84 words a day

Since I eventually am considering applying to graduate schools I figured at some point, probably sometime near the end of next summer, I should probably take the GRE. I looked up the test to see exactly what all was involved and apparently the general GRE is a three part test: Analytical writing, Verbal, and Quantitative. Additionally I will have to take the math subject GRE which looks to contain a large amount of calculus, a good bit of algebra, and the rest of the test is a grab bag of other mathematical subjects.
The analytical writing part looks pretty stupid; you end up writing two essays on some pretty random topics. It reminds me a lot of the ninth grade proficiency test we had to take in high school where if you don’t structure your essay in a particular cookie cutter format you wouldn’t score well regardless of how well written the essay was. None of the sample topics looked like they would be even remotely interesting. I am definitely not looking forward to this part of the test.
The quantitative part of the general test looks to be pretty much a joke. I haven’t really delved into it very far, but I suppose that the majority of my studying for this part will just be familiarizing myself with the various types of questions that are asked within the test. Maybe I am just being arrogant, but I don’t see this portion of the test challenging my mathematical skills in the slightest.
The math subject test is probably the most important part of the test, but given the amount of time I am already going to allot to study the various subjects that are included on the exam I don’t think I am going to have to spend a large amount of time studying for this test. I do however plan to get one of those GRE math subject exam study aids that includes a few practice tests so that I have a few practice tests that I can take just so I get a feel for the type of questions that will be on there.
That leaves just the verbal section of the general test. I started taking a practice test last night before dinner and while I didn’t get very far I did find an area where I am going to be very weak: analogies. I did maybe 10 of these last night and missed about 4 and at least one of the ones I got right was just a correct guess. Most of my problems stemmed from the fact that my vocabulary doesn’t include a lot of the words that are included in a lot of the analogies so I don’t even have a clue as to where to begin.
I decided that I needed to learn the words that were going to be on the test sometime before I took the test. So I found a list of words that you should know when taking the GRE and divided them up so that I would have looked up all the words within 60 days. It worked out to be 84 words a day. So today I started with the first 84 words and it is quite a mix of words. From words like able-bodied that I wouldn’t expect to be on a test like this, to words like abdomen that I wouldn’t expect would be on a list like this, to words like abbess which I wouldn’t ever expect to have to use in my life. Of course, I guess it is entirely possible I might someday find myself in a nunnery needing to speak to someone in authority. Then I will be glad to have learned the word abbess while studying for the GRE.

Winter Quarter

My schedule for winter quarter is pretty much set. I am currently enrolled in algebra, analysis, stats, and anthropology. I am still third on the waitlist for Italian, but with 13 people still on the waitlist I am still optimistic about them opening up another section. If I don’t end up getting into Italian by the Sunday prior to the start of winter quarter I think I am going to drop from the waitlist and enroll in the combinatorics course that is offered this quarter.
The combinatorics course both counts as a math elective and is recommended to students that are considering graduate studies in mathematics. Plus I have always found combinatorics to be pretty interesting. So in short I would love to be taking that course rather than Italian, but Italian is also a requirement for me to graduate and I am very nervous about having a gap between the courses again.
I got lucky last time in that I think I was probably over prepared for Italian 102 compared to the other students that were in my class, but I still was really rusty at the beginning of the quarter. This time I will have taken Italian at the same school as the rest of the students in the class only they most likely will have taken the class just the previous quarter. I know that I can study Italian some over the course of the next quarter just to keep it fresh, but to be perfectly honest that probably won’t happen. The plan over the summer was to spend some time each day learning Italian, but that got pushed to the backburner due to more pressing demands from the classes that I was currently enrolled in. Over the summer I took only 15 hours and this winter I will end up taking either 19 or 20 hours.
The only other point of uncertainty in my upcoming schedule is a seminar that is being offered about Lagrange and contemporaries. While I am not interested in making a career out of history of mathematics, I do find it interesting to read papers by the older mathematicians. Often times I have found that reading the original work by classical mathematicians makes it easier to understand the concept since the papers aren’t bogged down with modern notation. There is a history of math class that is offered that sounds really cool, but I am pretty certain that I can’t take it due to restrictions on how many courses that I can take within the math department. The seminar would count against that total as well, but it is only one hour so I don’t think it will make as big of a difference. My main concern is that I don’t know how much work the seminar is going to end up being. Even though it is only worth 1 hour adding it would give me six courses for the quarter something that seems rather crazy to me. I guess the only thing to do is to show up to the first meeting and see how much work will be involved.

