Unexpected examples of natural logarithm
Quite often, mathematics students become surprised by the fact that for a mathematician, the term “logarithm” and the expression $\log$ nearly always mean natural logarithm instead of the common...
View ArticleWhat is the difference between "expectation", "variance" for statistics...
It seems that there are two ideas of expectation, variance, etc. going on in our world.In any probability textbook:I have a random variable $X$, which is a function from the sample space to the real...
View ArticleSimplest proof of Taylor's theorem
I have for some time been trawling through the Internet looking for an aesthetic proof of Taylor's theorem.By which I mean this: there are plenty of proofs that introduce some arbitrary construct: no...
View ArticleCan a mathematics research paper have, just propositions & corollaries? [closed]
I am writing a research paper, in which I am proving some properties of new convolution operation $\star$ for some transform, like linearity, associativity, commutativity,distributivity, shift...
View ArticleSoftware Recommendation for Theorem Suggestions
So I am not sure if this software already exists or perhaps this is something that humanity has to embark on to finally have as a product. A bit about myself, I am student training in a sub-area of...
View ArticleRoadmap for self-learning pure mathematics from high school level onward....
Motivation:- I’m making this post because I know a lot of people who are genuinely interested in learning pure math but have no formal background or experience or help. Many of them are unsure how to...
View ArticleWhy is Willans formula for prime's not considered a valid formula?
So, I was watching this video on Willan's formula by Eric Rowland, and it was mentioned that this formula does not count for generating primes, as it is extremely hard and time consuming to compute. I...
View ArticleInteresting ways to write 2023 [closed]
The year 2023 is near and today I found this nice way to write that number:$\displaystyle\color{blue}{\pi}\left(\frac{(\pi !)!-\lceil\pi\rceil\pi !}{\pi^{\sqrt{\pi}}-\pi...
View ArticleMeaning of 'ring multiplication'
I saw a linear algebra lecture note. And I saw about proof of $(c_1c_2)A=c_1(c_2A)$.$$((c_1c_2)A)_{ij}=(c_1c_2)A_{ij} \text{defn. scalar multiplication}$$$$=c_1(c_2A_{ij}) \text{assoc. of ring...
View ArticleReferences for motives of stacks of principal bundles on curves
I would like to ask about some references regarding motives of stacks of principal bundles on curves. I saw this title from people working on geometric Langlands problems and I want to delve more into...
View ArticleHow to solve the ODEs $\frac{dy}{dx}=5x^2$ and $\frac{dy}{dx}=5y^2$, in an...
This is a simple question, that was asked as a trap in an interview.The expert asked to solve the 1st order ode $\frac{dy}{dx}=5x^2$.Recalling my undergraduate classes, without double thinking I...
View ArticleSearch engine/tools for math theorems in textbooks
I often find it challenging to search for math theorems that are only available in textbooks, especially when they are slightly more advanced (e.g., Harmonic Analysis). Unlike introductory topics (such...
View ArticleDifferent methods for Godel numbering [closed]
What are the different ways to construct a godel number?Reading different books on godels incompleteness theorem , i noticed that there are different ways to make a godel number.That made me wonder...
View ArticleRussell's Principia Mathematica status [duplicate]
I have recently read the excellent graphic novel "Logicomix" and I was wondering how Russell's work is considered in the modern mathematical community. I know that Wittgenstein and, much more formally...
View ArticleIs expression and its result is the same thing?
So, $\frac{1}{2}$ and $0.5$ are just two different ways to address the same object which is rational number $\frac{1}{2}$.What about more complex expressions? Like $\{a, b\} \cap \{b, c\}$ is just the...
View ArticleContinuity criteria in metric spaces
Let $(M, d_M)$ and $(N, d_N)$ be metric spaces. The following are the (equivalent) main characterizations o continuity for a function $f:M\to N$$(\forall x\in...
View ArticleA road to algebraic geometry [duplicate]
I am a person who leans strongly towards algebraic geometry and am looking forward to studying it in depth. I am going to lay out my plan to approach algebraic geometry, and I hope some people here can...
View ArticleDo the algebraic manipulations required in proofs eventually become natural...
I have been recently reading Walter Rudin's Principles of Mathematical Analysis and (reading the book's proof of the existence and uniqueness of n-th positive roots of positive reals, situated towards...
View ArticleOn the Geometric Origins of Cubics
I am just doing a little research on the geometric problems of the ancient geometers that lead to cubic equations. Two examples I have found are Archimdes On the Sphere and the Cylinder Bk 2, to cut a...
View ArticleThe symmetric space $\operatorname{SO}(n,\mathbb C) / \operatorname{SO}(n)$
I am looking for a reference for the symmetric space $\operatorname{SO}(n,\mathbb C) / \operatorname{SO}(n)$; I haven't been able to find any references on about it online. In particular, I would like...
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