look up the prime number theorem. it draws a connection between the natural log and the distribution of prime numbers.
also, mathetical beauty doesn't necessarily have to be succinct...at least not to me. i think a lot of beauty can come from the results, even if the process that leads to...
it might be: Chases and Escapes: The Mathematics of Pursuit and Evasion by Paul J. Nahin.
but it came out in july, so i don't know if it's the book you're talking about.
hope this helps
if you define the function, you just have to put f(x) as the first argument.
like
f:=x-> x^2;
plot(f(x),x=-10..10,y=-10..10);
that would plot the parabola x^2 with a window of -10 and 10 on the x-axis and the same on the y.
the help file for these programs are confusing, imo
plot(f(x),x=-10..10,y=-10..10);
will plot f(x) between -10 and 10 on the x-axis, and -10 and 10 on the y-axis.
there's other arguments you can insert in the code, but that is just a basic plot.
no...didn't nod off in class...it's community college, they even skipped the whole section on infinite series...go figure
but thanks, that makes sense now. i just didn't get that it's a consequence of switching the order of integration. it wasn't immediately obvious to me.
i was looking through a book and came across a double integral that was split into the product of two single integrals.
it was int (x^n)(y^n ) dxdy split into (int x^n dx)(int y^n dy)
i just finished a course in multivariable calculus(it was by no means thorough), and i didn't know that...
house of the rising sun?
first song i learned how to play!
i do believe it is
Am - C - D - F - Am - E
along those lines...it's been awhile since I've played it
i guess it kinda depends on what style of music you want to examine.
a lot of songs are based one the I - IV - V progression found in blues(something you probably already know), but a thing to notice is that the II - V - I progression(found a lot in jazz music) can be that same structure...
someone probably already posted this, but:
Two mathematicians are in a bar. The first one says to the second that the average person knows very little about basic math. The second one disagrees, and claims that most people can cope with a reasonable amount of math. The first mathematician...