"Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral ∫ a b f ( x ) d x {\displaystyle \int _{a}^{b}\!f(x)\,dx} \int _{a}^{b}\!f(x)\,dx is defined informally as the signed area of the region in the xy-plane that is bounded by the graph of f, the x-axis and the vertical lines x = a and x = b. The area above the x-axis adds to the total and that below the x-axis subtracts from the total."
Oh, is that all!
Welcome to more of me failing to learn advanced math. Well, okay, it's not 100% accurate to say that I'm failing, but I'm being thwarted and blocked just a bit by unnecessary obtuseness such as that just quoted. I suspect that there may be a definition of definite integrals out there somewhere which is somewhat more comprehensible to people who don't already know what definite integrals are. I also suspect that communication with the general public is not a strong point among STEM (Science, Technology, Engineering and Math) nerds, and I suspect that it may not be a strong point because, generally speaking, they despise us. They don't particularly want to help. Maybe I'm completely wrong about that because what the Hell do I know about math anyway because for the last 40 years, ever since I finished 10th grade and all of the math I was ever required to study, I've been running away from math. Or maybe it's not the general public at all which nerds tend to despise, but me in particularly, because I in particular tend to offend nerds in some way.
Then again, maybe I'm right. I'm not the first to suggest such a thing. For example, some people have noticed how computers tend to be made by nerds for nerds, and not for the general public; that is to say, the general public has difficulties with computers not because these difficulties are inherent but because the nerds who made the computers don't care much, generally speaking, about the general public and its difficulties. Which is somewhat shocking when you consider that it is the general public which is directly responsible for the nerds making all of those gazillions of dollars, euros, yen and so forth. But they don't have to care because the general public has not yet caught up with the nerds enough to be able to choose the more user-friendly ones from among them, to borrow a nerdly phrase. And don't come at me with Apple, saying that Apple is that user-friendly brand of nerd right before my eyes which I refuse to see. Apple is a rip-off, and ripping people off ain't friendly.
There are not yet enough computer nerds that they have to compete with each other for the approval of the general public. 100 years ago, auto mechanics were just as smug and unbearable as computer nerds are now. A meager supply of mechanics and a huge demand for their services gave them elite status, and they abused the situation and were assholes about it, preferring to be moody geniuses rather than to be helpful and nice and have lots of friends. Then more people learned how to make and fix automobiles, and all of a sudden it wasn't an elite profession any more, and those who had so recently thought of themselves as geniuses suddenly had trouble finding work, and they had no friends to help them.
Those who do not learn from history are condemned to repeat it, STEM nerds.
Showing posts with label calculus. Show all posts
Showing posts with label calculus. Show all posts
Tuesday, April 11, 2017
Monday, February 20, 2017
Maybe My Passion For Math HASN'T Been Ignited At Last
4 days ago I wrote on this blog that perhaps I was finally finding math interesting. But there has not been much progress on that front since then. For quite a while I couldn't find the problem in the Thomas/Finney textbook on calculus and analytic geometry about the speed at which the man's shadow moved and the rate at which its length changed as he walked toward a lamppost. It was such a long while that I actually began to wonder whether I had merely dreamed the problem, and whether calculus would actually be any help which such questions. Then I googled Thomas Finney man lamppost shadow and deduced that the problem was in the 3rd chapter. In the 5th edition it's on page 132.
But I haven't made much progress at all in studying the preceding 131 pages. Whenever I begin to try, it's the sort of torture which the other 5 friends on Friends appear to feel whenever Ross begins to try to tell them about paleontology. I have tended to give up very quickly, and read about something else instead -- the history of India, for example, or paleontology. (I've always been disappointed when the other friends shut Ross down; I feel like I would have found what he had to say about paleontology interesting. Of course, Ross is just a fictional character, and I don't know whether David Schwimmer and all of the writers of Friends all put together actually know anything at all about paleontology or not.)
Clearly, I'm a geek. Just still not much of a math geek. I even felt the torture just now when I looked at a couple of calculators for scientists and attempted to learn what the symbols mean. I know the signs for add, subtract, multiply, divide, X to the power of Y, roots, percent, and... that's about it. (And actually, the % key is only on the calculator for non-scientists.) Presumably, studying those 131 pages would explain many more of the keys for me.
It's just really hard, because I really hate it for some reason.
Is it all my math teachers' fault? No, I really doubt that. The math teachers I had represented a wide variety of personality types. There was no lack of love of the subject among them. And I had a big crush on one of them. Between all of that, and my native aptitude -- I mentioned in the previous post that I had factored 3-digit numbers in my head years before a math teacher told me that it was called factoring, and that those numbers which could only be divided by themselves and 1 were called prime numbers, and that one could refer to 125 as 5 to the 3rd power, and so on. Just to be clear: by the age of 5 or so, I had factored all of the numbers up to and past 1000 in my head, in addition to many much larger numbers such as 1 billion and 15,625 and 6561 -- between all of that, perhaps a passion for math would have been kindled in me back in school if it could at all have been.
