Foundations exam results

We got our foundations midterms back on Monday, but I was too busy to really do anything except homework and eat a lot of food until now to think about a blog to say anything about it. The median score was 67 and the grades ranged from 33 to 96. I think the IRQ was somewhere around 55-73, but my memory of the actual distribution is pretty fuzzy at this point. I was kind of surprised by my 94 as I thought that I had done better than a 94, but the 94 was still good enough for second in the class so I guess I can’t really complain too much.

I missed 2 points on 3b the problem where I couldn’t figure out the cryptic hint. I got to a point that required the same logic as used in problem 3a and I said by the same argument in 3a and he dinged me a couple of points. Then I missed 4 points from problem 5c. For problem 5 we were given 3 functions: f mapping from A to C, g mapping from B to D, and F mapping from A X B to C X D. With F(a,b)=(f(a), g(b)). The first part was to show that if f and g were injective then F was injective. The second part was to show that if f and g were surjective the F was surjective. Then part c said, “If f and g are both bijective, show that F is bijective and describe in terms of and ” I simply stated that F is bijective from parts a and b and then wrote he however apparently wanted some sort of justification beyond the fact that existed and dinged me the 4 points. I suppose in the end it isn’t that big of a deal, but it is kind of annoying that the problem seemed to be poorly worded. I am pretty certain that the student that got the 96 also missed 4 points on this problem so it wasn’t just me that found the wording to be a little off.

 

 

 

 

 

 

 

 

 

Homework Stuff

This week was a short week, but it seemed like everyone was trying to cram a bunch of stuff in before the break. I had homework due on Wednesday in 3 of my 4 classes and the forth class was Italian which only has homework due at the beginning and end of a chapter, but we are expected to be doing the workbook sections as we progress through the chapter.

 

The foundations homework was only three problems, but he managed to assign two pretty interesting proofs concerning counting of finite sets. I have really loved this class in that the homework tends to have some pretty difficult problems and a good portion of the problems that he assigns tend to be really interesting or at least provides useful results in terms of other problems that I find interesting.

 

The linear algebra homework wasn’t difficult, but it was tedious. One of the problems was to find an orthogonal basis of R⁴ that contained two vectors that we were given. I started the problem with two pretty basic vectors and then things got pretty ugly. I ended up starting over with vectors that seemed to cancel out some of the ugliness, but still ended up with a fourth vector that was pretty scary looking.

 

The stats homework started out pretty interesting for a change. She added a part to the first problem to figure out the sample size that was required in order to obtain a certain confidence and a certain power. I spent quite of bit of time to find the correct answer and stumbled through quite of bit of stuff that wasn’t in the book in the process. It turns out that this is a calculation she expected us to use Minitab for, but it was much more interesting my way. Unfortunately the rest of the assignment was far from interesting as it was mostly must looking through the cookbook and finding a formula to use to solve the given problem.

Another math exam!

Well I didn’t get much sleep last night since I realized that I did the wrong set of problems for my foundations homework and I had to do an entire set of problems before the exam today in addition to maybe studying a little for the exam. At least the problems weren’t too difficult and I managed to get 2 hours sleep, plus a half hour nap in the math lounge before class.

The exam itself didn’t seem too difficult and I finished it with about 10 minutes to spare. There was an induction problem involving binomial coefficients that I was expecting and two computational problems that I was kind of surprised to see, but they were pretty easy. Problem three involved two proofs in set theory I can’t remember what they were, but part b said we could use part a and something we proved in class to prove it. I’m not certain exactly what he meant by what we proved in class so I just did the proof directly without appealing to any other proofs. Leaving the exam I felt like I was handing in a paper that was perfect, but of course I fully expect him to ding me a couple places with a “show more details” comment. I’ve pretty much given up on the idea of turning in a perfect exam in any of my math classes, it is just too easy to either screw up a computation somehow or not prove something that you thought was safe to use.

I hate the snow!

