Intereting Posts

Prove that a complex-valued entire function is identically zero.
$f_n(x_n)\to f(x) $ implies $f$ continuous – a question about the proof
How can I calculate “most popular” more accurately?
Series Summation,Convergence
product is twice a square
explanation for a combinatorial identity involving the binomial coefficient
Is $B = A^2 + A – 6I$ invertible when $A^2 + 2A = 3I$?
Asymptotics of $1^n + 2^{n-1} + 3^{n-2} +\cdots + (n-1)^2 + n^1$
Do you know any almost identities?
Upper/lower bound on covariance two dependent random random variables.
Motivation for the importance of topology
Examples of group-theoretic results more easily obtained through topology or geometry
Equality of positive rational numbers.
calculating angle in circle
The dual of the Sobolev space $W^{k,p}$

Let $ Y = \{ (1,1),(0,0\} \subset \mathbb A_k^2$. Find the $ \mathbb I(Y)$.

As if $f(x,y) \in \mathbb I(Y)$ then as $f(0,0)=0$ hence constant term of $f$ is zero and as $f(1,1)=0$ therefore sum of the coefficients of $f(x,y)$ is zero. But how can we describe this set properly?

- Connection between algebraic geometry and complex analysis?
- The image of the diagonal map in scheme
- What is the equation describing a three dimensional, 14 point Star?
- Intuition Behind, or Canonical Examples of Finite Type Morphisms
- Hartshorne, exercise II.2.18: a ring morphism is surjective if it induces a homeomorphism into a closed subset, and the sheaf map is surjective
- Does the fibres being equal dimensional imply flatness?

- Localization of a ring which is not a domain
- When does $\mathfrak{a}B\cap A = \mathfrak{a}$?
- Every maximal ideal is principal. Is $R$ principal?
- geometric motivation for negative self-intersection
- Is a function in an ideal? Verification by hand and Macaulay 2
- Ring with spectrum homeomorphic to a given topological space
- What are the irreducible components of $V(xy-z^3,xz-y^3)$ in $\mathbb{A}^3_K$?
- Hypersurfaces meet everything of dimension at least 1 in projective space
- Why isn't $\mathbb{C}/(xz-y)$ a flat $\mathbb{C}$-module
- Image of the Veronese Embedding

Note that $f\in (x,y)\cap (x-1,y-1)$. Now try to show this: $$(x,y)\cap (x-1,y-1)=(x-y,x(x-1),y(y-1)).$$

Furthermore, $$(x-y,x(x-1),y(y-1))=(x-y,x^2-y).$$

- Adjoint functors
- What is the primary source of Hilbert's famous “man in the street” statement?
- Modified gambler's ruin problem: quit when going bankruptcy or losing $k$ dollars in all
- Group cohomology or classical approach for class field theory?
- Can we construct a $\mathbb Q$-basis for the Pythagorean closure of $\mathbb Q?$
- Yet another definition of Lebesgue integral
- Closest points on two line segments
- Proving an Entire Function is a Polynomial
- How many limit points in $\{\sin(2^n)\}$? How many can there be in a general sequence?
- How do the $L^p$ spaces lie in each other?
- Book recommendation to prepare for geometry in the International Mathematical Olympiad
- Degree of minimum polynomial at most n without Cayley-Hamilton?
- Evaluating and proving $\lim_{x\to\infty}\frac{\sin x}x$
- If $f(x)$ and $g(x)$ are Riemann integrable and $f(x)\leq h(x)\leq g(x)$, must $h(x)$ be Riemann integrable?
- How to prove that if $\lim_{n \rightarrow \infty}a_n=A$, then $\lim_{n \rightarrow \infty}\frac{a_1+…+a_n}{n}=A$