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.

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.

## Comments

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

exactif $~$\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.