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comment How can I determine the function for summing a series of integers?
arrange the numbers in a triangle: $${}$$o$${}$$o o$${}$$o o o$${}$$o o o o$${}$$o o o o o ... How many dots are there in the whole triangle?
Jul
22
comment How do you self-study Functional Analysis?
real analysis in the most introductory-level sense. The italics are what we covered
Jul
22
revised How do you self-study Functional Analysis?
less amb8guity
Jul
22
revised How do you self-study Functional Analysis?
added 10 characters in body
Jul
22
asked How do you self-study Functional Analysis?
Jul
21
comment Exercises in category theory for a non-working mathematican (undergrad)
Martin, your comment essentially amounts to 'it was easy for me so I don't see why you should be having any problems'
Jul
21
comment Do all distributions of R.V.s have a singular part and a continuous part?
I see! I had not properly understood.
Jul
21
accepted Do all distributions of R.V.s have a singular part and a continuous part?
Jul
19
comment Coming up with short “magical” proofs
Thank you so much for not using the word 'mathemagic' in your post
Jul
19
comment A question about the convergence of series.
Theyre all fals.....
Jul
7
accepted What is the difference between a calculus and an algebra?
Jul
7
comment How to approximate large sum of exponential variables
I don't understand your indexing. If $i_1\neq i_2 \neq \dots \neq i_k \neq \dots \neq i_N$ (As I believe you meant?), then how can we be summing over these variables up to $N$? (These are variables which we are summing over which will range from 1 to N; what do you mean by '$\neq$'?) Also, if inside the $\exp$ we have: $$\Large-r_{i_{0k+1}}-r_{i_{1k+1}}-r_{i_{2k+1}}-\dots-r_{i_N}$$, shouldn't $N=n\cdot k+1$ for some $n\in \mathbb{N}$? Sorry if I am misunderstanding something.
Jul
7
revised How to approximate large sum of exponential variables
just formatted & fixed a small typo in the indicies of the summation formula
Jul
7
suggested suggested edit on How to approximate large sum of exponential variables
Jul
7
revised How to approximate large sum of exponential variables
just a small typo in the indicies of the summation formula
Jul
7
suggested suggested edit on How to approximate large sum of exponential variables
Jul
2
awarded  Curious
Jun
24
comment Finding the integral of $\cos\theta \cdot dt$ in terms of the integral of $\sin\theta \cdot dt$
@Gerard, it might! Does it stay within these bounds?
Jun
23
comment Finding the integral of $\cos\theta \cdot dt$ in terms of the integral of $\sin\theta \cdot dt$
This is not answerable for general $\theta(t)$; the function could do literally anything on $[0,T]$. What if $\theta(t)=4\pi Tt$? Then $\cos(\theta(t))$ would look exactly the same as the cosine of a sawtooth function since cosine takes on the same value multiple times. The same holds for sine. This goes away if $\theta(t)$'s range is within $[0,T\pi]$. It may help to consider that: $$\int_0^T\cos(\theta(t))dt+i\int_0^T\sin(\theta(t))dt=\int_0^T e^{i\theta(t)}dt=\int_{-\infty}^\infty \mathbf{1}_{[0,T]}(t)e^{i\theta(t)}dt$$ which might be easier to integrate, depending on what $\theta(t)$ is.
Jun
23
revised What is the difference between a calculus and an algebra?
edited title