wordsworth

So calculus has gotten really really hard. Any I haven’t been able to do as much as usual because essays and stuff. So I still haven’t taken the first test. To be honest I should probably go back and re watch all of part B because I got really stuck on all those problems.  I am going to try to do at least one hour a week from now until the end of school and then this will probably extend into summer? So ya. But anyway back to the hard stuff. I have done some work with the problems in the book because I wanted to understand derivatives more.

Anyway, within the videos I really got stuck on a^x derivatives. Right when I thought I was getting derivatives down they throw in something new. I think I will be able to understand it but I have to do a lot more practice.  I guess that figuring out the derivative of a^x is more like a theory then actually solving an equations. Finding the derivative of a^x means that I will then be able to solve other equations of the same for in an easier fashion. So I guess it is good that I know the derivative. Either way it was not all that fun to learn.

The next problem I had was the value of e. Apparently it is call a moving exponent? Anyway, first you are supposed to use a logarithm to figure it out. Whenever we used logarithm in high school things got interesting because some were on the for ln so I thought people were saying my name when they were not.  The teacher did a lot of equations on the board and then they became e. And that is what magic is.

So now I have to work on problem set two and then work on the first exam! Woot! This has taken me a lot longer then I originally anticipated. I guess this math is just hard. So next week I will be working on problem set two and hopefully be able to understand things more.

Anyway, on an un math related topic I had to go to some thesis presentations for one of my classes. The one that I went to was one by Candice Frances, the girl that dad invited to go to dinner with us over the parent weekend. I thought she had a really good presentations. A majority of her participants were not New College students, which I found interesting. Her 15 minute presentation was very informative and her method was very intricate. Then after her presentation the panel ask her an hours worth of questions. Most of them I did not understand because they asked about specific pages in her thesis. She definitely knew her topic. The audience was not able to ask questions at all, though even if I could I do not know what I would ask. After the questions everyone in the audience had to leave so that the panel could talk to Candice along. Then she had to leave to so that the panel could decide whether or not Candice passed her thesis. I am pretty sure that she passed though I did not stay around to find out.

 When gratitude runs dry it is still possible to give what counts – trust, transparency, sincerity.

Jumping right back into this math is hard after you have been away from it for two weeks. I understood a little of what was happening so that is good. Right now my cognitive psych class is talking about memory, a lot about implicit vs. explicit memory and which is more common. Anyway, it is funny because this last video I watched used the words implicit and explicit and all I could think about is psychology stuff. I have a test in psych tomorrow so that might also be why my mind is associating with things in that way. Anyway I am almost to the first test. I wonder how that will go. I will probably do some practice problems from the book before I jump right into the test. I need to review notes too. They are all scattered between my note books so that should be fun to find.

Not much else to report on. I have a big number theory test on Wednesday. It is not huge but it is the second of three tests so I still need to do good on it. We are working in this program called Maple which is really cool. I still do not quite know why we are working on it but maybe that will be clear later on. I also have a bunch of essays to work on so that will be what I am spending most of my time on. I am also just combining my time today with the 3 hours I plan to spend tomorrow. So 6 hours will be on Monday along with this written thing.

So I did a couple hours last this week just in the book. I was trying to see if I could do a couple extra problems based on what I had learned while doing problem set 1. It seems to be good practice, though I am still getting tripped up a lot. Got to look a bit closer at what I am learning I think. Maybe watch the videos a few more times? I do not know. Anyway, the fractions are what seem to cause the most problems. I think I know what I am doing when it comes to equations like ( x^2 + 2)^2. You have to take the derivative of the function as a whole, replacing the inner equation with the variable u. Then you have to take the derivative of the equation inside the parenthesis. Then you multiply them together, so you have an equation that is 2x2u = 2×2(x^2+2) and so on. The ones that stil trip me up involve fractions. I think I understand how to do the parts, the numerator and denominator, but the fraction that messes me up. The problems would be something like [ ( x^2 + 2)^2 ] / [ (x^3 + 3]. So what do I do with this? I guess I will have to find out. Probable more online digging. I should really make folders for all my online resources. That would make going back or making a review for the test a bit easier.

Ok so today I did a lot of math. I mean a lot. I finish all of problem set 1. There was quite a bit left to accomplish. It took a long time because I had to look up how to do some of the problems on the internet. It took a bit of digging. There is quite a bit that I still do not understand. A few of the problems I looked up in the answer key. Even the answered did not make sense. However, the derivatives that I once found confusing got seemingly easier. I figured out the simple ones. It seemed very straight forward and I felt a little stupid for not remembering how to do it sooner. For example if you have an equation that like x^4+3x^3+x^2+x+5 the derivative would be something like 4x^3+9x^2+2x+1. What you do is take the power and multiply it by the number before the x, I do not remember the word for that number. Anyway, after I figured that out the rest of these seemed easy. There are a few that have set derivatives, such as sine and cosine. Then the chain rule involves equations that are multiplied by each other.  Those seemed pretty easy as well, once I figured that out.

