Category: math & science

Calculus 1 Day X, or Teachers make a difference

There are only six or so more meetings of my calculus class, and one of those is for the final exam. So… long story short, I’m PROBABLY getting a B. Unless I ace the final AND my professor loads on ridiculous amounts of extra credit opportunities that I’d also have to ace, an A is impossible this semester. I’m pretty sure to get a B though, unless I just stop working, or if in the next week, ol’ Prof serves up some wicked hard crazy impossible-to-remember shit.

The thing is, it’s so much of a bummer. I don’t recall ever having worked so hard on something, and then getting such lackluster results. The curse of being a “gifted child,” I guess? Sure, I’ve failed tests and even courses in my day — but not after trying to pass. I only failed before because I was truant or lazy or just didn’t pay attention…

Now, I’m not FAILING calculus. But I am trying really hard to do well, and I’m not meeting my goal! It’s depressing. Do you know what a 5.0 unit ‘B’ does to a girl’s GPA? 😦

God help me not get a C! I don’t even know what I’d do in that case! Maybe quit college and go back to the Navy.

So I’m bummed, but still trying to at least correct myself enough that I feel semi-prepared for Calculus II next month. And I thought it would be worth talking about speech class today, too:

I only have ten minutes between math and speech classes, so I hustle, use the little girls’ room, and mow down an apple and maybe some nuts on the way to the latter class. Usually I arrive with a couple of minutes to spare, so I stand outside, eating my apple. Why? Because I’m seemingly the only person at my school who a) doesn’t eat in buildings/rooms where you’re not supposed to eat in the first place, and b) realizes that nobody wants to hear me eating! Ugh!

Anyway, so today I was eating my apple outside of class as usual, when the teacher came out (I call her a teacher, not a professor, because that’s what she calls herself).

“To what do I owe the honor of having you in my class?” she asked.

Whoa.

To be honest, yes, her class is annoyingly cake-like sometimes. It’s easy, and frustratingly so at times. Some things I’m just good at, experienced at, or “get.” (Calculus apparently ain’t one of them!) I know this, but I don’t like talking about it. I don’t want to seem arrogant to anybody, but even more so, I don’t want to BE arrogant. That’s not who I want to be. Humility is great, plus, no one knows everything… so even if I were the world’s leading authority on speech, I’m sure I could still learn things from people in this class I’m taking.

So anyway, I felt a little awkward because once people identify/label you as “smart” in some way, they just look at you differently, and sometimes treat you differently. I don’t want that (though yes, I did when I was younger, but that’s another story).

So Ms. R. elaborated on what she was asking, and asked me about my previous courses and things. It made sense to her why I am one of her top students. She asked me my major, and I literally laughed at myself when I answered, “Physics.” I’m sure a lot of people hear that and think, “Whoa, smarty smart smart!” but when I say it (more like confess it), what I’m thinking inside is, “Yeah, that’s what I want to learn about, but am I going to be able to hack it?”

My teacher thanked me for being a model student (her words), and I thanked her for what I took implicitly as a compliment. Now that I’m writing, it makes me think about the different times we thank people. When I was in Japan, it seemed like there was always a contest to see who could be the last person to say “Arigatou gozaimashita!” But that’s another post for… someday when I’m not devoting most of my time to thinking/studying/practicing/lamenting over calculus.

The point is that my calculus grade is bumming me out, but my speech teacher did add just the touch of individual attention and kindness to my day that really makes teachers wonderful. Not all of them of course. But some of them. Yeah. Did Ms. R. know she would at least get me off thinking about my calc grade for a minute? No, but she did, and she’s evening brightening my day a little bit right now, as I think about the fact that she really didn’t need to go out of her way to talk to me. Teachers have no idea sometimes.

Calculus 1 Day 14

I have only a tiny, tiny bit of computer programming knowledge, but I think it’s really helped me with some mathematical concepts (also my background working on electronics helps now and then).

But today as I was looking at average speed v. instantaneous speed v. acceleration, I thought what I’m sure many people have said over the centuries: math seems like a language. It seems like an explanation of things. But it’s not fluent (at least not yet to me) like a spoken language. It seems more like an instructional, logical computer language.

