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Part of what makes (re)learning basis math difficult is the lack of math textbooks written for adults. Most math books are either too advanced (assume prior kno

by ivan_ah 13y ago

Part of what makes (re)learning basis math difficult is the lack of math textbooks written for adults. Most math books are either too advanced (assume prior knowledge) or too basic (assume reader is retarded). In both cases, an otherwise intelligent adult with some gaps in their knowledge will get discouraged. I wrote a math textbook which starts off from the very basics (numbers, equations, functions) and proceeds all the way to university level topics like calculus and mechanics. Check out the "No bullshit guide to math and physics:" http://minireference.com http://minireference.com

bobbles 13y ago
This is what I tend to struggle with when reading maths textbooks. Example from your page: Suppose that you monitor the file size during the entire download and observe that it is described by the function: f(t)=0.002t2[MB]. - 'Supposed that it is described by the function' - Where does this function come from? Is it derived from something else?
- ivan_ah 13y ago
  I understand your unease. In this case I totally pulled this equation f(t)=0.002t^2 out of nowhere. It is just "some" function that satisfies f(0)=0 and f(600sec)=720MB. I basically skipped (invented) the modelling step. In practice you would observe the download size f as a function of time t, and then ask yourself "which function f(t) correctly describes what I see." I wanted to describe a download that gets faster and faster with time, so I picked a quadratic function f(t)=At^2 as a template, then chose A=0.002 so the function matches the problem statement. Suppose instead I wanted the download rate to be uniform (constant download speed), then the function which describes the file size would be of the form f(t) = mt+b. More specifically, the function would be f(t)=720/600t+0=1.2t. (You can check that f(0)=0 and f(600)=720, as in the problem setting). In general, once you become familiar with the main function families f(t)=mx+b, f(t)=ax^2+bx+c, f(t)=Aexp(kx), f(t)=ln(x), f(t)=Asin(kx-ϕ), etc, you will be able to describe real-world phenomena by using one of these equations. This ability to "model" the real world through mathematical equations is one of the super-powers that comes with math knowledge, but my download example doesn't quite manage to communicate that. I will have to rework it... For a slightly better example of "modelling" using equations, check out page 26 in the PDF preview: http://cnd.mcgill.ca/~ivan/miniref/miniref_v4_preview.pdf#page=26 http://cnd.mcgill.ca/~ivan/miniref/miniref_v4_preview.pdf#pa...

by ivan_ah 13y ago

bobbles 13y ago

This is what I tend to struggle with when reading maths textbooks. Example from your page: Suppose that you monitor the file size during the entire download and observe that it is described by the function: f(t)=0.002t2[MB]. - 'Supposed that it is described by the function' - Where does this function come from? Is it derived from something else?

ivan_ah 13y ago
I understand your unease. In this case I totally pulled this equation f(t)=0.002t^2 out of nowhere. It is just "some" function that satisfies f(0)=0 and f(600sec)=720MB. I basically skipped (invented) the modelling step. In practice you would observe the download size f as a function of time t, and then ask yourself "which function f(t) correctly describes what I see." I wanted to describe a download that gets faster and faster with time, so I picked a quadratic function f(t)=At^2 as a template, then chose A=0.002 so the function matches the problem statement. Suppose instead I wanted the download rate to be uniform (constant download speed), then the function which describes the file size would be of the form f(t) = mt+b. More specifically, the function would be f(t)=720/600t+0=1.2t. (You can check that f(0)=0 and f(600)=720, as in the problem setting). In general, once you become familiar with the main function families f(t)=mx+b, f(t)=ax^2+bx+c, f(t)=Aexp(kx), f(t)=ln(x), f(t)=Asin(kx-ϕ), etc, you will be able to describe real-world phenomena by using one of these equations. This ability to "model" the real world through mathematical equations is one of the super-powers that comes with math knowledge, but my download example doesn't quite manage to communicate that. I will have to rework it... For a slightly better example of "modelling" using equations, check out page 26 in the PDF preview: http://cnd.mcgill.ca/~ivan/miniref/miniref_v4_preview.pdf#page=26 http://cnd.mcgill.ca/~ivan/miniref/miniref_v4_preview.pdf#pa...