2018 Math Summer Camp

Description: This year we will host a summer camp for high school students to learn explicit construction of elliptic curves with prescribed order over finite fields. It is an integration of advanced mathematics and programming (Python on Sage Math). The motivation behind the summer camp is to provide high school students a glimpse into mathematical research and to encourage them to pursue higher education.

There is no registration fee for the Summer Camp, and lunch will be provided free of charge. Just bring your curiosity and your love for mathematics. Twenty-five rising juniors and seniors will be selected.

Support: The Summer Camp and the ensuing Math Circle are supported by the MAA Dolciani Mathematics Enrichment Grants (DMEG). We are extremely grateful to have full support from the Mary P. Dolciani Halloran Foundation.

Location: Georgia Southern University – Armstrong Campus, 11935 Abercorn St., Savannah, Ga 31419

Date/Time: July 9 – July 13/ 10:30 AM – 2:30 PM

HOW TO APPLY: Please fill the form here, and send us a copy of your high school transcript to Dr. Duc Huynh at dhuynh@georgiasouthern.edu. The deadline for applying to the summer camp is June 15, 2018.

About us: Directors – Mrs. Jan Avila and Dr. Duc Huynh, Undergraduate mentors –  Chanukya Badri, Ayman Bagabas, and Keyur Patel

Elliptic curves: The study of elliptic curves is a relatively new area of mathematics that has been actively researched in the last few decades. Elliptic curves have been used in solving longstanding unsolved problems in number theory such as Fermat’s Last Theorem. Applications of elliptic curves include integer factorization and Elliptic Curve Cryptography (ECC). ECC is an encryption method used to keep digital transmission of data safe; it requires less resources than other non-ECC methods. In this Summer Camp, we will learn how to construct elliptic curves of prescribed security requirements.

Example: Let $\mathbb{F}_{1931} = \{1,2,\ldots, 1930,1931\}$.  The curve $E: Y^2 = X^3 + 443X + 1045$ has order $2018$ over the field $\mathbb{F}_{1931}$.  The graph of $E$ over $\mathbb{F}_{1931}$ is below:

The graph of $E$ over the real numbers $\mathbb{R}$ is below:

And the graph of $E$ over the complex numbers $\mathbb{C}$ is the delicious donut below: