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Apr
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Oct
17
comment Which mathematical ideas have done most to change history?
According to Aaron Brown, the "perfection" of derivative exchange (in which the BSM equation played a part) has caused derivatives to replace currency (hence the trillions of notional $ exchanged each year). A change in the currency system is on historical scale.
Oct
15
comment Which mathematical ideas have done most to change history?
A general audience probably wants to hear why they should care, something that is interesting to them, but maybe history-altering is not the way to go about this. War, disease, famine, exploitation, and tsunamis are history-altering, but not much fun. Small is beautiful.
Oct
9
comment Linear Algebra Texts?
This isn't exactly what you asked for, but maybe answers your question. math.miami.edu/~ec/book does abstract and then linear algebra. That makes for a nice flow, perhaps nicer than matrices → vector spaces. It is also short; I think that makes it gentle.
Sep
22
comment How to respond to “I was never much good at maths at school.”
Introducing oneself by topic area rather than "mathematician" can head off unpleasantries. If you say "I work on Wada basins" the other person will say "What's that?" rather than remember back to classroom torture.
Sep
14
comment Why do we teach calculus students the derivative as a limit?
You can do derivatives over ℤ without travelling off onto philosophical side roads. With a lagged difference operator (setting $h=1$) you can show that diff(1,4,9,16,25) = 3,5,7,9. This is simple enough that even non-university students could understand. One can't treat sinc this way, but maybe you could introduce h↓0 second (talk about 1/.00000003 and 1/−.000000003), after they understand symbolic differentiation of polynomials.
Sep
14
comment What should be offered in undergraduate mathematics that's currently not (or isn't usually)?
My undergraduate mathematics classes involved zero critical thinking and zero play. I don't think which subject matters, but typical areas could be approached so that students ask & answer questions like "Why do we want it to be this way?", "What would happen if we did it another way?", and "What would be the pro's and con's of doing it that way instead?". Time for this could come at the expense of covering more material.
Aug
13
revised How to write popular mathematics well?
Does
Aug
13
revised How to write popular mathematics well?
like / lie / spdf // this is getting longer
Aug
13
revised How to write popular mathematics well?
like / lie / spdf // this is getting longer
Aug
13
revised How to write popular mathematics well?
like / lie / spdf
Aug
11
revised How to write popular mathematics well?
complex simple
Aug
10
revised How to write popular mathematics well?
exupéry
Aug
10
revised How to write popular mathematics well?
emotional honesty
Aug
9
revised How to write popular mathematics well?
variables & formulae
Aug
6
revised How to write popular mathematics well?
added 401 characters in body
Aug
6
revised How to write popular mathematics well?
thurston
Aug
2
awarded  Necromancer
Aug
1
revised How to write popular mathematics well?
cut out extraneous info, not transition sentences
Aug
1
comment How to write popular mathematics well?
Here is some evidence about pictures. I lifted some pictures from Allen Hatcher's AT book and posted them on a website frequented by teens. They were reblogged/liked ~800 times. How many teens do you think navigated to math.cornell.edu/~hatcher/AT/ATpage.html and read any of his wonderful book? (Probably more after seeing the picture.) This is the power of brevity with the internet as distribution.