I was pleasantly surprised by this essay. Whenever someone approaches me because they are learning "advanced math" in reference to calculus I suppress an internal eyeroll. This is a personal...
I was pleasantly surprised by this essay. Whenever someone approaches me because they are learning "advanced math" in reference to calculus I suppress an internal eyeroll. This is a personal failing. But it feels akin to a USian calling travel to Canada "traveling abroad" or coining oneself a bibliophile after reading some Shakespeare.
But I am impressed with the depth and wonder that the author experienced. He recognizes the mystery and breadth than draw mathematicians into committing their life to the subject. The author also does well to describe the mindset and setbacks experienced studying subjects like math. A continuous struggle to stretch your mind and incorporate new concepts. A perseverance to see intangible world that all mathematicians agree is there. Even years away from math I will inspect a concept I used to struggle with and find that with time my mind has continued to digest and what once seemed formal now feels natural and obvious.
Agreed on all points. One challenge I would present is the following. In any other field would material potentially covered in high school or first year of a degree program be called advanced?...
Agreed on all points. One challenge I would present is the following. In any other field would material potentially covered in high school or first year of a degree program be called advanced? Intro physics uses calculus as a prerequisite, does that mean newton's laws are advanced physics?
Edit: the point I am trying to illustrate is that as a society we do extremely poorly exposing students to mathematical concepts. I am not diminishing the effort people put into learning calculus. I taught it for 5 years, I know the struggle students go through. There is just no context in our society for what advanced math is.
I find that this is a personal frustration of mine. I am a grad student in a math department (my area of study is statistics) and I love math. But it is impossible to share this joy with others...
There is just no context in our society for what advanced math is.
I find that this is a personal frustration of mine. I am a grad student in a math department (my area of study is statistics) and I love math. But it is impossible to share this joy with others because as soon as you mention the word "math" they default to thinking about some 7th grade math class they struggled in and they feel disgusted.
I try to explain that higher level study in math is closer to the study of philosophy than, say, engineering, and that math perhaps shouldn't be thought of as being about numbers so much as being about axioms from which we abstract underlying "truths."
I mean, if I had a dime for every time someone saw a textbook or homework of mine where I told them it was for a math class and they said "but where are all the numbers," I'd have a lot of dimes. But I think if you think math is about numbers, you're missing the point. Perhaps "quantities" or "structures" would be better terms.
Regardless, many people start hating math at some point in grade school and live with that sense of disgust for the rest of lives. All I want to do is to share the sentiment that math is actually kind of cool, and probably nothing like what you think it is.
I think typically there are two physics courses: one for engineering + science majors, and one for everyone else. The math in the latter does not require calculus. (As a result, formulas and...
Intro physics uses calculus as a prerequisite
I think typically there are two physics courses: one for engineering + science majors, and one for everyone else. The math in the latter does not require calculus. (As a result, formulas and concepts are basically presented as magic because students don’t have the math skills to comprehend where they come from)
I'm halfway-ish through a mechanical engineering degree after taking a 10 year break from college. To try and catch up a bit, since almost all the classes delve into calculus to some degree, and...
I'm halfway-ish through a mechanical engineering degree after taking a 10 year break from college. To try and catch up a bit, since almost all the classes delve into calculus to some degree, and some quite deeply, I watched through most of this playlist: https://youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
Full disclosure, I haven't finished watching all of it, but I thought it did a great job of explaining the theory of calculus.
I like that sentence about the intangible world. Calculus was when I felt I actually "got" math, because I had a professor who was just awesome at helping me look at that world, so to speak. It...
I like that sentence about the intangible world. Calculus was when I felt I actually "got" math, because I had a professor who was just awesome at helping me look at that world, so to speak. It changed how I reasoned about things, and how I visualize stuff. My degree was a B.S. in Philosophy, so I ended up taking classes in things like symbolic logic and epistemology not long after, and it really felt like I'd put together a hella-good lens of analysis with all these bits and pieces.
That professor though, I can't praise him enough. I was someone who'd thought math was just beyond me, and I think in retrospect I just had shit teachers. That guy was willing to dive in however which way made sense to me, and that was just great.
I was pleasantly surprised by this essay. Whenever someone approaches me because they are learning "advanced math" in reference to calculus I suppress an internal eyeroll. This is a personal failing. But it feels akin to a USian calling travel to Canada "traveling abroad" or coining oneself a bibliophile after reading some Shakespeare.
But I am impressed with the depth and wonder that the author experienced. He recognizes the mystery and breadth than draw mathematicians into committing their life to the subject. The author also does well to describe the mindset and setbacks experienced studying subjects like math. A continuous struggle to stretch your mind and incorporate new concepts. A perseverance to see intangible world that all mathematicians agree is there. Even years away from math I will inspect a concept I used to struggle with and find that with time my mind has continued to digest and what once seemed formal now feels natural and obvious.
Agreed on all points. One challenge I would present is the following. In any other field would material potentially covered in high school or first year of a degree program be called advanced? Intro physics uses calculus as a prerequisite, does that mean newton's laws are advanced physics?
Edit: the point I am trying to illustrate is that as a society we do extremely poorly exposing students to mathematical concepts. I am not diminishing the effort people put into learning calculus. I taught it for 5 years, I know the struggle students go through. There is just no context in our society for what advanced math is.
I find that this is a personal frustration of mine. I am a grad student in a math department (my area of study is statistics) and I love math. But it is impossible to share this joy with others because as soon as you mention the word "math" they default to thinking about some 7th grade math class they struggled in and they feel disgusted.
I try to explain that higher level study in math is closer to the study of philosophy than, say, engineering, and that math perhaps shouldn't be thought of as being about numbers so much as being about axioms from which we abstract underlying "truths."
I mean, if I had a dime for every time someone saw a textbook or homework of mine where I told them it was for a math class and they said "but where are all the numbers," I'd have a lot of dimes. But I think if you think math is about numbers, you're missing the point. Perhaps "quantities" or "structures" would be better terms.
Regardless, many people start hating math at some point in grade school and live with that sense of disgust for the rest of lives. All I want to do is to share the sentiment that math is actually kind of cool, and probably nothing like what you think it is.
I think typically there are two physics courses: one for engineering + science majors, and one for everyone else. The math in the latter does not require calculus. (As a result, formulas and concepts are basically presented as magic because students don’t have the math skills to comprehend where they come from)
I'm halfway-ish through a mechanical engineering degree after taking a 10 year break from college. To try and catch up a bit, since almost all the classes delve into calculus to some degree, and some quite deeply, I watched through most of this playlist: https://youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
Full disclosure, I haven't finished watching all of it, but I thought it did a great job of explaining the theory of calculus.
I like that sentence about the intangible world. Calculus was when I felt I actually "got" math, because I had a professor who was just awesome at helping me look at that world, so to speak. It changed how I reasoned about things, and how I visualize stuff. My degree was a B.S. in Philosophy, so I ended up taking classes in things like symbolic logic and epistemology not long after, and it really felt like I'd put together a hella-good lens of analysis with all these bits and pieces.
That professor though, I can't praise him enough. I was someone who'd thought math was just beyond me, and I think in retrospect I just had shit teachers. That guy was willing to dive in however which way made sense to me, and that was just great.
Mirror for those hit by the paywall:
https://archive.is/ja0Rb