Well I had this grand plan to get most of my homework due this week done today so that I could focus my attention on my Italian quiz and foundations exam the rest of the week. Unfortunately I woke up this morning with a sinus headache and for some reason it decided to snow today as well. The combination of the two left me unmotivated for the entire day and I am mainly just goofed off in the math lounge most of the day.

While I didn’t accomplish any of the goals on my to-do list for today, I don’t think I can say that the entire day was wasted. Linear Algebra was really interesting to me today; we were working with orthronormal bases for subspaces and defined the perp function on an orthogonal set of vectors. He spent a good portion of the time today proving that if W is a subspace of R^N than all vectors in R^N can be uniquely decomposed into vectors from W and perp W. This proof was really interesting to me in that it was probably the first time where I truly was able to somewhat visualize what was happening. Rather than a mindless manipulation of various symbols, I felt like I was truly understanding exactly what was happening and pretty much I was able to follow my nose and find the next step on my own rather than have to have it shown to me by the professor.

In addition to the exciting Linear Algebra class I also got more of my schedule in order for next quarter. I registered for Data Analysis II. I know I was going to give up on the stats minor, but my Arts and Sciences advisor talked me into giving it another shot. So I went online today to sign up for the waitlist and was surprised to see that the class was no longer full. So now I have two classes scheduled out of the five I think I that I would like to take. At this rate my schedule should be complete before this quarter is over!

The results are in

Well the results are in for the Linear Algebra midterm and I scored a 93! I am very excited about this grade since I really want to get an A in the class and now with a solid performance on the final I can accomplish that goal. My solutions on both of the problems that people had trouble with were good enough to earn full credit and I only lost 3 points for my messed up eigenspace computation. I lost 3 points for being an idiot and finding the dimension of the row space of a 15×19 matrix with nullity equal to 5 rather than the dimension of the column space like the question asked. Finally my definition of a basis of a vector space wasn’t good enough for full credit apparently so I lost a point there.

I really got concerned today looking at peoples solutions that they were handing in…most of them had used some trick I have yet to look up to show directly that A^TA=( A^TA)^T so I was starting to doubt my own solution from the exam that I was going to hand in again. I was panicked that I had missed my chance to correct a mistake from the test. I’m sure whatever trick they used was probably a much cleaner proof, but I guess it doesn’t really matter in the end as long as the proof you give is correct.

I really found the distribution of the grades to be pretty interesting, especially considering that 67 is the cutoff for a C- and he claims that he isn’t going to curve the final grades at all. The grades ranged from 25-93 with a median score of 49. I’m not sure where the quartiles landed for the distribution, but even so it looks like more than half the class is looking at failing the course. Of course the extra credit could help some of them, but the problems were only worth 10 points on the test so at most you are looking at jumping the median to 59 which is still quite a bit below failing. I can’t see him failing half the class and so I am pretty confident that the bar to earn an A in the class will be lowered somewhat as the end of the course draws nearer. 

Linear Algebra update

Okay so the Linear Algebra exams are graded, but they weren’t returned to us since a large portion of the class totally messed up two of the questions on transposed matrices. The one where we had to prove that A^TA is a symmetric matrix and the other one where we had to show that A^TA is defined. So we have to write the solutions up for these before the next class even if we got them right on the exam. Not certain what my grade was, but he said the range was from 25-92 and since I was thinking I probably got a 92 or so and I am pretty confident in my answers on the trouble problems I have a good feeling about the 92 being my paper…I just hope I am not disappointed!

Linear Algebra Exam Update

Well I finally decided that I should shower and attempt to do something productive today. I was trying to remember the matrix from the Linear Algebra exam from yesterday, but I am not having much luck. I know the bottom two rows were identical, but can’t remember them and that the first column was 2 in the first row and the rest zero, but beyond that I am out of luck. I did look into the result of applying a matrix to its eigenvectors and I was right when I thought that I should have got a scalar multiple of the eigenvector. So I screwed up the computation someplace…knowing the way he graded last time I will probably get zinged pretty good for that, but I probably still am looking at a score in the low to mid 90’s. Plus I feel much better it was a computational mistake rather than a conceptual misunderstanding.  Now I know all I need is to practice the computation more rather than have to work to understand the concepts. I am starting to feel pretty good about the final in this class.

