How to properly punctuate "for all" after mathematical expressions?
One thing about mathematical writing that has always puzzled me is how to properly punctuate "for all" after a mathematical expression. Let me give you an example.A function $f:\mathbb{R}\to...
View Articlereferences to explore validity of my assumption
The gist of this approach is to encode the zeta function into a space, similar to how number theorists like to encode sequences into generating functions to leverage analytic properties. I will refer...
View ArticleIs there a simple name for a line segment joining the midpoints of 2 opposite...
What I already know:A line segment between the midpoints of opposite edges of a square (or any quadrilateral) is called a bimedian.A line segment between the midpoints of 2 edges of a triangle is...
View ArticleA book for abstract algebra with high school level
Any book that I find on abstract algebra is somehow advanced and not OK for self-learning. I am high-school student with high-school math knowledge. Please someone tell me a book can be fine on...
View Article*easy* examples of fact in one area of maths proven by a different area of maths
Example (something I raised my hand to ask when I was in secondary school):How do you know that $\dfrac{a!}{b!(a-b)!}$ is necessarily an integer whenever $a$ and $b$ are natural numbers such that...
View ArticleRequest for crazy integrals
I'm a sucker for exotic integrals like the one evaluated in this post. I don't really know why, but I just can't get enough of the amazing closed forms that some are able to come up with.So, what are...
View ArticleIn poset category elements are objects while in group category elements are...
In a categorical poset, the elements of the poset are objects of the category, whereas in a categorical group, the elements are arrows. why does such an apparent asymmetry exist, and how can I...
View ArticleIs there a geometric interpretation of $F_p,\ F_{p^n}$ and $\overline{F_p}?$
I have been doing some exercises about finite fields lately and I think I've obtained some understanding of what they are. What seems to be missing though is some kind of picture. Learning to work with...
View ArticleWhat is the optimal strategy for increasing my 'mathematical maturity'? Depth...
My apologies for such a general question, but as a 'math enthusiast', I've often wondered what the optimal strategy is to increase my mathematical maturity. Broadly, should I aim to hunker down &...
View ArticleHow do you get GCD from an integral?
I was looking at this post and I am trying to reverse-engineer integrals that will have the $\gcd$ function in the solution. However, I am struggling to understand where the $\gcd$ actually comes from....
View ArticleWhat can we learn about a group by studying its monoid of subsets?
If $G$ is a group, then $M(G)=2^G$ is has a monoid structure when we define $AB$ to be $\{ab|a\in A,b\in B\}$ and $1_{M(G)}=\{1\}$. How much of the structure of $G$ can be recovered by studying the...
View ArticleWhat problems will arise if we define matrix multiplication this way?
$a\in \mathbb{R}^n$$a=(a_1,a_2,\dots,a_n)$ lets define this to be equivalent to $(a_1,a_2,\dots,a_n,0,0,0 \dots,0)$ (finite many zeros) by this I think we can make an $n \times m$ matrix $A$ equivalent...
View ArticleHow certain distributions can be treated as normal distribution?
Normal distribution is stated to have a symmetrical bell-shaped curve, with mean = median = mode, with data point values basically derived from a large sample representative of the population.But, real...
View ArticleIs it not smart to answer old questions? [migrated]
I randomly found some questions I thought very interesting or probably I would have asked during my school time. However, you will see that no one even tried to answer it at all although been tagged...
View ArticleWhen do graphs have a Hamiltonian Cycle and H-Path?
what are the formulas for Hamiltonian Cycle and Hamiltonian Path existence within a graph? What are the formulas for when complete graphs, complete bipartite etc have H-cycles?A graph has a H-cycle...
View ArticleCan the golden ratio accurately be expressed in terms of $e$ and $\pi$
I was playing around with numbers when I noticed that $\sqrt e$ was very somewhat close to $\phi$ And so, I took it upon myself to try to find a way to express the golden ratio in terms of the infamous...
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I've seen this theorem credited to Viette, but what's the correct way to call...
Here is the drawing (taken from here) that credits this theorem to Viette (I suspect François Viète is referenced). I would like to know whether this is accurate or not. Some videos (here and here), as...
View ArticleWhy does set-theoretic union and intersection operate on reverse logic?
In set theory, $A \cup B$ is logically defined as $\{x : x \in A \lor x \in B\}$. In set theory, the result of unionizing A with B is a bigger set, but in logic, "or" is a softening operation.In set...
View ArticleCollection of surprising identities and equations.
What are some surprising equations/identities that you have seen, which you would not have expected?This could be complex numbers, trigonometric identities, combinatorial results, algebraic results,...
View ArticleWhat books do you recomend for a student beginning to study hardy spaces of...
I'm interested in multi-dimensional complex analysis and stumbled upon these spaces called hardy spaces. I'm specifically interested in hardy spaces of the bidisk but the internet couldn't guide me to...
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