with institutions apparently losing transcripts send directly, so this ensures that they will definitely have a copy when they process my application.

Tom writes that he’d like to take a Probability Theory I course. I read the description and agree that it sounds like fun. Very rudimentary probability theory and combinatorics were covered in my Statistics class many years ago, and in the Discrete Mathematics course I took this past spring. I enjoyed both, and would like to take a course covering these area in greater depth. UIS doesn’t appear to have any single course matching the one Tom pointed out, apparently dividing it among several courses in Statistics. The catalog does list a related course that I’d like to take, MAT 442 – Probability Modeling and Computer Simulation:

Explores the principles and concepts of probability theory and introduces computer simulation methodology. Topics include fundamental concepts of probability, random variables, random number generators, probability distributions, mathematical expectation, introduction of simulation, concepts in sampling, sampling models, estimation, and discrete event stochastic processes.

This course would be applicable to my minor, but it appears that it is not yet offered as an online course. Once course that I definitely want to take (and is required for my minor) is MAT 403 – Abstract Algebra:

Topics include group theory, rings, and fields.

That seems like a rather terse description for an amazingly large subject area. I’ve learned a little of it on my own in my quest to understand Reed-Solomon codes, which are commonly used for error correction on digital media (such as CDs and hard drives) and in communication. R-S codes are based on solving simultaneous equations over Galois fields.

And speaking of Évariste Galois, I’ve been reading The Equation That Couldn’t Be Solved by Mario Livio, a popular book covering symmetries and group theory, the latter having been discovered by Galois in his quest to determine which equations are solvable by radicals (e.g., the quadratic formula). In addition to covering the basics of group theory and how it relates to symmetry and permutations, Livio has done some research into Galois’ life and untimely death.

If I am accepted to the degree program I’m applying for, I’ll have to take an upper division Linear Algebra course. The course I just took should prepare me well for it; the description of the upper division course at the university lists the same topics with the addition of quadratic forms and canonical forms.

Professor Sekhon said that he considered giving an open-book test, but chose not to do so. Instead, he will let us refer to the sample final he gave out on Monday for our practice, and will let us write our own “cheat sheet” on one letter-size sheet of paper for use on the final. He handed out blank paper and gave us time in class today to write one. I spent the time copying nearly every important theorem and definition in the book onto the sheet in fairly small handwriting, using both sides of the sheet.

I joked that sheets of paper should be made larger. The Professor was surprised to see my sheet, and said that I was the one person in class that didn’t need any. But I feel more comfortable having the information available in case I have trouble remembering any of the material under the pressure of the final exam. It has happened to me before…

Anyhow, I expect that I’ll get a score of at least 90%.

I completed the exam fairly quickly, but other students were still working on it past 9:15, so there wasn’t time for any lecture. But we’ll still have an exam on the section on geometric interpretation of linear transforms tomorrow morning.

The final exam is on Thursday. Professor Sekhon handed out a sample final exam for us to study, and it doesn’t look too bad.

I’ve enjoyed the class, and will miss it a bit when it’s over, but on the other hand I won’t have to get up at 5:30 AM any more, and that has been a bit of a drag.

The final problem was a proof, which if I recall correctly was:

Given a matrix A whose columns form an orthonormal basis for a vector space, prove that A^T = A^-1.

The instructor gave the hint that we could do this by proving that A^TA = I.

I remembered that R(A), the column space of A, is orthogonal to N(A^T), the nullspace of the transpose of A, and that the direct sum of R(A) and N(A^T) is Rⁿ. But I couldn’t figure out where to take it from there.

People got all bent out of shape when Talking Barbie said “math is hard”. Did those people ever take math classes requiring proofs?

Update: I got an A (just barely) because I got partial credit for a problem I thought I’d completely missed, and Professor Sekhon decided to make the proof an extra-credit problem.

The proof turns out to be quite simple. Each element P_ij of the product A^TA is the dot product of two columns of A. Since the columns are orthonormal, P_ij is 1 if i=j and 0 if i≠j, since the dot product of a normal vector with itself must be one, and the dot product of a vector with an orthogonal vector is 0. Too bad I couldn’t think of that yesterday.

The class is fun so far, and not as difficult as Intermediate Calculus (third semester) was.

In American Government, I missed four questions out of fifty, but got four of the five bonus questions right, for a score of 50 out of 50. However, the instructor decided that one question didn’t have a correct answer anong the choices, and is dropping that question. I convinced him that there were two valid answers on another question, so he is giving credit for that one. As a result, my actual percentage is over 100%, though I’m not sure that it will count as such in the averaging.

I really need to find time to work on written papers for American Government.

Computing an matrix of cofactors (and its transpose, the adjoint) is pretty tedious too. It doesn’t appear that the HP 49G+ has a built-in function to do that, so I wrote these during class.

  MINOR:
« UNROT ROW- DROP SWAP COL- DROP DET »

COFACTORS:
« DUP SIZE DUP 1 GET R→I
→ a s n
«  1 n FOR i
1 n FOR j
a i j MINOR
-1 i j + ^ *
NEXT
NEXT
s →ARRY
»
»

ADJOINT:
« COFACTORS TRAN » 

There were six problems on the quiz. I solved four of them quickly, and skipped one that looked hard, with the intention of coming back to it. The sixth problem wasn’t hard, but it involved a lot of tedious calculations. I worked the whole problem, discovered that I’d made an error with the sign of one coefficient, and had to start over. I think I made a different minor error the second time, and just as I was near finishing that attempt, the professor said that the time was up.
I’ll start setting my alarm for 5:30 AM. I’m glad this class is only for another five weeks.

I feel like a zombie as I shuffle around in the morning getting up, showering, shaving, brushing my teeth, dressing, etc. It reminds me of Fred the Baker in the old Dunkin’ Donuts television ads, shuffling around repeating “Time to make the donuts…” Fortunately by the time I get to class I’m reasonably alert. I try to mostly avoid caffeine, though if I really needed it in the morning drinking half a can of diet Coke (but not the caffeine-free kind I usually buy) would keep me alert for a few hours.

There’s one week left in my Public Speaking class. Tomorrow evening I have to present my persuassive speach, the topic of which is that President George W. Bush should be impeached. I’ve just spent a few hours updating my outline, researching and citing additional references in support of my arguments. This is by far the most difficult of the assignments, and I need to practice delivering it a lot today and tomorrow. I’ll probably have to cut some material to keep it within the seven minute limit.

Beyond that, there’s one more speech then the final exam. The last speech is a brief Public Service Announcement. A friend suggested as a topic that I recommend that girls and young women (up to age 26) get vaccinated for the Human Papilloma Virus (HPV). HPV causes half of all cervical cancers; cervical cancer is the second most common cancer in women, which causes 3,700 deaths per year. The new vaccine is almost 100% effective at preventing HPV infection.

After Public Speaking is over, I’ll have a six week course in American Government. I hope that one is as interesting and fun as Public Speaking has been.