First day

Today was the first day of spring quarter. So I went to classes and whatnot, but there really wasn’t any homework that I needed to start on right away so I pretty much just goofed off in the lounge between classes.
I started the day at 8:30 in the morning with Italian. Today was pretty much a joke, we got a syllabus and talked for a few minutes about what we did for break and then left for the day.
Then I went to algebra where we started right in with definitions of various structures that we are going to be studying this quarter. It was interesting to learn, but we haven’t really covered enough to begin a serious attempt at the first homework so I’m going to wait until Wed to start working on it.
Third in line was number theory where I was hoping that my rant from last night would prove to be unjustified. Sadly enough I don’t think I went far enough in my rant. First more on the grading policies of this class…there are five tests, but only four of them count for the grade. “Class participation” won’t be precisely defined until tomorrow, but there are a total of 45 points to earn…25 of which is extra credit… I managed to keep a straight face through all of this, but I was unsuccessful a few times later.
After going over the grading scheme she then announced that the course was going to be about proving things. I was totally shocked by this since I typically try to take math classes that don’t actually involve any math. Personally I am worried that this doing math in a math class thing will catch on and then all my math classes will require math.
We did get some content today at least. She defined divisibility, GCD, and LCM and did a very basic proof involving divisibility. And after she completed that proof came the money line for the entire day today, “Does anyone remember how to do a proof by contradiction?” I foresee that line becoming a running joke in the math lounge in the days to come.
Anyway I as I was sitting in this class I couldn’t help, but think that I was sitting in the wrong class. At first I thought it was just me, but pretty much everyone in the class that I know was thinking the same thing. If there was another math elective offered this quarter or dropping the class wouldn’t screw up my aid I would drop the class in a heartbeat, but the other math electives aren’t really anything that looks even remotely interesting to me. So I guess there isn’t much to do, but hope she realizes that the way she is teaching this course is probably close to two levels below what those of us taking the course were anticipating.
Finally I finished up the day in analysis. I wasn’t really able to get much of a handle on how this course is going to play out. It was annoying that that she presented a theorem and then spent a large amount of time explaining it trough hand waving, but she didn’t even manage to start the proof. Seems strange now that she basically presented something without proof, but perhaps she will give a proof next class.

It is offical number theory is going to be annoying!

I know I should just go to bed since I have to be up crazy early tomorrow, but I just received an email from the professor of my number theory class and I can’t stop laughing about it. It was just your basic welcome to the class email that provided a link to the syllabus in addition to informing students about a last minute change of rooms. Honestly I am glad that she emailed it out tonight since I don’t think that I would have been able to control my laughter in class on first reading of the syllabus.
To begin with the syllabus is FOUR pages long and that doesn’t even include the schedule which appears to be mostly in the “to be determined category.” Seriously a four page syllabus? I’m pretty sure this is a math course for math majors and not some sort of GEC course. I may be wrong, but my guess is that every student in the class understands how a math class works. The professor I had for combinatorics last quarter and we all managed to figure it out.
I’m sure most students upon seeing that the syllabus was four pages long did exactly what I did, skipped to the part that explained how the final grade would be calculated. There were a couple of odd things I noticed in this section. The first one being there are FIVE, 1 hour exams, but there is no final. That is just stupid! Seriously schedule a 2 hour midterm in the late afternoon and have a 2 hour final and be done with it. Or failing that cut out a couple of the exams in favor of a 2 hour final. Just anything that doesn’t have me dealing with the stress of an exam every other week.
I figured that the four page syllabus and five exams were the end of the strangeness, but it turns out I was wrong. Continuing down the list of how the grade is calculated there is the total number of points for “class participation”!! After reading this I stopped and checked that I did indeed have the syllabus for number theory and not for some random lit class. I’m not certain what “class participation” even means in the context of a math class, but it seems to be to be dangerously close to basing grades on attendance and it is my understanding that that would be against departmental policy. I’m sure I could read the syllabus to find a precise definition of “class participation”, but I’m tired and the thing is four pages long.

