Network Science

By Myla James, Shania Johnson, Maya Mukerjee, and Savitha Saminathan.

 

Graph Theory

Here’s some definitions to help you understand our assignment:

Nodes – vertex/point.
Edges – lines connecting vertices.
Adjacent – two nodes (vertices) are adjacent if they share an edge (line).
Degree – number of edges adjacent to a particular node.

We started this problem set with learning about the difference between connected and disconnected graphs.

Connected Graph – able to travel from one node to any other through its edges.
Disconnected graph – more complex; it has components.
Components – parts of the graphs that are connected.

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Knot Theory

by Erin Gottschalk, Simon Johnson, Meghan, Elizabeth Nguyen, and Brooke Rogers*.

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

What We Did:

Knot theory has many different applications in math including algebra and geometry, and (outside of math) physics. We learned that we can use algebraic techniques to describe knots. When trying to understand knot theory we learned that it is very helpful to work in a group and read the definitions out loud. Us working together was key in understanding knot theory.

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Surfaces

By Elizabeth Datskevych, Nina Hadley, Sabrina James, and Rachel Ruff

In our problem set for the classification of surfaces, we learned many things about dimensions, folding, and the shapes folding makes. First we learned about what a dimension is. The definition of a dimension in this math is the direction an object can go. For example a bird can go up/down, left/right, and back/forth. Next we learned about folding and twisting objects. Diagram A shows a square with arrows on its side, which are the directions to fold. When you fold you match the arrows according to if they look-alike. So when you fold Diagram A it makes a cylinder. Now Diagram B has one arrow pointing the opposite of the other so you would twist before connecting the sides. Diagram B makes a Mobius band. We could make other shapes using the arrows such as the Klein bottle, and the torus. This topic was very fun and cool and it is a subject everyone will enjoy!!!!!!!!!!!!!!!!!!!!!!!#girlstalkmath #girlsrock #blog2017

Classification of Surfaces

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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Mathematical Epidemiology

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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Quantum Mechanics

By Kathryn Benedict, Olivia Fugikawa, Denna Huang, and Eleanor McAdon

Intro

Quantum mechanics is a subfield of physics. Like with any other major area of study, physics is divided into many smaller categories. Classical physics is the main one, which includes Newton’s Laws of Motion and basic principles of mechanics, like inertia and friction. Things get weird when you delve into modern physics, which includes special relativity, general relativity, and quantum mechanics. Special relativity deals with particles moving at the speed of light, general relativity works with incredibly massive objects and quantum mechanics is the physics of subatomic particles. This is what we worked on for the past two weeks and what our blog post is about!

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Network Science

by Kayla Aguilar, Maris James, and Aynsley Szczesniak.

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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Elliptic Curve Cryptography

By Noa Bearman, Kimberly Cruz Lopez, Tina Lin, Xintong Xiang, and Maria Neri Otero*

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

Screen Shot 2017-06-29 at 1.50.17 PM

Introduction

Have you ever tried to send a secret message to a friend? Did it work? Was it secure? Well, one way to do so in a more secure way is by using Elliptic Curve Cryptography (ECC). Most people have never heard of ECC before, and two weeks ago, neither did we. However, in the past two weeks, we have been learning how to use this exciting application of the techniques of algebraic geometry and abstract algebra applied to the ancient art of keeping messages secure. ECC was first introduced by Victor Miller and Neal Koblitz in 1985. It was proposed as an alternative to other forms of cryptography with public-key systems such as DSA and RSA. Public-key systems involve the use of two different kinds of keys: a public key that is available to the public and a private key in which only the owner knows. The applications of ECC has been growing and has recently gained a lot of attention in industry and academia. The following information below will go more in-depth on what ECC is, how it works, its advantages, its disadvantages, and our progression throughout this course.

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Knot Theory

By Nethania Okyere, Rachel Rozansky, Ashleigh Taylor, and Sylvia Towey

Knot Theory

The knot theory are two mathematical branches of topology. Its simply a loop in 3 dimensional space( doesn’t intersect itself). Knots can be described in various ways. Given a method of description, however, there may be more than one description that represents the same knot. For example, a common method of describing a knot is using a knot diagram. Any given knot can be drawn in many different ways using a knot diagram.

1knots knot theory

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