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

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.