Bitching about a class before it starts…

Well winter quarter is officially over and I have a week off before heading into spring quarter. Number theory is the class that I am the most excited for, but I’ve already purchased the book for the class and I think I am going to end up being disappointed. A large amount of the book is devoted to “How to structure proofs.” Umm…I thought that was what the Foundations of Higher Mathematics course was for. The course description seems to suggest that we would learn about algebraic methods in number theory, but the book doesn’t seem to mention algebraic structures at all. Plus the optional topic in the course description that I was most interested in was elliptic curves and once again the book doesn’t mention elliptic curves at all…well there is a short section on the history of Fermat’s Last Theorem so I suppose I can’t say that there is no mention of elliptic curves. I hope I am wrong about this course and it turns out to be an interesting course, but I fear that we are going to spend nearly a month on material that was already covered in the foundations course.

Combinatorics Final

I took it yesterday and it was pretty insane. Pretty much the same format as the midterm 10 questions, do 4 of the first 7 and 2 of the last 3. The first problem was a joke…pretty much a straight forward application of the principle of inclusion-exclusion. I goofed around with the second problem a little, but part B asked if 2 graphs were isomorphic or not…I was pretty certain they were, but I wasn’t able to find an isomorphism so I ended up skipping the problem.
The second problem I did was pretty easy as well. There was some parts about an equivalence relation and then a proof, given G a graph and H and K connected subgraphs of G with a non-null intersection show that the union of H and K was connected. Turns out that wasn’t that difficult of a problem.
The third problem I did wasn’t really difficult, but it was time consuming. The first 2 parts were to define what a tree was and give a general method for constructing a spanning tree of a connected graph. The third part gave 3 trees with 6 edges and asked to find all trees, up to an isomorphism, with 7 edges containing the given trees. That wasn’t hard, but then the part about showing that there were no duplicates took about a page of work to get through.
The fourth problem I did was where things started to go downhill. Part A asked whether or not the graph of knight moves on a 5×5 chessboard had a Hamiltonian cycle, this wasn’t hard since I had messed around with the 5×5 board previously and had a pretty good pretty good argument for why any Hamiltonian path of such a graph could be assumed to start at the bottom left corner of the board. Part B was again pretty easy in that it only asked if the Peterson graph had a Hamiltonian cycle, so proof by example was a pretty much all that was necessary. Part C however was to so that the graph of a D dimensional cube had a Hamiltonian cycle; I got a proof of sorts using inductive reasoning, but well it was mostly a bunch of hand waving.
The fifth problem again was a trouble spot…it was inclusion-exclusion again, but I kept messing up the counting. I left some work on there, but never got a solution of any sort. I pretty much felt like I had to work on that problem since the problem I skipped was to prove 1 of 3 theorems: Hall’s theorem, Delwar’s theorem, or inclusion-exclusion. I probably could have wrote something for a couple of these, but honestly in the in it would probably be mostly just hand-waving…plus I ran out of time.
The last problem was to just provide definitions. I think I did alright on this one, except my definition of a set family didn’t really seem like it was what he was looking for, but well I couldn’t really think of any other way to define it.

Algebra Exam results

We got the results back on Monday, but well I have been busy with things so I didn’t get around to writing about them until now. I did about as well as I expected I had done on Friday getting a 98. Surprisingly the class as a whole did not do well at all. The median score on the first exam was 67 and then quite a few people dropped, yet the median score on the second exam was 63. I could tell on Monday when he was going over the exam that he was pretty upset about the scores on the exam. He kept saying, “I thought you understood.” I think it is really cool that he seems to care so much about whether or not his students succeed.
On a related note he has started hinting around that he will be the instructor for algebra II next quarter. I’m not really sure how I feel about this…I think he is a cool guy, but right now he is a group theorist teaching us group theory. I just wonder how much of his enthusiasm will be around next quarter when we are learning about rings. Oh well I guess it can’t be too difficult to teach the basics of algebra even if it is outside your area of specialty.