Even the factoring in my head has never been fun. It's always been tedious. I didn't start doing it because it was fun, but because I often couldn't stop doing it when my mind my wasn't occupied with something I found interesting, like history or music.
So -- put the Nobel for Physics and the Fields Medal on hold for now. I apologize to my vast numbers of fans if they're disappointed now because I got their hopes up about the math. For now, you'll have to settle for me being a literary genius, profound philosopher and all-around adorable person, as usual, and for me being able to tell when a candidate in the primaries no longer has a chance before most people, although maybe not before Rachel Maddow and Barack Obama, and things like that.
But I haven't made much progress at all in studying the preceding 131 pages. Whenever I begin to try, it's the sort of torture which the other 5 friends on Friends appear to feel whenever Ross begins to try to tell them about paleontology. I have tended to give up very quickly, and read about something else instead -- the history of India, for example, or paleontology. (I've always been disappointed when the other friends shut Ross down; I feel like I would have found what he had to say about paleontology interesting. Of course, Ross is just a fictional character, and I don't know whether David Schwimmer and all of the writers of Friends all put together actually know anything at all about paleontology or not.)
Clearly, I'm a geek. Just still not much of a math geek. I even felt the torture just now when I looked at a couple of calculators for scientists and attempted to learn what the symbols mean. I know the signs for add, subtract, multiply, divide, X to the power of Y, roots, percent, and... that's about it. (And actually, the % key is only on the calculator for non-scientists.) Presumably, studying those 131 pages would explain many more of the keys for me.
It's just really hard, because I really hate it for some reason.
Is it all my math teachers' fault? No, I really doubt that. The math teachers I had represented a wide variety of personality types. There was no lack of love of the subject among them. And I had a big crush on one of them. Between all of that, and my native aptitude -- I mentioned in the previous post that I had factored 3-digit numbers in my head years before a math teacher told me that it was called factoring, and that those numbers which could only be divided by themselves and 1 were called prime numbers, and that one could refer to 125 as 5 to the 3rd power, and so on. Just to be clear: by the age of 5 or so, I had factored all of the numbers up to and past 1000 in my head, in addition to many much larger numbers such as 1 billion and 15,625 and 6561 -- between all of that, perhaps a passion for math would have been kindled in me back in school if it could at all have been.
Even the factoring in my head has never been fun. It's always been tedious. I didn't start doing it because it was fun, but because I often couldn't stop doing it when my mind my wasn't occupied with something I found interesting, like history or music.
So -- put the Nobel for Physics and the Fields Medal on hold for now. I apologize to my vast numbers of fans if they're disappointed now because I got their hopes up about the math. For now, you'll have to settle for me being a literary genius, profound philosopher and all-around adorable person, as usual, and for me being able to tell when a candidate in the primaries no longer has a chance before most people, although maybe not before Rachel Maddow and Barack Obama, and things like that.
Thursday, February 16, 2017
Am I Finally Developing An Interest In Math?
I've always been freakishly good at doing arithmetic in my head. Not quite as good as Rain Man, but definitely unusual. However, I've never found mathematics to be interesting. I wonder whether that's an unusual combination of aptitude and disinterest. I stopped taking math classes in high school as soon as I was allowed to, at the end of 10th grade, when the algebra and geometry courses I had completed met the minimum requirements for graduation.
My younger brother took more advanced math courses. Much more advanced. My brother is literally a rocket scientist. He's got a Bachelor's and Master's of Science from MIT. As an undergrad he had a summer internship working for Martin Marietta and NASA on the Space Shuttle. Then between the Bachelor's and the Master's he took two years off from school and worked for a private company which has sent all sorts of things into orbit. A genuine rocket scientist. We're very proud of the little genius.
Every couple of years, I get an urge to study some more advanced math, and engineering and physics. The urge usually passes very quickly, but then again, it keeps coming back. About 30 years ago I had the urge, and my brother gave me this:
It's the 5th edition of Calculus and Analytic Geometry by George B Thomas and Ross L Finney, both professors at MIT when the 5th edition was published in 1979. It was a worn-out copy, my brother was done with it. I don't know whether he had studied this book in high school in preparation for MIT, or if it was the textbook for a freshman class he took at MIT, or maybe both.