Quite a bit of the problems were difficult for me to understand. There were a few involving multiple equations. F(x) can equal multiple equations. A few of these are involved in finding what numbers corresponding to the variables a and b. Once I figured out how to do that first equation like this the next one was easier. They are still hard though.

Internet searches proved very useful. I had quite a bit of questions. It is pretty easy to look at the problems and then see the solutions. But connecting the two parts seems a bit harder. The middle step does not work in my head all the time. That is where the internet comes in. Examples help me a lot. I have to start taking more notes about what I fine confusing and what cites help me. Either way it seems to all work out in the end. I think I might understand about 50% of what I have learned so far. Another 30% would involve me refreshing my memory with some supplemental area, such as the internet or the calculus book. The last 20% I just do not know or understand anything about. I guess that is the part I would have to look more closely at.

Math just does not make sense. I just do not get it. Right now it is all geared towards psychology. So if someone wants to rant I can analyze it all kind of. At least that is the point I am working towards. Trying to think analytically with math just does not come as naturally to me. I guess psychology is more of a riddle I have the key to and math is a whole other language, like sandskrit or something really hard like that. I am really not good at riddles though

So I did not do all that much work last week. I had to do a lot of studying for exams and then write an essay for my medicine class using basically the book because my notes did not even talk about the topic I was writing about (since I was actually talking a lot about the development of medicine in the Enlightenment and we had just started talking about it kind of). So yesterday I decided to take a few hours and look more into the Slopes and Derivatives section ( since last time I had only done one problem, gotten it wrong, and moved on to something else). I did a little bit of looking online to find some of the formulas because I forgot to bring my notes book back with me from college. I found a couple random guides that help me on the first couple sets. I only did the problems that I had to but I think later today I will go back and do a few extra problems, just so I can feel comfortable in the fact that I understand the material.

This post might not make that much sense because I just woke up about ten minutes before I started typing. There is not much left to say though since I did not do that much work.

I am hoping to finish the problem set within the next couple of days. Then I can move on to part B.

So today I tried to master the first problem set. It did not go quite as planned. Some of the problems were easy. I figured out the first graphing ones by using the amazing, stupendous technological advancement known as the google. I did not search for the problems of course, if I want the answers there is an answer sheet already on the site. No, I went looking for ways to translate and change the scale of certain geometric equations (what the first problem set equations ask you to do). This is basically what we were talking about on the car ride to New College. I figured out, probably for the third time, how to graph the equation y = x^2 – 2x – 1. Because of the x^2 we know that the equation results in a parabola when it is graphed. The normal axis of symmetry for a parabola is at (0,0) because y = x^2. In our original equations that other numbers represent the translation done on the parent equation, the y = x^2. The first step in finding the x and y coordinates for the axis of symmetry is by completing the square. This process changes the formula to look like this: y = (x – 1)^2 -2. In this case the y coordinate is indicated by the -2. The x coordinate is indicated by the -1 attached to the x. For some reason, which I cannot remember and which is also link to another equation about parabolas that I cannot remember, the sign for the x coordinate is always the opposite of what it appears. In this case the -1 changes to a 1. So then, for this equations, the coordinates for the axis od symmetry is (1,-2) and then you graph it. There are a bunch of other equations that have translations, most of which are more difficult. I think that y = 1/x is one of the most difficult to graph once other numbers are involved.

Velocities and rates of change are hard as well. It is all just basic physics really. Therefore it causes terrifying flashback to the red x’s and green check marks that went up whenever you submitted homework answers to the UT Austin website. That is where our homework assignments came from for physics. Luckily we were given several tries before we got the answer completely wrong or right. Whenever I would get a problem set dome early I would always feel as though I had missed something. So yeah the velocity once where a little tricky and again the almighty google saves the day, adding more notes to my notebook so that I can remember all this stuff later.

The last set of problems I attempted where the slope and derivative equations. These got a little harder. My friend Zach offered to help me with the calculus if I had any questions. I will probably take him up on that. For some reason I think he well be really good at explaining things in a way that will make sense. I will probably ask for help on these derivative equations because I am having trouble getting the right answers.

Well that’s all for now.

