@ComTruise No, I am just going through the "Help me solve this" guides to see how they do it and hoping that I am fortunate enough to do well on the test.
maybe your teacher just doesnt know how to communicate with you. I bet if you go to office hours or meet after class they will be able to help you more.
use the ebook, homework, quizzes and infinite practice tests to get familiar with the questions that will be on the test. as long as you don't do this too late, you will be able to ask questions about what you don't understand along the way, either in class or in office hours or even through email
@PedroTamaroff Knowing Math is great, but destroying someone's future computer science career just because he didn't do well in a course that had nothing to do with his career is just wrong.
But anyways, that's not the discussion. It's that I have a test and the teacher will put questions that will be mind-boggling.
@seaturtles Suppose we're given $n$ integers $a_1,\ldots,a_n$. Then there exists $1\leqslant k\leqslant \ell\leqslant n$ such that $a_k+a_{k+1}+\ldots+a_\ell$ is divisible by $n$.
while one can use anything from calculus 3 to group theory in computer science applications, depending on what you want to be and do all you should need is some practical linear algebra and discrete math knowledge/intuition
The question was from a job interview I had today, and the interviewer asserted it could be done without long calculations, but it's not at all clear to me how to do that
I agree with you. I think they would say that it's an indicator of general intelligence, flexibility of thinking, and how you handle yourself when confronted with new problems
I think I read somewhere that Google did a study and found that performance on brainteasers had essentially 0 correlation with performance on the job (at least at google)
Yeah, my area is finance stuff, so it definitely involves an understanding of prob and stats. Although I've gotten brainteasers at pure software firms as well
AFAIK, I only know that a sextic cannot be solved by elliptic functions - I have in general no idea about holomorphic functions of single variable. I just don't know enough alg. topology to appreciate Abhyankar's proof yet.
The elliptic function case is respectively easier : You have to prove that $A_6$ is not isomorphic to $\rm{PSL}_2(\Bbb F_p)$ for any prime $p$.
It's a near miss, though : $A_6 \cong \rm{PSL}_2(\Bbb F_9)$
$$\int_{0}^{\frac{\pi}{2}}\frac{1}{(1+x^2)(1+\tan x)}\,\mathrm dx$$
My Try: Let
$$\tag1 I = \int_{0}^{\frac{\pi}{2}}\frac{1}{(1+x^2)(1+\tan x)}\,\mathrm dx.$$
Put $x=\frac{\pi}{2}-x$. Using $\int_{0}^{a}f(x)\,\mathrm dx = \int_{0}^{a}f(a-x)\,\mathrm dx$.
So $$\tag2 I = \int_{0}^{\frac{\pi}{2}...
@BalarkaSen by that condition $f$ is monotone increasing, therefore differentiable almost everywhere. However, by the condition given it is nowhere differentiable.
$$\int_{0}^{\frac{\pi}{2}}\frac{1}{(1+x^2)(1+\tan x)}\,\mathrm dx$$
My Try: Let
$$\tag1 I = \int_{0}^{\frac{\pi}{2}}\frac{1}{(1+x^2)(1+\tan x)}\,\mathrm dx.$$
Put $x=\frac{\pi}{2}-x$. Using $\int_{0}^{a}f(x)\,\mathrm dx = \int_{0}^{a}f(a-x)\,\mathrm dx$.
So $$\tag2 I = \int_{0}^{\frac{\pi}{2}...
