Muggles' Guide to Harry Potter/Characters/Professor Vector

Overview
Professor Septima Vector is the Arithmancy professor at Hogwarts School of Witchcraft and Wizardry.

Analysis
From the construction of the word arithmancy = arith- + -mancy, it's evidently magic to do with numbers. In the real world, arithmancy means divination using numbers, but in the Harry Potter world it seems to include also numerology, the study of magical properties of numbers. The professor's name, Vector, may hint that arithmancy in the Wizarding world could include more sophisticated mathematics.

In the Harry Potter world, numbers are often inscribed in places, such as tombs, pyramids, and monuments. These numbers supposedly have meaning, either hiding a secret message or protecting the site with a curse. Arithmancy, if applied correctly, allows the practitioner to interpret these findings.

Gringotts curse breakers are required to have sufficient knowledge of Arithmancy.

Questions

 * 1) Hermione repeatedly states that Arithmancy is very useful. What kind of things might be taught in an Arithmancy class, that Hermione would see as being particularly useful?