So for these videos there are two separate teachers. The first 50 minute video is taught by the professor and the videos about the general rules for differentiation are taught by a substitute. The information taught by the teacher seemed pretty complex. He is trying to prove the parts of a previous equation involving sin and cos. In order to do this he must some a geometric proof, which pretty obviously involves drawing a picture. Sine and Cosine are usually represented with a unit circle, which means that theta – a greek letter that relates to angles. A circle is 2theta or 360 degrees. The first step in these proofs is to replace delta x with theta. Pretty straight forward… maybe. It is kinda hard to describe in words but basically you draw a circle with an angle created that ends in the center. The arc within the angle is the arc-length-theta. The vertical length of the angle, the line that would make a triangular shape within the pie shaped angle, is what sin(theta) measures.  So basically in class the teacher made a bow and arrow on the board. The equations is (2sin(theta)/2theta), where 2sin(theta) is the bow string and 2theta is the bow. This equation equals 1 when theta goes to zero. As theta gets smaller the bow part looks almost straight and the string and bow would merge to become one. As the teacher said “short pieces of curves are nearly straight.” There were a bunch of other proof part like this one, usually involving circles and thetas. Some were pretty easy to understand, and basically straight forward, others were more confusing.

So this video was pretty interesting. The professor stopped class what seemed half way through, I guess that class was over. Then during the next class there was a substitute teacher. On the video you could hear the rumblings of the students. That is what happens when there is a substitute. The class gets all rumbly, every time. Anyway we talked about the Rules for Derivatives. He went back over what the teacher did, but only slightly. These rules have to do with the general derivative equations. These do not confuse me as must because they are straight forward formulas. You look at the problem and if it looks a certain way then you set it up in a corresponding fashion. For example if you have a problem in the form (uv)’ ( the ‘ means it is the derivative of the functions within the parenthesis) equals u’v+uv’. Therefore you must know the derivatives of both of the functions u and v. The Product Rule changes one variable at a time. I think my problem lies in actually finding the derivative. I need to see some more examples. I will look up some more on the internet and see if I can replicate the examples.

The substitute was a bit more confusing than the normal teacher, but I should probably watch the videos again.  

Today I took a look at the calculus book. It is pretty helpful. I tried to look through the chapter on derivatives to see if any of it made sense. I looked at the problems first, which probably was not the best idea, so of course I had no idea what they were asking me to solve. I mean I knew what the equations where saying, I could understand the notation and such, but when I went to check my answers they were not right and I could not understand why I got them wrong. So then I went back to the previous chapter to see what that was about. Chapter  1: Introduction to Calculus, 1.5: A review of trigonometry. I took a lot of notes on the chapter. Read it a few times. And then did some of the homework problems. They went ok, but I think I still have to work on them. I did not do that many problems. Now I have more to do. Which is great because I still may not understand it? I am not sure. But anyway I will start working on it again tomorrow and see how far I get. First the video and then the book and then the homework problems. Seems like a great plan to me.

And now for some math jokes that I recently heard and thought where funny:

Q: What did one math book say to the other?

A: Don’t bother me I’ve got my own problems!

Q: What do you call a number that can’t keep still?

A: A roamin’ numeral

This math class did not go that bad. I was able to understand it some more so that is good. This class was about derivatives, which seem to be parts of math that are not terribly difficult. The teacher described that different types as two different “flavors,” specific formulas and general formulas. The general formals seem a bit abstract. But the specific formulas seem to be a bit easier. That is because they have a known formula to follow, I think, or at least they have a certain outcome. Apparently you need both of these types of formulas for polynomials so I guess I will be dealing with all of them eventually.

There are a bunch of things with trigonometry. I do not really like trig. A lot of that has to do with the fact that I did not like geometry I think. Something with the “try” at the end of those two words. It just seems to spell doom. Some of the formulas can be a bit confusing. The class had a really weird moment though when the teacher was explaining a property of Sin(a+b). The teacher said it was one thing and then a bunch of the students said that he was wrong. Then the teacher changed it and I knew that it was wrong. It just seemed wrong. And then a bunch more students protested so the teacher changed it back. He said that the first way was the right way. The most annoying part was that teacher seemed like he did not know which one was the right equation. Sometimes it is easy to tell when the teacher is asking a question where they know the answer and they are just testing you. But in this case I was really concerned that the teacher did not know what he was talking about. It was one of those weird “ya I was totally testing you” times when you really do not know what you are talking about and want to make people think you are.  But I guess that the teacher really did know what he was talking about? I am not sure. But eventually he got it right? I guess. It was kind of hard to tell.

Either way we moved on but he did the same thing when he came to the extended equation for a cosine function. It was just really bazar. I did not like it at all. Made me loose a bit of my confidence in his ability to teach. Other than that the videos are going well. I am hopefully able to grasp some of the information better with this new material. This section also has the videos with the teaching assistances so those will be helpfully if I start to loose understanding.  I am pretty interested in the way the next videos will go. For some reason it feels like there are not that many left but I think that is because I am getting done with part A when there is still part B left.