Topology

The other day I bought the book: Introduction to Topology by Theodore W. Gamelin and Robert Everist Greene. I had wanted to study some Topology on my own for awhile now, but I wasn’t really certain what kind of book to get. This book while first written in 1983 was cheap so it had something going to for it and before buying it I read to preface to try and get an idea of what kind of mathematical background that they were assuming. I read the following passage, “In the strict logical sense, the book is almost independent of prior mathematical knowledge. Only familiarity with the real numbers and some basic set theory, such as countability and uncountability, is needed in this strict sense. Readers who are not to some extent familiar with the subject called “rigorous calculus” may find the material a strain on their capacity to absorb abstraction without concrete motivation.”
Well I’m not certain what “familiarity with the real numbers” means precisely, but giving the number of math classes that I have taken I assume I have to be close and I just finished taking a course that included some work on basic set theory. I’m not sure what “rigorous calculus” is, but since the quotation marks are original to the author I am guessing it is probably a fuzzy concept, besides the “rigorous calculus” is only needed for motivation and not for understanding the concepts. So I figured the book was written at about my level.
Yesterday during lunch I decided to start working my way through the book. I got as far as page 3 when I discover this: “Let S be any set and let B(s) denote the set of bounded real-valued functions on S. Endowed with the metric: d(f, g)=sup{|f(s) – g(s)| : s element of S}.” I have no clue as to what this even means so I think I am going to put the book away for awhile and come back to it. I guess next time I look to buy a math book for self study I will read more than just the assumed mathematical knowledge part and actually read the first couple of pages to see if everything makes sense.

A couple final grades

I took my Italian final yesterday and afterwards I was pretty bummed since I was now expecting to get a B in the class. I had a B going into the final so and I was pretty confident with most of the final, but one of the two longer essays was pretty bad in my opinion. So I kind of figured I would end up with a slightly lower B than what I went into the final with. This morning however the grade for Italian was posted and I was surprised to see that I had got an A- in the class. I think an A- was about the best grade I could have got going in so I must have done better on the essay than I had thought.
In other final grade related news the grade for my stat class was also posted. I ended up with an A- so in the end slacking off on the homework didn’t really affect my grade significantly. I’ll just take the A- as a wakeup call to take the homework more seriously next quarter. I just hope the homework has more interesting problems next quarter compared to this quarter.

Linear Algebra Final

Today was the Linear Algebra final. For the two midterms I was really off the mark when I tried to guess what would be on there and although my scores were okay I found myself panicking during the exam since I was having to produce stuff that I didn’t feel like I was 100% certain on. As a result I think I might have gone a little overboard preparing for this final since it was ridiculously easy.
There were 5 true/false questions and 5 fill-in-the-blank questions to start the test. The true false questions were really easy and only one fill in the blank question really made me stop and think: If A is symmetric and orthogonal then A2 is… It took me a minute to realize that if a matrix is orthogonal then AT=A-1 and therefore A2 had to be identity.
From there, there were a few questions about definitions that were mostly a joke. The only one I remember was the question about what it meant to say that a set of vectors v1, v2, v3…vk were orthronormal. I only remember this one since I started to write the definition one way and then just wrote that vi dotted with vj was equal to 1 if i equaled j and equal to 0 if i did not equal j. It was much quicker that writing out a definition in words.
Then there were the computational problems. Three of the problems I had pretty much expected: one problem to calculate the eigenspaces of a given matrix, one problem in which the eigenvalues of a matrix were given, but the matrix wasn’t, and one problem where Gram-Schmidt process was required. The other two computations were kind of surprising to see on the exam. They were just problems that I didn’t see as something that would be on the exam since they were pretty basic.
The first was a problem with two parts: Give a 2X2 system of equations such that 2 given vectors were solutions and the zero vector was not a solution and find the equation of a line from the given parametric form. Find the equation of a line from the given parametric form! Are you kidding me? The other part of the problem wasn’t much better, but it did involve solving a system of equations so I guess I kind of expected that type of problem on there.
The other computational problem was about linear independence. First there were three vectors in R3 and it asked if they were linearly independent so I put them in a matrix and found the determinant wasn’t equal to zero and concluded they were. Then it asked to express e1 as a linear combination of 3 given vectors and the answer was obvious enough that I didn’t need to do more than look at them to find it so I probably lost a couple points there. Finally it asked whether 4 vectors in R4 formed a basis for R4 so it was pretty much the same as the first problem only this time the determinant was zero so they didn’t form a basis.
Obviously I feel like I did really well on this exam and as a result I am almost certain to end up with an A in the class, but I am kind of disappointed that the exam was so easy. This was the one class that I could count on to be a challenge the entire quarter and it let me down at the end of the quarter although to be honest I think I was just really well prepared for the final. The girl I studied with last week was asking me a couple of last minute questions and a lot of people were hovering to hear me answer so perhaps I was just quite a bit more prepared than most of the students in the class.

