# 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).