I still have that old worn copy of the Thomas/Finney that my brother gave me. But I still haven't looked at it much. I'm currently having another one of those urges to make myself interested in math. But that's just the problem: math remains excruciatingly boring to me. But now I've been looking at that textbook, paging through it. And also looking at other books such as Blatt and Weisskopf's Theoretical Nuclear Physics, Rojensky's Electromagnetic Fields and Waves and Tolstov's Fourier Series. Looking for something which I can honestly say that I find interesting.
I may have found something. Thomas and Finney may have been rather sly when it came to education. There are a lot of word problems for the students to solve in their textbook, problems demonstrating some applications of calculus and analytic geometry, and one of those problems has actually caught my attention. That's right: something in a math book has begun to interest me.
I can't find that problem right now. I think it's somewhere in the first 50 pages or so of this textbook which runs to well over 900 pages. And it's a collage freshman textbook. Freshmen at MIT, which is certainly not the same thing as freshmen everywhere, but still. Early on in a freshman math textbook, there was a problem which I don't know how to solve.
Yes, it was arrogant of me, but I had wondered whether, in addition to boring me, this textbook would also teach me anything, or not. Arrogant, yes. But, for example, I was factoring 3-digit numbers in my head as a small child, years before a math teacher introduced me to the term "factor." Without finding it interesting. Just because it was there in my head.
But somewhere toward the front of Thomas/Finney 5th ed is a problem which, reconstructed from memory, goes something like this: a person of height X is walking at speed Y directly toward a streetlamp of height Z. Determine the rate at which the length of X's shadow decreases.
I can't do that. But apparently the first chapter or two of this textbook will show me how to do it. (Assuming I'm smart enough to understand what the book says.)
And that is interesting. That is definitely an example of something this textbook could teach me. And, apparently, that's just the beginning of introductory calculus. Just scratching the surface.
That's pretty cool.
So, you realize what this means, right? That's right: I'm going to be the first person to win a Nobel Prize in Literature and another one in Physics, plus a Fields Medal.
My younger brother took more advanced math courses. Much more advanced. My brother is literally a rocket scientist. He's got a Bachelor's and Master's of Science from MIT. As an undergrad he had a summer internship working for Martin Marietta and NASA on the Space Shuttle. Then between the Bachelor's and the Master's he took two years off from school and worked for a private company which has sent all sorts of things into orbit. A genuine rocket scientist. We're very proud of the little genius.
Every couple of years, I get an urge to study some more advanced math, and engineering and physics. The urge usually passes very quickly, but then again, it keeps coming back. About 30 years ago I had the urge, and my brother gave me this:
It's the 5th edition of Calculus and Analytic Geometry by George B Thomas and Ross L Finney, both professors at MIT when the 5th edition was published in 1979. It was a worn-out copy, my brother was done with it. I don't know whether he had studied this book in high school in preparation for MIT, or if it was the textbook for a freshman class he took at MIT, or maybe both.
I still have that old worn copy of the Thomas/Finney that my brother gave me. But I still haven't looked at it much. I'm currently having another one of those urges to make myself interested in math. But that's just the problem: math remains excruciatingly boring to me. But now I've been looking at that textbook, paging through it. And also looking at other books such as Blatt and Weisskopf's Theoretical Nuclear Physics, Rojensky's Electromagnetic Fields and Waves and Tolstov's Fourier Series. Looking for something which I can honestly say that I find interesting.
I may have found something. Thomas and Finney may have been rather sly when it came to education. There are a lot of word problems for the students to solve in their textbook, problems demonstrating some applications of calculus and analytic geometry, and one of those problems has actually caught my attention. That's right: something in a math book has begun to interest me.
I can't find that problem right now. I think it's somewhere in the first 50 pages or so of this textbook which runs to well over 900 pages. And it's a collage freshman textbook. Freshmen at MIT, which is certainly not the same thing as freshmen everywhere, but still. Early on in a freshman math textbook, there was a problem which I don't know how to solve.
Yes, it was arrogant of me, but I had wondered whether, in addition to boring me, this textbook would also teach me anything, or not. Arrogant, yes. But, for example, I was factoring 3-digit numbers in my head as a small child, years before a math teacher introduced me to the term "factor." Without finding it interesting. Just because it was there in my head.
But somewhere toward the front of Thomas/Finney 5th ed is a problem which, reconstructed from memory, goes something like this: a person of height X is walking at speed Y directly toward a streetlamp of height Z. Determine the rate at which the length of X's shadow decreases.
I can't do that. But apparently the first chapter or two of this textbook will show me how to do it. (Assuming I'm smart enough to understand what the book says.)
And that is interesting. That is definitely an example of something this textbook could teach me. And, apparently, that's just the beginning of introductory calculus. Just scratching the surface.
That's pretty cool.
So, you realize what this means, right? That's right: I'm going to be the first person to win a Nobel Prize in Literature and another one in Physics, plus a Fields Medal.
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