# Stanford University Mathematics Camp Staff Applications

We are **actively recruiting** undergraduates, recent grads, and graduate students to work as Teaching Assistants for the Stanford University Mathematics Camp (SUMaC) this summer! We have *numerous open positions* and encourage your students to apply as soon as possible for full consideration:

- SUMaC Online TA, Program II
- SUMaC Residential Counselor, Program I or Program II
- SUMaC Head Counselor, Program I or Program II

The position descriptions are linked above and employment dates can be found here, along with the direct link to the application. Below, you will find a list of the math topics that our staff should be familiar with for each program. Please feel free to direct any questions to spcsemploy@stanford.edu.

This is an exciting opportunity to **mentor** and **inspire** academically motivated high school students curious about math. Along the way, we hope our staff are also able to further grow their **passion** for mathematics, sharing their interests and knowledge in a **supportive**, **diverse**, and **inclusive** **community**.

Please be advised of the topics candidates for the SUMaC program should be familiar with.

**Program I: Abstract Algebra and Number Theory**

- A standard course in abstract algebra or modern algebra is considered a minimum requirement; however, a candidate who has taken an undergraduate course in number theory with topics in algebra covered in other courses may qualify
- Groups: product groups, subgroups, quotient groups, homomorphisms, isomorphisms
- Rings
- Fields including finite fields and field extensions
- Vector spaces
- Modular arithmetic
- Introductory Number Theory
- Cryptography

**Program II: Algebraic Topology**

- Groups: product groups, subgroups, quotient groups, homomorphisms, isomorphisms, free groups, free products
- Point-set topology
- Topology of surfaces, including quotient topology/ID spaces
- Euler characteristic of a surface, and classification of compact surfaces
- Fundamental group and some familiarity of higher homotopy groups
- Selfert-Van Kampen theorem
- Homology groups, in particular, simplicial homology
- Mayer-Vietoris sequence