Scheduling Woes

Okay so I don’t have class today and am basically getting nothing accomplished. It is after noon already and I haven’t even showered yet! But I have managed to write four blog posts for a blog I just decided to start this morning so that is something I guess. I suppose later I can finish my Foundations homework, study Italian some, and maybe even start on my stats homework, but for now I am just going to enjoy the feeling of not having to be anywhere today.

My day so far hasn’t been totally unproductive in that I tried to schedule classes for winter quarter earlier this morning. The email I got from the registrar said that whatever algorithm they use to decide who gets to schedule when says that I could register for classes starting at 11:30 today. And they mean 11:30 when I logged in at 11:29:59 it told me I couldn’t register until 11:30. I don’t know when people starting registering for classes, but it must have been awhile ago since everything so far has been a disaster.

My plan was to take Anthropology 201, Intermediate Italian I, Algebra I, and Data Analysis II. Well the Data Analysis II class was full, so I said well that decides it I am done trying to be a stats minor! Probably  a silly way to decide something major like that, but well I am certainly not going to struggle to get into a class that I am going to hate.

With Stats out I looked for something else to take instead and decided I would try to start the Analysis sequence this next quarter even though the math counseling office advised against taking Analysis until after taking at least a couple quarters of Algebra. They think we should be more used to proofs before jumping into Analysis, but in the end it is just a recommendation and not a formal prerequisite. Besides once next quarter starts I get an actual math advisor rather than just the math counseling office. So I signed up for Analysis, but the class was full already. I ended up 9^th on the waitlist, but I am pretty sure that I will get in since there is another section already posted, but not yet open to register in.

Then I went to schedule Algebra class and again the class was full. This kind of really perturbed me since the math counseling office recommends that you take Algebra before Analysis you would think that most people taking Foundations would be taking Algebra the next quarter. This quarter there are three sections of foundations and yet there is only one section of Algebra next quarter. Still I am only third on the waitlist so odds are I will be able to somehow find my way into the class.

The next class I tried to schedule was Italian and wouldn’t you know it that class was full as well. There were only two sections and one of them conflicted with the Algebra class so I had to schedule the 11:30 section, but it didn’t matter since both of them were full. I’m only the third on the waitlist, but I still am really nervous about this since I don’t want to have any gap in time between taking Italian courses. I suppose in the end some people won’t pass 102 or they will open another section of 103, but I reserve the right to freak out until then.

Finally, I tried to schedule Anthropology and this time I was amazed that there were sections open that I could schedule immediately. I kind of figured it would be like every other GEC class I’ve taken in that I would have to search around until I found one that fit my schedule, wasn’t full, and fulfilled a requirement that I had left. I’m not extremely excited about this class except that it fulfills my last social science requirement so that is pretty cool I guess.

So in short I tried to schedule classes today and managed to actually get 1 class scheduled. I am supposed to meet with my Arts and Sciences advisor on Thursday to go over my schedule…I was hoping that she would say your grades since coming back have been great and you are making good progress let’s just skip these meetings every quarter, but now I’m afraid she is going to look at my attempts to schedule this quarter and think I need to continue to meet with her over scheduling every quarter. Oh well she tends to be a nice lady and she sometimes will break the rules and register me for classes early so maybe meeting with her isn’t all that bad of an idea!