Then I was thinking about our world, I don’t know, like The Matrix or something like that. The world, existence, all of our movements, the movement of the particles smaller even than electrons… like an incredibly written and executed computer program written by God. Honestly, just thinking how technology has progressed just since I became aware of it in my life, it doesn’t seem crazy to me to think about existence in this sort of way. Maybe a long time ago, I’d have thought the world was too complex to be written (and its complexity is part of the reason I do believe and feel awed by God). But now I feel like infinite complexity…

Well, I actually don’t have time to be writing anything lengthy. My point is that I’m being reminded of the things that made me want to become a mathematician probably eight years ago. I think it’s pretty lame that so many people think of math+engineering, math+economics, math+concrete. To me, it seems so abstract, and always makes me ask questions that would really only be welcome in a philosophy class. Yet it is incredibly applicable to the physical world. Is it the code underlying our reality? Or is it a language we’ve created to describe our reality? The beautiful concepts suggested by math — are they simply expressions of what is otherwise less clear in our physical reality?

Ugh, I have no time. Really, I love it though. I truly do love it.

Calculus 1 Day 12

Today in class we learned to differentiate inverse trigonometric functions… which isn’t that difficult or interesting, really. Then we spent a long time talking about complex numbers, and how many things had been “hidden” from us throughout our lives learning mathematics.

I can’t decide if I think my professor is a really smart guy, or a bit of an ass. Probably every day he brings up some point or intricacy or method that he claims no one else will tell us, and is absent from every textbook out there — despite being totally legitimate. Probably every day he says that this or that teacher or author didn’t/doesn’t truly understand a given concept. He talks about the high failure rate of Calculus 1 all across the country, and how much lower the failure rate is in his classes. He brings up things we’ve already learned, and tells us we’ve been lied to or given half the truth. He goes on about how “some of you think there’s a worldwide shortage of parentheses,” and not only the fact that many of the students make notation errors (especially ≈ versus ≡ versus = versus another one I don’t know how to type in here), but the fact that many textbooks “get it wrong.”

I dunno. I believe what he says. I understand that being lazy about notation causes ambiguity. I appreciate application problems and in depth explanations and images of the concepts. I’ve definitely had teachers who totally mechanized math. Made it a series of boring steps. I just… I don’t know. I wish my professor would be a little more positive, I guess? I mean, maybe the guy who wrote our textbook was really a terrible mathematician. So why do we keep revisiting that point? I’d rather Prof. would say, “Oh, and so-and-so invented this stuff we’re looking at right now. What a genius, right?” I know I’m not the most positive person in the world, but I do try not to criticize people all the time.

So… complex numbers. Very cool stuff. I remember when I was a kid, wondering why during the first week or every math class, it seemed like they’d define the different sets of numbers. We never really got to understand the differences, and were never tested on what was what. I think I only knew some of the sets because I heard them repeated so many times. But today we went over that a little bit again, and I realized that it’s like I’m only starting to do math. Algebra is like the language. Geometry is like drawing (visualizing, writing). Trigonometry I can’t come up with some simile for, but is really pretty cool (largely because I find it easiest). And calculus? Calculus I don’t know, of course, but I get this feeling I’m on the brink of something. On the brink of some real, abstract, beautiful mathematics.

Not going to be an ornithologist

I was going to–and will still, in a minute–write about not majoring in biology. Then I logged in here, and I saw that I have 43 followers. Probably that is not many, but still… I’m pretty surprised. Seriously.

Well, I’ve adequately expressed my surprise; now back to biology.

When I went to make my first ‘academic plan’ or whatever the tentative schedule is that we GI-billers must keep on file, I said I intended to major in general biology. And I did intend to. It makes sense in many ways. Lots of fields, let alone jobs, are based in biology. Probably a lot of biology knowledge would be useful in case of some sort of apocalyptic situation. I am super interested in health, fitness, preventing illness, animals, gardening, and other stuff involving living things. I think I might even be the youngest bird watcher in the world (I’m 25).

But death makes me sad.  Not all of it, of course, but enough of it that I can’t see myself working with endangered species, giving mice cancer, or collecting specimens.

The whole specimen thing is what got me thinking of this again today (I figured out bio wasn’t for me months ago). NPR has an article up about some folks’ article saying that collecting specimens of wild animals is maybe not always the best thing to do. I’m not writing to weigh in on that debate, although, as a former Girl Scout, I don’t take anything out of its place myself… Except a pretty rock once in a while, for the bird bath. Anyway, the article had a picture with it of some birds pinned down.

