Clik here to view.
Cursive in Lang’s “Algebra” [closed]
I was reading Serge Lang’s “Algebra”, the revised third edition. In p. 53, Lang introduces a concept of a category with a special cursive which I’ve never seen before. It is shown above. For me, it...
View ArticleIs there a word that encompasses both "definitions" and "theorems"? [closed]
I sometimes write sentences like this:To prove the desired result, the following notions will be handy.What follows is a usually a sequence of definitions, theorems and proofs. Therefore, I don't think...
View ArticleNaming Convention of Mathematical Ideas [closed]
What are the criteria or conventions for naming theorems and inequalities after mathematicians? Are there examples where the naming has been controversial or changed over time?For example, would Cauchy...
View ArticleCategory-theoretic description of the real numbers
The familiar number sets $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$ all have "natural constructions", which indicate, why they are mathematically interesting.For example, equipping $\mathbb{N}$ with the...
View ArticleWhat elements of logic should a math undergrad master to understand...
Why should a math student understand logic before understanding and doing proofs? Why is it necessary?It's true that the formal language of logic is useful, but, for example, where's the practical use...
View ArticleThought experiment: Cheat code to pure mathematics [closed]
Suppose that we are visited (in 2024) by a time traveler from the far future. It turns out that they are a pure mathematician. We get a chance to communicate with them, however practical limitations...
View ArticleFermat's last Theorem and elliptic curve cryptography
AFAIR, elliptic curve cryptography became popular soon after Fermat's last Theorem had been proven. Is it just a coincidence, or some important cryptographic properties of elliptic curves follow from...
View ArticleIs solving problems in this way low-level and should be avoided? [closed]
IntroductionRecently I have been reading the book "Thinking Mathematically" by John Mason at al.I demonstrated using the method from the book to solve problems to a friend. He thought the process is...
View ArticleLoss of Interest for Mathematics? [closed]
I will begin with a word of introduction. Mathematics entered my life when I was in my 8-th year of school, and fairly quickly, through burning passion, it moved me to a possible career in the Field....
View ArticleWhat motivated Democritus to discover the volume of a cone?
In the works of Archimedes, it is mentioned that Democritus was the first to discover that the volume of a cone is 1/3 that of the cylinder with the same base and same height.I am curious to know about...
View ArticleDoes "Doing a thing to both sides of an equation" have a name?
A two part question.1True or False: when working with an equation or inequality, everything that you do is either:a substitution, oran operation performed on each sideNote that algebraic or numerical...
View ArticleClik here to view.
Proof of how many tangents can be drawn in a given domain
I saw that the area where the tangent line can be drawn is divided into the corresponding divided area as shown in the picture below based on the tangent line drawn from the inflection point of the...
View ArticleSmooth paths at the cusp of $V(x^2 + y^2 - z^3)$
I'm trying to understand how smooth paths on a real algebraic surface are related to its Zariski tangent space.Consider a "pinched cone" $X = V(x^2 + y^2 - z^3)$. At a regular point $p = (1, 0, 1)$,we...
View Articlereference request for a book on high dimensional probability and data...
I hope someone can help with this. I am a statistician looking for a good book on high dimensional probability and data analysis. Basically I am looking for the equivalent of Terry Tao's 2 volume set...
View ArticleWhere can Carmichael Function be applied?
I know that Carmichael function written usually as $\lambda(n)$ is defined like this:$$\lambda(2) = 1\\\lambda(4) = 2\\\lambda(2^k) = 2^{k-2}\\\lambda(p^k)=p^{k-1}(p-1)\\\lambda(n) = lcm...
View ArticleDifferent version of Brocard's problem
By chance, I learned about Brocard's problem, one of the unsolved problems in mathematics. I've been thinking about this problem and I'm wondering if it's okay to think about it this way.We are trying...
View ArticleClik here to view.
Can general N-adic Kravchuk-based wavelets with overlap and perfect...
BackgroundA previous question of mine lead me up to the concept of Kravchuk polynomials for a minimal basis of three polynomials of order 1,2 and 3.Simultaneously in the multiresolution analysis of...
View ArticleHow to define the magnitude of a rotation in $\mathbb{R}^n$?
Is there some well established way on how to quantify rotations in $\mathbb{R}^n$? To say which rotation is greater and which is smaller?In $\mathbb{R}^2$ the rotation is characterized by a single...
View ArticleWhere can I download a full list of all primes below $10^{15}$?
I would like to do some computing on a large list of primes. Unfortunately my computer is not strong enough to quickly generate such a list, so I'm looking to download a file that already contains...
View ArticleGood Book On Combinatorics
What is your recommendation for an in-depth introductory combinatoric book? A book that doesn't just tell you about the multiplication principle, but rather shows the whole logic behind the questions...
View Article