130 reputation
19
bio website nilaykumar.com/about
location New York, United States
age 20
visits member for 10 months
seen 2 days ago

Junior at Columbia University, studying mathematics and physics.


Mar
23
revised Closed orbits of complete flags in $\mathbb{C}^n$
edited tags
Mar
12
revised $\dim (A/I) \le \dim (A)$
added a reference
Mar
12
answered $\dim (A/I) \le \dim (A)$
Mar
12
asked Closed orbits of complete flags in $\mathbb{C}^n$
Jan
4
comment Finding frame bundles
What exactly do you mean by 'finding' a frame bundle? Isn't a frame bundle just the a principal G-bundle where the fiber over $x\in M$ is isomorphic to the group of (orthogonal in the Riemannian case) frames at $P_x$?
Sep
11
awarded  Enthusiast
Aug
29
answered Partial derivatives, don't know how to solve it
Aug
27
awarded  Citizen Patrol
Aug
27
revised Find all intermediate fields of extension $\mathbb{Q}(\sqrt{2} , \sqrt{3}) : \mathbb{Q}$ without using Galois correspondence.
Minor typos
Aug
27
answered Find all intermediate fields of extension $\mathbb{Q}(\sqrt{2} , \sqrt{3}) : \mathbb{Q}$ without using Galois correspondence.
Aug
27
comment Find all intermediate fields of extension $\mathbb{Q}(\sqrt{2} , \sqrt{3}) : \mathbb{Q}$ without using Galois correspondence.
Perhaps you can take advantage of the fact that $\mathbb{Q}(\sqrt{2},\sqrt{3})=\mathbb{Q}(\sqrt{2}+\sqrt{3})$?
Aug
27
comment Possible Research Topics for High School
Ask a friendly math professor from a university near you! Who knows -- someone might be willing to take you on for a summer project!
Aug
26
awarded  Commentator
Aug
25
comment A hint to show that $S^n$ is infinite
As you mention, the stereographic projection yields a bijection from a subset of $S^n$ to an $n$-dimensional Euclidean space, which is infinite (assuming $n\neq 0$).
Aug
25
comment What is Xa = X (a= indice) in the given function y=6x-x²
Treat it as an unknown variable. Solve for the area in terms of $x$.
Aug
25
comment What is Xa = X (a= indice) in the given function y=6x-x²
Ah, sorry, I misunderstood. As Ragnar says below, $x_A$ is likely the $x$-value of the point $A$.
Aug
25
comment What is Xa = X (a= indice) in the given function y=6x-x²
By surface of the rectangle, do you mean area? Once you've computed where the parabola touches the axis, you know the width of the rectangle. Now all you need to do is compute the height. I'm not sure what the $x_a$ denotes.
Aug
25
comment Confused about differentiation
I think it's always worth spending time familiarizing yourself with the intuition behind mathematical concepts, even (especially) if you don't have the time to delve into the rigorous details. Learning things from first principles is always enlightening, but really what is important is understanding why certain mathematical statements are plausible -- why things should be the way they should be. Having a loose sketch of the math in your head is useful when it comes to problem solving. If there's a technical detail you don't quite remember from calculus, you can always just look it up again.
Aug
25
comment Confused about differentiation
Yes, that is the correct intuitive picture of what is happening. To summarize what you're saying in slightly tighter notation: you can compute rise/run ($\Delta y/\Delta x$), but if you take a limit $$\lim_{\Delta x\to 0}\frac{\Delta y}{\Delta x}$$ you no longer are talking about rise/run. You're now (loosely speaking) thinking of infinitesimal changes, which is why we use the notation $dy/dx$ and not $\Delta y/\Delta x$. You can treat these as infinitesimals on their own (just $dy$ or just $dx$), and you will get the correct answer, but really what is happening is just the chain rule.
Aug
25
comment Confused about differentiation
I agree with AlexR. Perhaps I underestimate students of this day and age, but I would not expect them to see differentials in a first course on calculus. Differential geometry, certainly. But in this context, positing that the notation is "perfectly clean" is a tad unreasonable.