Stupid Algebra Tricks

I normally am pretty good at seeing algebra tricks, but last week on my foundations homework I totally couldn’t find one even though I knew that had to be one there. I was trying to prove that if x is an integer that 6 divides x³-x. I started off easy enough showing that it was true for x=1 and then assumed that was true for an arbitrary natural number x. I then tried to show it was true for x+1 and I got stuck after showing that (x+1)³-(x+1)=3x²+3x+x³-x. I knew there had to be some algebraic trick to showing that 6 divides 3x²+3x, but try as I might I couldn’t figure it out. In the end I gave up and just used induction to show that 6 divides 3x²+3x. I tried to tell myself that I have a proof that is 100% correct and to just let it go, but not being able to see the trick bugged me and I couldn’t let it go so I decided to go on a fishing expedition to the professors office hours. I showed up with my correct proof and under the guise making sure that it was written up in a way that people would understand managed to get him to tell me the algebraic trick! 3x²+3x=3x(x+1) which I knew, but somehow my brain never made the connection that 2 either divides x or x+1. I feel kind of stupid now, but I suppose in the end it is good to miss some of these tricks now and again so I can learn to work through proofs without having to resort to finding some sort of trick every time. Plus I doubt I will ever fail to make the connection that 2 divides either x or x+1 ever again.

My class schedule

When I scheduled classes this quarter I was excited that there were never any big gaps between my classes and I only had to go outside once between my classes! In the end I’ve decided that gaps between classes really do wonders for my sanity. I am taking 4 classes this quarter: Foundations of Higher Mathematics, Beginning Linear Algebra, Data Analysis I, and Beginning Italian II.

The foundations class has been pretty boring so far, but it is definitely something that I see as useful. So far we have covered basic logic, proof techniques, some basic number theory (basically just to give us something to practice proofs on), basic set theory, and now we are starting to work with functions some. It is boring because it is all mostly stuff everyone in the class already knows, but it is very useful in that it is a good overview of what kind of things we are going to be expected to know in later classes. Plus we are getting it all defined in a much more formal way. Already I have been noticing that reading math texts seems to be much easier now and I think this has a lot to do with this class.

Linear Algebra has been interesting so far, but I am kind of concerned about this class. I feel like I have an okay grasp on the material, but there is so much there that I am just unsure about. The first exam went pretty well I guess, I got an 81 and the median score was a 65. I missed 12 points the problem that nobody got more than 8 points on and missed the other 7 points, because of what I considered overly harsh grading. We took the second exam yesterday and I am less sure about this one, there was a lot of stuff on there that I wasn’t expecting. Opening up the exam and seeing…for an arbitrary matrix A show that A^TA is a symmetric matrix…was quite a shock to my system. It wasn’t that difficult, you just have to calculate (A^TA)_ij and (A^TA)_ji and from there it was pretty quick to show that they were the same, it just was so unexpected that it sort of threw me off for the rest of the exam. Then the last question involved computing the eigenspaces of a given matrix…I am pretty certain that I found the correct spaces since he pretty much gave away the eigenvalues, but I applied the matrix to the eigenvectors that I got and the result for one wasn’t a scalar multiple of the eigenvector. So either my understanding of the concept is off or I screwed up the calculation somewhere.

Of all my classes my stats class is probably the one I hate the most. The majority of the class is graduate students that are studying something within the biological sciences. Most of the material is really basic and the text that we are using for the course is a text that is sometimes used in high school stats classes. The result is a very boring lecture that I dread going to. This class has me reconsidering my stats minor, it really is a shame since I think stats seems interesting, but there are two more classes in this sequence that I have to take and I am not certain I can hack sitting through them.

My Italian class has been a source of much stress so far this quarter. Since I don’t learn languages very well at all I went into the class with a goal of getting a C so I could move on to the next course. Since the first major quiz of the quarter I have been right on the borderline of A and A- in the class. So I have revised my goal to getting an A in the class, but I still feel like I have very little understanding of Italian so every quiz and assignment is a source of major stress. I am beginning to think that perhaps I except too much in terms of understanding in a beginning level language course and that in reality I am probably progressing quite well, but I still can’t shake that feeling of being lost whenever I do something related to Italian.