# 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:

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 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.

• 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).