Tagged Questions
7
votes
2answers
105 views
Algebraic geometry in representation theory?
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, ...
1
vote
2answers
94 views
What's the most elegant way of rotating a 3-dimensional co-ordinate system?
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)- ...
1
vote
0answers
57 views
A gratifying re-encounter with a piece of math that was out of my mind
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 ...
48
votes
39answers
5k views
What are some examples of a mathematical result being counterintuitive?
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 ...
3
votes
1answer
134 views
A Formal and Precise treatment of Simplification?
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 ...
5
votes
7answers
3k views
practical uses of matrix multiplication
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 ...
15
votes
15answers
627 views
List of Local to Global principles
What are some of the local to global principles in different areas of mathematics?
8
votes
8answers
382 views
Elevator pitch for a (sub)field of maths?
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 ...
10
votes
6answers
2k views
Best intuitive metaphors for math concepts (of any level)
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)?
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37
votes
13answers
1k views
Surprising Generalizations
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 ...