Hm. How do I express myself on this? Death for scientific progress, and potentially conservation, is still just… Not my cup of tea. I dunno.  I’m really not that much of a softy or anything, and I do eat meat (though I admit I was a vegetarian for about eight years), but there is something about dead birds in particular that just stirs me terribly. I have several images in my mind of experiences with birds, but the most haunting is the goldfinch memory. Last year, for a few months, my husband and I had a goldfinch feeder hanging from our balcony. We could get about eight or nine lesser goldfinches on there at once, and they became one of my favorite animals in the world. They’re so small, so pretty, and have such a lovely call. Also, I love the way they fly; it’s like they launch themselves like little arrows, and land only wherever they catch a grip. It’s just a plus that feeding them is less messy than feeding, say, house finches.

Anyway, one day, I got home around 4 pm, and I think I was even in a good mood. I’d gotten an A on a math or Japanese exam or something. But my husband had a sad look, and he took me to the glass door to see a goldfinch that was somehow stuck at the bottom of the door. K. said it had just happened, and he was glad I was home because he didn’t know what to do. The bird had flown into the door.

Well, I carefully got outside (because I couldn’t slide the door much, the bird being stuck in the track somewhat). I released the bird from where it was stuck… I think it was just that these birds have hook like feet… and it was just frozen. But it was alive. I could see it looking around as it lay in my hand. Did it move? Was its heart beating hard and fast? I don’t know because my own heartbeat had gotten louder. At first, I put the bird down in a planter, hoping it would fly away on its own. But it was cold and very windy that day, so I picked up the tiny creature again, feeling like a dangerous, giant, unsophisticated thing myself, and I placed it instead on the soil of a potted plant I had nearby. The level of soil was low enough compared to the rim of the pot that I thought this would provide better shelter. Of course I went inside to consult Google, hoping that other people recommended the course of action I had intuitively taken. They did, but I had doubts. I felt extremely sad, and I cried much  harder over this than I had over other things that most people would consider much more significant. I guess, in my Eden, harmless little birds are immortal. I felt bad because it was my door that hurt the bird. It appeared to me one of its feet might be broken. What do I do? I felt bad picking up the creature, looking at it, putting it down, picking it up again. Maybe it was too stunned then to even have been afraid of me. How should I know? The few moments that I had held the bird are like a very long time in my memory, because the feelings were so strong. I felt powerful in a terrible way.

I think I was thinking about my next step, once I paused crying, and looked out the glass door again. I didn’t see the bird in the pot anymore though. I went out to see, and indeed, it must’ve managed to fly away. Of course my dark imagination would speculate that the bird would just starve because its foot was broken, or this or that. I don’t know what happened ultimately. I don’t even know the typical lifespan of a goldfinch anyway. But I knew that even when these sort of stories have happy endings, they are too much for me. I hate pain and death and fear in creatures like this. Of course we must all hate these things in all of creation, mustn’t we? But maybe it’s just more poignant to me with birds because of what they can symbolize. Untainted nature. Innocent existence. Beauty. Freedom. Absence of ego. The marvelous, intricacy of all that God has made: those specially shaped feet, those tiny feathers, the deep black beak, the always moving eyes — not to mention every little bone and organ and cell and organic compound…

Even to help these creatures, I couldn’t hurt one. I couldn’t look at a single dead one without feeling sad. This whatever it is isn’t the only reason, nor, I realize, is it exactly a “reason,” why I don’t want to study biology beyond what I already have.

I have more thoughts and feelings on this sort of thing, you know, involving conservation, creation, and so on. But it’s so complex. I just wanted to take a few minutes to write down what happened with the goldfinch. I think it may even be an insight into love. What is a little bird to me, that I should be so moved thinking of it, many months after I even saw it? What is man, O Lord, that you should look at him? It is something I have been thinking lately, too, about the fundamental goodness of humanity, and about Christ. It is easy enough to say, “I do not deserve this,” or “I am unworthy,” or “I have sinned,” or even, “I cannot stop sinning.” It is easy to feel inadequate, guilty, and other things. It is true that we do not gain redemption ourselves, but only by the grace of God. It is true that Christ died for our sins. But it is also true that God loved us before he saved us; he loved us — loves us — even in our most disgusting, miserable, evil-doing states. It makes no sense, but that is love, I think. And I think the fact that God loves me and provides for my eternal salvation even when I am the worst, confirms that I am “good,” like he said in Genesis. I am not only the sum of my good and bad works. We are all creatures loved by God. Why? Well, why do I love the little goldfinch? I don’t know, but I feel it.

