"Would be great to have an e..."


by Eric Rogstad Feb 10 2016

Would be great to have an example of the kind of formula one might expect to see.


Jason Gross

Might one of the following examples work?

The Riemann hypothesis asserts that the real part of every non-trivial zero of the Riemann zeta function $~$\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}$~$ is equal to $~$\frac{1}{2}$~$.

(Stealing from Wikipedia): A sequence of groups and group homomorphisms $~$G_0 \xrightarrow{f_1} G_1 \xrightarrow{f_2} G_2 \xrightarrow{f_3} \cdots \xrightarrow{f_n} G_n$~$ is called exact if $~$\text{im}(f_k) = \text{ker}(f_{k+1})$~$ for $~$0 \le k < n$~$.

(Also paraphrased from Wikipedia): Given an $~$n\times n$~$ matrix $~$A$~$ whose elements are $~$a_{i,j}$~$, we can define the determinant $~$\det(A) = \sum_{\sigma\in S_n}\text{sgn}(\sigma) \prod_{i=1}^n a_{i,\sigma_i}$~$ where $~$S_n$~$ is the symmetric group on $~$n$~$ elements.

I'm a bit worried, though, that "standard research notation" in one discipline is foreign to mathematicians in other disciplines.

Patrick LaVictoire

I suggest we can assume that almost everyone in Math 3 is familiar with either calculus concepts or discrete math concepts, but we can't assume abstract algebra or number theory or real analysis, etc.

So the zeta function equation would be a fair example (one might want to state that $~$s$~$ is complex), but the other two would not. Another fair example might be L'Hopital's Rule or the Fundamental Theorem of Calculus.

Joe Zeng

Made a page of examples here. Tell me what you think.