By Camilla Fratta, Ananya Jain, Sydney Mason, Gabby Matejowsky, and Nevaeh Pinkney*.

*Nevaeh helped the group work through the problem set but was unfortunately unable to attend camp during the blog writing.

Mathematical Epidemiology explores the realm of mathematics applied to public health. It relies on modeling to use known information about certain scenarios regarding the spread of diseases and then uses it to predict future outcomes. By the end of the problem set, our group learned about the challenging process that comes with trying to predict population sizes in order to control the spreading of diseases. The equations that are faced in this branch of mathematics are at the heart of mathematical modeling.

Mathematical Models and Modeling

A mathematical model is an equation used to predict or model the most likely results to occur in a real-world situation.  We used these types of equations to model the spread of a disease in a population, tracking the flow of populations from susceptible to infected to recovered.  In real life scenarios, there are too many variables to fully account for, so we only were able to place a few in our equations. This made the models less accurate, but at the same time very useful to us in our problem set.  They gave us a good idea of how things worked in an actual epidemic and helped us to understand what mathematical modeling really is.

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By Camille Clark, Layke Jones, Isabella Lane, Aza McFadden*, and Lizbeth Otero.

*Aza helped the group work through the problem set but was unfortunately unable to attend camp during the blog writing.

Cryptography is a field of coding and decoding information. It relies on the framework of number theory. Therefore, it can be used to connect theories as well as teaching others the fundamental properties of integers. Relevant number theory topics are modular arithmetic, prime factorization, greatest common divisor, and theorems such as the Chinese Remainder Theorem and Euler’s Theorem. This blog post will focus on the first three topics.

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by Kayla Aguilar, Maris James, and Aynsley S.

Data is all around us, but it has to be studied in some way, right? How else are we supposed to know what it’s about? That’s what graph theory and network science are for! To organize and connect data mathematicians use networks and graphs as well as scientific computing (like coding).

Network science is an application-based study of graphs. To understand network science, we first have to understand the graphs:

Graph Theory

Graphs represent data through nodes, which are the separate points of a graph, and edges, which connect the nodes. There are two types of graphs: directed and undirected graphs. Directed graphs rely on the order of the vertices to be the same, while undirected graphs don’t rely on the order of the nodes.

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By Ayanna Blake, Lisa Oommen*, Myla Marve, Tamarr Moore, Caylah Vickers, and Lily Zeng.

*Lisa helped the group work through the problem set but was unfortunately unable to attend camp during the blog writing.

The Girls Talk Math camp is about female high school students from different places who discuss mathematics, mathematicians, and theories. We were split up into groups and were assigned different math topics to learn. Our topic was classification of surfaces, which is listed under the umbrella topic of abstract geometry.

We thought the surfaces project was very interesting and cool to learn about, because it introduced us to college level math and allowed us to understand different parts of geometry. Along with gaining knowledge of surfaces, we also got to learn about other groups topics. Campers presented their topics on the last day and helped us to perceive the significance of the different subjects.

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