ratios, proportions, percentages, roots and exponents,
compound interest, basic
lengths, areas, and volumes
Then to get to computing topics with
a minimum of work:
some basic algebra, think of it
as arithmetic but with
symbols instead of actual
numerical values
can pass up plane geometry, or
just learn the Pythagorean theorem
and do see a good, simple proof (will
see it again with some nice generalizations in linear
algebra)
should touch on trigonometry,
such as can do in just a few hours,
that is, without a whole
one semester course
for calculus, here is the world's
shortest but still basically correct
course in calculus:
There are two parts to calculus,
differentiation and integration.
In a car, look at the odometer and a from it construct what the speedometer
reads. That's differentiation. Then
look at the speedometer for, say, a minute, and from those readings construct the change in that minute in the odometer. That is integration. So, each of these two undoes what the other one does, and that is the
fundamental theorem of calculus.
For more, maybe do some linear algebra -- the above will give you sufficient prerequisites. For linear algebra, look on the Internet for a text that is highly recommended (by a professor at a famous university, e.g., MIT, Princeton, Harvard, Stanford, Berkeley) and claimed to be a relatively elementary view.
That should be enough for a lot in
the early parts of
computing, computer science, and machine learning.
With a good teacher, might get through the whole thing in a month, a really good teacher, in a week.
Uh, I know VERY well what I'm talking about: I hold a Ph.D. in math with a lot in computing from a world famous research university. I taught computer science at Georgetown and Ohio State and math at Indiana University and Ohio State. I've published in pure and applied math, mathematical statistics, computer science, and
artificial intelligence. I've done serious applications of math and computing to US national security. Twice I saved FedEx from going out of business, once with some computing with a little math and once with just some math and a little computing.
basic arithmetic
ratios, proportions, percentages, roots and exponents, compound interest, basic lengths, areas, and volumes
Then to get to computing topics with a minimum of work:
some basic algebra, think of it as arithmetic but with symbols instead of actual numerical values
can pass up plane geometry, or just learn the Pythagorean theorem and do see a good, simple proof (will see it again with some nice generalizations in linear algebra)
should touch on trigonometry, such as can do in just a few hours, that is, without a whole one semester course
for calculus, here is the world's shortest but still basically correct course in calculus:
There are two parts to calculus, differentiation and integration. In a car, look at the odometer and a from it construct what the speedometer reads. That's differentiation. Then look at the speedometer for, say, a minute, and from those readings construct the change in that minute in the odometer. That is integration. So, each of these two undoes what the other one does, and that is the fundamental theorem of calculus.
For more, maybe do some linear algebra -- the above will give you sufficient prerequisites. For linear algebra, look on the Internet for a text that is highly recommended (by a professor at a famous university, e.g., MIT, Princeton, Harvard, Stanford, Berkeley) and claimed to be a relatively elementary view.
That should be enough for a lot in the early parts of computing, computer science, and machine learning.
With a good teacher, might get through the whole thing in a month, a really good teacher, in a week.
Uh, I know VERY well what I'm talking about: I hold a Ph.D. in math with a lot in computing from a world famous research university. I taught computer science at Georgetown and Ohio State and math at Indiana University and Ohio State. I've published in pure and applied math, mathematical statistics, computer science, and artificial intelligence. I've done serious applications of math and computing to US national security. Twice I saved FedEx from going out of business, once with some computing with a little math and once with just some math and a little computing.