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Aug
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answered Find 2 square numbers with certain distance
Aug
1
comment How find the maximum of the value $x^2_{1}+x^2_{2}+\cdots+x^2_{2014}$
Tips: 1) First try the problem with $2014$ replaced with $3.$ 2) Interpret the condition $x_1+x_2+x_3=0$ as the $x_i$ lying in a plane, and you want to maximize $x_1^2+x_2^2+x_3^3$ -- the square of the distance between the plane and the origin. Use geometric ideas!
Jul
31
comment The 3rd and 4th Critical Point?
@Winther My bad. I'm clearly up too late.
Jul
31
comment Bezout's bound and resultants - reference request
Try this.
Jul
30
answered In an extension of finitely generated $k$-algebras the contraction of a maximal ideal is also maximal
Jul
27
comment How do you calculate this limit $\lim_{n\to\infty}\sum_{k=1}^{n} \frac{k}{n^2+k^2}$?
Hint: $S(n) = \frac{1}{n} \sum_{k=1}^{\infty} \frac{(k/n)}{1+(k/n)^2}.$ Think about Riemann sums.
Jul
24
comment How do we know that $\mathbb{Q}$ is the initial field of characteristic $0$?
Every field of characteristic 0 has a copy of Q embedded in it. Any field map Q to F must send 1 to 1, and then the rest is determined.
Jul
23
comment Contraction mapping principle application
@Nick Differential.