I heard that today algebraic geometry plays some significant role in representation theory, which is a little surprising because when I learnt representation theory it is basically algebra, topology, ...
For two dimensional rotation of $x$ and $y$ axes anticlockwise by $\varphi$, the equation that transforms $P(x,y) \rightarrow P(x',y')$, $x'=x \cos(\varphi)+y \sin(\varphi)$ and $y'=y \cos(\varphi)- ...
A series of real numbers is said to be conditionally convergent if it is convergent but not absolutely convergent. By rearranging the terms of a conditionally convergent series we can make the ...
As I procrastinate studying for my Maths Exams, I want to know what are some cool examples of where math counters intuition. My first and favorite experience of this is Gabriel's Horn that you see in ...
I am looking to gain a deeper understanding of, and increase my own skill in "Mathematical Simplification". But I've been finding the concept overly vague and haven't been able to find any good ...
The use of matrix multiplication is usually given with graphics initially (scalings, translations, rotations, etc). Then there are more in-depth examples such as counting the number of walks between ...
What are some of the local to global principles in different areas of mathematics?
When I first saw the title of this question, I forgot for a moment I was on meta, and thought it was asking about quick, catchy, attractive, informative one-or-two-liner summaries of various fields of ...
Frequently, we introduce a new concept with a formal definition, then immediately say "Intuitively, what this means is..." What are the absolute best metaphors you've seen (for concepts of any level)? ...
I just learned (thanks to Harry Gindi's answer on MO and to Qiaochu Yuan's blog post on AoPS) that the chinese remainder theorem and Lagrange interpolation are really just two instances of the same ...