updates
Why is being onto necessary for a function to have inverse?
I know that a function needs to be one-to-one so that it can have an inverse but could someone please explain why a function (in addition to being one-to-...
Apr 14, 2026
Archive: Updates
updates
Differences between homography and transformation matrix
I'm wondering whats the differences between a homography and a transformation matrix? For me it's kinda look like the same? Or is homography jus...
Apr 14, 2026
updates
chain homotopy equivalence and quasi-isomorphism
Suppose $(C,d)$ and $(D,\delta)$ are two chain complexes over a field and $f:C\to D$ is a chain map. We say $f$ is a quasi-isomorphism if it induces an is...
Apr 14, 2026
updates
Definition of convolution?
Why do we use $x - y$ rather than $x + y$ in the definition of the convolution? Is it just convention? (If we are thinking of convolutions as weighted ave...
Apr 14, 2026
updates
Why isn't lambda notation popular among mathematicians?
I am relatively new to the world of academical mathematics, but I have noticed that most, if not all, mathematical textbooks that I've had the chance...
Apr 14, 2026
updates
Direction of Greatest Increase
Problem: Find the direction of greatest increase at $P$. $$f(x,y)=4x^2+y^2+2y$$ $$P=(1,2,12)$$ Solution: The greatest increase in $f(x,y)$ at $P$ can be a...
Apr 14, 2026
updates
How to find out how big a ball is?
Ok, This is probably a really simple question but. I need to know how I can find out how big a ball is. For example, a tennis ball is 2 1/2 inches big, bu...
Apr 14, 2026
updates
Basis of the polynomial vector space
I don't understand how to find a basis for a polynomial vector space. Can someone help me with an example?
Apr 13, 2026
updates
Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
Let $a,b$ be positive integers. When $$k = \frac{a^2 + b^2}{ab+1}$$ is an integer, it is a square. Proof 1: (Ngô Bảo Châu): Rearrange to get $a^2-akb+b^2-...
Apr 13, 2026
updates
Where do Mathematicians Get Inspiration for Pi Formulas?
Question: Where do people get their inspirations for $\pi$ formulas? Where do they begin with these ideas? Equations such as$$\dfrac 2\pi=1-5\left(\dfrac ...
Apr 13, 2026
