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FShrike

London, UK

School student who has learnt almost all their maths/computer science informally from the internet, who enjoys helping others and likes to challenge everything; every statement must be proven, where possible. Using this site to learn for myself, and to help others learn, as I have enjoyed doing both my whole life.

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Top Questions

Where does one learn how to apply categorical algebra and higher abstractions to algebraic topology?

algebraic-topology reference-request self-learning simplicial-stuff higher-category-theory asked Jan 5 at 22:14

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A natural discovery of $e$ as $\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^n$ - what is unrigorous here?

real-analysis calculus sequences-and-series limits asked Sep 16, 2021 at 16:33

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How does one appropriately navigate the situation of having a lot of prior knowledge before applying to university + courses not on main interests?

mathematics application undergraduate university communication asked Apr 2, 2022 at 19:00

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The matrix logarithm is well-defined - but how can we algebraically see that it is inverse to the exponential, as a finite polynomial?

linear-algebra matrix-calculus matrix-exponential functional-calculus asked Jul 14, 2022 at 0:17

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How does one tutor an A-level student past the derivative paradox?

secondary-education calculus teaching derivative asked Jul 28, 2021 at 9:53

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Rigorously, why do the Laplace and Fourier transforms “reveal” the sinusoidal or exponential decomposition at their peaks?

fourier-analysis fourier-series laplace-transform fourier-transform asked Aug 20, 2021 at 23:21

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How does one come up with the continued fraction for the arctangent? $\arctan x=\frac{x}{1+}\frac{x^2}{3+}\frac{(2x)^2}{5+}\cdots$

real-analysis limits trigonometry proof-explanation continued-fractions asked Aug 20, 2022 at 12:14

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When should continued fraction expansions which start from an original value, converge to that same value? $\tan x=x/1-x^2/3-x^2/5-\dots$

real-analysis sequences-and-series limits continued-fractions asked Aug 23, 2022 at 11:49

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How can I find the asymptotics of $h\int_0^{\pi}\frac{\sin^2(i\pi-he^{it})}{\sinh^2(he^{it})}dt$, $h\to0$, to evaluate a certain contour integral?

complex-analysis asymptotics contour-integration asked Jul 7, 2022 at 16:49

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How might one make this Gaussian integral derivation of Stirling's approximation more airtight?

real-analysis asymptotics approximation gamma-function asked Oct 26, 2021 at 15:12

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Top Answers

Conjecture: The sequence $\frac{2}{n} \sum_{i=1}^n \sqrt{\frac{n}{i-\frac{1}{2}}-1}$ converges to $\pi$

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Homology in a picture? (Is this picture just metaphorical, or a rigorous example that can be formalized?)

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Understanding the definition of "Indefinite integral".

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Integral of $1 / \sqrt x$ using Limits

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Topological version of second isomorphism theorem

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Why does it take me so long to solve relatively easy problems and what can I do about it?

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Integral $\int_{-1}^{1} \frac{x}{1-x^2} \,dx$

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Applying theorems and properties to solve indeterminate limits

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Fubini's theorem and reparameterisation

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Prove the existence of a point $c$.

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Integral: $\displaystyle\int_0^1\!\frac{x}{\operatorname{artanh} x} \, {\rm d}x\overset{?}{=}\frac{7\zeta(3)}{\pi^2}$

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Link between exact sequence and short exact sequence

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Prove or disprove: If $a_n$ is Cauchy, is $\lfloor a_n \rfloor$ Cauchy?

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Elements of $\mathbb{Z}_6 / \mathbb{Z}_2$

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Why $g$ is strict epimorphism if $g \circ f$ is a strict epimorphism?

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Proof that $\sum_{n=1}^\infty\frac{F_n}{3^n n} = \frac{\ln(\phi+1)}{\sqrt{5}}$

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Why topological spaces in Baire category theorem are required to be Hausdorff?

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How to integrate $\int_{-\infty}^{+\infty}\text{sech}^2(\beta t) \int_{-\infty}^{t} (t-s)^{1-q}~\text{tanh}(\beta s)\text{sech}^2(\beta s) ds~dt$

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‘Lies to children’ in mathematics and statistics education

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How is rational number a group under addition if some non-rational numbers can be represented as a sum of rational numbers?

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Are infinities included in the closure of the real set $\overline{\mathbb{R}}$

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$g(x)\approx0\implies g'(x)\approx0?$

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Is homeomorphism preserved by homotopy equivalence?

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How can I prove that $\pi+\pi^2$ is irrational?

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Does $i*\arcsin(x) = \operatorname{arccosh}(x)$

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Eigenvalues of $A$ from $\operatorname{Tr}(A),\operatorname{Tr}(A^2),\ldots,\operatorname{Tr}(A^d)$?

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Question from MIT integration Bee 2023 final: Evaluate $\int^1_0 (\sum^\infty_{n=0}\frac{\left\lfloor 2^nx\right\rfloor}{3^n})^2{\rm d}x$

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How are the following integrals equivalent?

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Euler-Mascheroni Constant in the Cosine Integral?

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Evaluate $\lim_{x \to 0} \frac{\sin(3x)}{\sin(4x)}$ without using L'Hopital's rule.

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