general
What book is good in studying beginning optimization?
Recently, I heard some talks about Optimization. And I am beginning to love that field. I want to study beginning optimization, what book can you recommen...
Apr 12, 2026
Archive: General
general
How would I solve this for the indicated variable?
$a^{ 2 }x+(a-1)=(a+1)x$; for $x$ I have been able to manipulate and solve for the indicated variable in these type of equations pretty easily until I came...
Apr 12, 2026
general
Product space definition
Herebelow, all passages in Billingsley $(1995)$ to get to definition of product spaces: The standard construction of the general process involves product ...
Apr 12, 2026
general
Summary of different Fourier Transforms / Fourier Series
I am currently writing my PhD and would like to display a table summing up the different kind of Fourier Transforms and Fourier Series. Here is the table ...
Apr 12, 2026
general
How to prove that homology is a functor?
Is a homology operator $H_k:(cKom) \rightarrow (Ab)$ a functor? I know this is a really simple question, but I'm not familiar with category theory an...
Apr 12, 2026
general
The power series sinh(x) around x=ln(2)
I want to find the series of Sinh(x) around x=ln(2) . I solved it using 2 different method . First method: $$\sinh(x)=\frac{e^{x}-e^{-x}}{2}=\frac{e^{(x-\...
Apr 12, 2026
general
How to prove the distributive property of cross product
That is, how to prove the following identity: $$a \times (b+c) = a \times b + a \times c$$ where the $\times$ represents cross product of two vectors in 3...
Apr 12, 2026
general
Explain proof by contradiction.
Would anyone mind explaining me how proof by contradiction works? I have a very vague understanding of it so I always avoid using it when it comes to disc...
Apr 12, 2026
general
Combination formula: n-1 choose -1
This is actually a question involving the recurrence relation in binomial coefficient formula, which is $${n \choose k} = {n-1 \choose k-1} + {n-1 \choose...
Apr 12, 2026
general
Dichotomous search algorithm in numeric optimization
If we assume that $\phi$ is convex and continuous in $[a,b]$, it is obvius that, in this interval, $\phi$ has a minimizer. The goal is know what point is ...
Apr 12, 2026
