Your favourite application of the Baire Category Theorem
I think I remember reading somewhere that the Baire Category Theorem is supposedly quite powerful. Whether that is true or not, it's my favourite the...
21 Apr 2026 1 READS
Archive: General
Volume of the region bounded by $z=1-x-y$
This is a very standard exercise in Calculus. The point of this question is, well, I'm able to solve it, but I'm struggling to make out why I�...
21 Apr 2026 1 READS
Find the inverse of a linear transformation
Can you please clarify whether, for the following question, I need to use the definition of linear transformation, or something else? Compute the inverse ...
21 Apr 2026 1 READS
From convex set to convex function
The definition of a convex set is geometrically intuitive. But the definition of convex function doesn't seem so intuitive: $S \subset \mathbb{R}^n$ ...
21 Apr 2026 1 READS
Having problem with tom Dieck's algebraic topology text
(An online PDF of the text Algebraic Topology by Tammo tom Dieck can be found here.) This question is really soft. I'm having problem reading this te...
21 Apr 2026 1 READS
How to find first four terms in Maclaurin Series
Find the first four non-zero terms of the Maclaurin series for $x^3 \sin(x^2)$. I found the derivatives and got as following: first derivative = $2x^3 \co...
21 Apr 2026 1 READS
Sides of a quadrilateral
In a triangle, with sides say $a,b,c$ we know that $a+b\geq{c}$ and $|a-b|\leq{c}$. What are the inequalities we can form given the sides of the quadrilat...
21 Apr 2026 1 READS
What is meant by "Cantor topology"?
I would like to know what is meant by Cantor topology. Looking at Wikipedia, I was linked to this page about Cantor space Maybe I am no good reader (engli...
21 Apr 2026 1 READS
Physics-projectile motion-finding the angle
An object is fired from a cliff 50m high, at an initial velocity of 100 m/s at an unknown angle. You have to find the angle required to fire the object to...
21 Apr 2026 1 READS
Explain Normalization in Layman's term
Can someone explain me what is Normalization in Layman's term ? If we have a vector a, we normalize it by dividing it by |a|. That is $$\frac {a}{|a|...
21 Apr 2026 1 READS
