# Math 3

A reader at the **Math 3** level can read the sorts of things that a research-level mathematician could — if you’re Math 3, it’s okay to throw LaTeX formulas straight at you, using standard notation, with a minimum of handholding.

At the Math 3 level, different schools of mathematics may have their own standard notation, so somebody who is Math 3 in one discipline or subject may not necessarily be Math 3 in another.

## Writing for a Math 3 audience

When writing for a Math 3 audience, all bets are off on readability. You can use as much formal notation as you like in order to define your point properly and clearly.

Children:

- Math 3 example statements
If you can read these formulas, you’re in Math 3!

Parents:

- Mathematics
Mathematics is the study of numbers and other ideal objects that can be described by axioms.

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

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.

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.

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

@12y I think that’s a fair assumption for the moment. Later as Arbital grows the requisites can be refined to Calculus 0, 1, 2, 3; abstract algebra 0, 1, 2, 3 etc. Or else pages can just make use of specific pages as requisites (e.g. do you know what a ‘group homomorphism’ is).