Foundations Final

I just finished the foundations final. It was kind of annoying in that a lot of the problems were either really similar to previous exam problems or previous homework problems. I think I ended up doing pretty well on the exam, but there is a chance that I didn’t answer number 8 at all. I remember working through the proof on all three parts, but since I skipped it since it was annoying for me to write up I got a sinking feeling just a minute ago that I may not have written up the answer. Even if I didn’t each problem is only worth 10% of the grade on the final so I will likely still do really well in the class.
I also kind of freaked out when it came to problem 10a. The problem was if A and B are finite sets with the same number of elements and f is an injective function mapping A to B show that f is bijective. The problem said that we were allowed to use the fundamental property of finite sets, but we had to state it “clearly.” For a minute or so I kind of blanked on what the property even was, let alone trying to state it clearly. I eventually just said that the property said that a finite set couldn’t be equinumerous to a proper subset of itself. No clue if that is stating it clearly, but it was the best I could come up with.
Other than those two issues there really wasn’t much else I wasn’t entirely sure on. I had some question as to whether I could use the fact that a rational summed with an irrational is irrational, but I checked the book afterwards and that proof was like the first on in the section on irrational numbers so I assume it was something we were allowed to use. Also on problem 9 I just restated 9b in a way that it was exactly 9a and then said that by 9a this was true and thus the result I wanted followed from definitions at that point. I really needed to get out of the room at this point and I didn’t want to bother with rewriting out a proof I had already written so hopefully he doesn’t ding me much for this.
The final grade in this class is likely to be an A- or A. I screwed up a problem on the first exam and that left me trying to play catch up and I was probably a B+ after the second exam, but if I didn’t answer problem 8 on the final that is going to leave me at the mercy of how he scales the grades as to if I get an A in the class or not. I suppose in reality it doesn’t really matter much whether I got an A- or an A.

Stats Final

Well my finals week officially started today at 11:30 when I started taking my stats exam. It was conveniently scheduled such that it conflicted with the trim-a-tree party in the math lounge, so that makes twice this quarter that I have missed a math department function due to my stats class. Not that I am really concerned with it, plus I got done with the exam in time to ingest a large quantity of processed sugar so I suppose I didn’t miss out on the main point of the party anyway.
As for the exam I think I did fairly well on it. There was one problem on there that gave me fits and I am certain that I missed it, but I should still end up with an A on the test. I was surprised at the amount of conceptual problems compared to the amount of computational problems. There were 4 sections each various problems on the same set of data and I think each section excepting 3 only had 1 computational problem and section 3 didn’t have any computation at all.
My final grade in this class will probably fall in the A- or B+ range since my homework grade for the class is pretty low. Had I cared even a little bit about the homework I probably wouldn’t have made so many careless errors and been able to get an A in the class, but I suppose in the end it doesn’t really matter all that much. Hopefully next quarter the homework will be at least somewhat interesting, but even if it isn’t I am going to try and put more effort into it than I did this quarter.