 

Calculus 1 Day 8

Haven’t started class yet, but it should be intense. Yesterday was. The thing is that calculus itself doesn’t seem too bad; only the aspects of algebra that I never completely mastered are now haunting me. It’s cool though because now I am having to go back and fill in the old holes in my skill set. This class is the most challenging I’ve had in college so far… But that makes it fun… I really didn’t like my pre-calc class, for example, because it was like a giant review of a few concepts in algebra and trig. (My calculus prof also says that pre-calc courses should focus on the binomial theorem, which mine did not; so for all I know, I really missed out.)

Anyway, it would be nice to write more, but everything is in a rush lately. Have I mentioned we’re moving today? Yeah, I packed boxes in lieu of studying last night.

Calculus 1 Day 3

I haven’t begun today’s homework, but class was excellent. Even though I was thrown by today’s quiz, many concepts were reinforced after it, and I feel like I have a better grasp of everything we’ve covered so far. Today we started talking about infinite limits. It was so wonderful because that’s like half the reason I have loved math for so many years. I knew the day would come when I would be studying more conceptual things, and I’m so excited that day is here. It will only get more fascinating. It’s also wonderful because so far I get it. The material makes sense. In fact, some problems we looked at I had to “solve” in previous courses… except in those courses, you memorized rules, and though these rules would get a correct solution, the “why” and “how” were completely missing. Calculus has already taught me at least one “why/how.” I know it’s still early, but I think I’m going to really like this professor; he doesn’t ask us to press the “I believe” button.

Calculus 1 Day 2

I have only a few more problems to work on this evening. I wish I had more time, because I’d like to look at some Khan Academy videos or something as well!

For now I am just satisfied that my husband is home, I am having a beer, and something I have been praying about appears not to be a worry anymore. It’s crazy how kind God is. I don’t write much about God anymore. I did as a teen (of course, then I wrote all the time). Anyway, it’s just that there are too many things about him. What can I say? You know the line from the psalm, “What is man that you should look at him?” or something like that? (Sorry, I admit I have not read a psalm outside of Mass in a long time). Well, I feel like, “What is man that he/she/I should write about God? I’m not St. Augustine. The more I learn, the less I feel I know. I’m totally okay about that, but… I just feel arrogant if I make too many assertions about God. I feel like it’s enough to say that he loves you and me and every person that you and I can’t even imagine anyone could love!

And he answers prayers. And he pierces your soul so that you question your own prayers, asking, “What I am praying for, is it right? Is my will your will, God? I know what I want and what I am asking, but I don’t want to ask if it isn’t what you want.”

Oh, so many thoughts! So many questions. But I really am satisfied because I like wondering about things. Wouldn’t it be a concern if God didn’t seem infinitely wondrous?

So anyway, day two of calculus wasn’t terrible. So far I am back and forth between feeling I totally understand, and feeling I understand nothing. It’s so fascinating, and the abstraction my professor keeps saying will throw some people off just reminds me why I’ve been so adamant about studying math, regardless of my major. Many people see math as some wonderfully concrete, understandable “thing.” It appeals to a lot of people who just like order. But there’s more than order and balance and strict applicability. There’s a beauty to it that I actually feel ridiculous beginning to talk about, just because I know I am so early in my math education. But I felt this even when I was learning high school trigonometry.

Now that I am older, and have seen the application of some mathematics in the real world, having worked on electronics, and learned JUST A LITTLE BIT about some of the engineering problems on ships, math is just so much cooler. Some of the concepts get reinforced. It just seems like math is underneath everything, down inside it… or, no. That’s like electrons and things. Math is more like music, isn’t it? The music is represented by symbols on paper, or it can be memorized. It can be played in many ways, felt, and heard. It is perceived, but what is it? Just so many sound waves? No.

So I don’t know how this class will go. It’s going to be tiring to complete this course in the eight weeks allotted. But it’s so stimulating. Well, back to it!