Oral Exam

I have been in the process of getting sick all week and this morning I woke up extremely sick, but I had to turn in my stats homework and my Italian oral exam was today. So I got up, took some cold medicine, and headed out into the frigid weather to make the trip to campus.
I got to campus about a half an hour early and headed to the math lounge so my partner for the oral exam in Italian and I could go over the outlines of what we were going to say in response to the various prompts. There were 3 prompts: 2 students talk about what they did last weekend and make plans for the following weekend, a customer and a store clerk in a clothing store, and 2 students in their last year of college discuss plans for the future.
The format was you drew a prompt from the hat and then you had to have an 8 minute conversation based on the prompt that you drew. Most of the class wanted to do the weekend prompt, but we thought the prompt was boring so we wanted one of the others. Preferably the clothing store prompt since we had a really good outline there and it was the easiest one to extend if we got towards the end of our preparation and still had a lot of time left.
When we got there she said that she had decided to let both students draw and then decide which prompt they would prefer. I thought that is awesome we don’t have to do the weekend prompt, but after my partner drew that prompt she replaced it before allowing me to draw. Fortunately I drew the talk about future plans prompt rather than the weekend prompt.
Overall I think things went pretty well. We managed to make the entire dialog pretty funny and even included the running gag from class about me having 10 children someday. She was laughing most of the time we were talking and after we were done she said we did really well with the future tense and thanked us for doing something other than the boring weekend prompt. Hopefully the humor distracted her from what I am sure was a ton of grammatical and pronunciation errors.

Group Studying

I’ve always been told that studying in a group is better than studying on your own, but every time I have attempted to study in a group it hasn’t really been something that was productive for me. As a result I have always assumed that I just preferred to study alone. I think what most caused me to shy away from group study is that prior to this point every time I studied in a group it was a group that was in some way assigned to me.

Today I was hanging out in the math lounge when a girl that I share both stats and linear algebra classes with came up to me to make certain that the problems in her textbook matched the problems in the textbook that the homework due tomorrow were assigned from. We ended up chatting a little bit about the stats homework that is due Friday and then the subject of the linear algebra final came up. I pulled up the sample exams that he provided on my computer and we spent a good deal of time talking through the problems on both of them that weren’t purely computational. I really felt like talking things through with her really helped both of us a lot in terms of understanding the concepts. Suddenly it wasn’t enough to understand the problem; we had to understand it well enough to be able to explain it to someone else.

I think the key to working in a group is finding people that you are compatible with. The girl I was working with today thinks about things in a very similar way that I do and that made it very easy to communicate fairly complex ideas to each other. Unfortunately she is an actuarial sciences major rather than a traditional math major so other than two more stats courses this year I probably won’t have any classes with her. I do want to try to start studying with other people at least some of the time just to see if it helps me out any; so I guess I am on the lookout for someone that thinks like I do.

Today was a good day!

I was going to write something about my bad day yesterday, but really there is too much from yesterday that I really don’t even want to think about. So instead I figured I would write about the great day that I am having today.

Last night I just wanted the day to be over so I went to bed fairly early even though I had Italian homework and an Italian quiz to study for. So I had to get up early so that I could get the homework done and maybe study a little bit for the Italian quiz. I got to campus early enough that I had to swipe into the library and was able to get my Italian homework done much more quickly that I had imagined so I had plenty of time to study for the quiz.

My first class today was foundations and a lecture on infinite sets. I took a class several years ago while I wasn’t yet able to return to school full time that had a little bit of set theory in it and one of the things that always bugged me was that while I understood the argument that since the rational numbers could be written as a list they had to be countable I’ve always thought that argument seemed more like hand waving than mathematics. Well today in discussing countable infinite sets the professor mentioned the set of ordered pairs NxN and started to list them out in a chart. I was immediately able to see the bijection from NxN to N and realized that there was a bijection from Q to a subset of NxN and thus Q was a countable set. I suppose that I didn’t really learn anything new in terms of facts, but I certainly got a deeper understanding of a concept that previously I had just kept around as a memorized fact.

Then my Italian quiz turned out to be a lot easier than I had expected. I am certain that I didn’t get a perfect on it, but I think I did well enough that I will have an A in the class going into the oral exam and final. Kind of surprising given that I got a B in the previous class and was really only hoping to get a C in this class. I am kind of nervous about the essay format of the final though so hopefully it isn’t too hard.