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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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.

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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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RSA Encryption Cryptography

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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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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Monte Carlo and the Coding Tale

By: Michelle Chen, Cameron Farrar, Laura O’Sullivan, and Cat Bassett

Introduction

Everything we do in life has a chance. That chance may come from picking the right card, picking a certain marble out of a bag or maybe deciding to give the first person who walks through a random door $100. Essentially,each chance has a certain trade-off of benefits. Often times we think about the chances as something will happen over the chance of something else taking place as we weigh possible outcomes. This is called risk analysis. One of the ways we can determine risk is we can use Monte Carlo simulations to replicate real life situations a large number of times in order to observe the long-term patterns without having the complications (cost, labor, materials, etc.) of manual repetition.

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Mathematical Modeling (Fluid Dynamics)

By: Annie Huang, Heesue Kim, Sophie Gilliam, and Sylvia Towey

Hi guys!

Welcome to the Girls Talk Math blog today! This blog is to show you guys what we have learned and accomplished with fluid dynamics. At first, we (Annie, Heesue, Sophie, Sylvia) thought this was a very difficult topic but after some explanation and experiment, we learned how easy it is to work with the different topics thanks to the Girls Talk Math Camp held on the UNC Chapel Hill campus. Today we will be giving you a brief intro to mathematical modeling, Bernoulli’s principle, Dimensional Analysis, and Projectile motion.

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Number Systems

By Miranda Copenhaver, Nancy Hindman*, Efiotu Jagun, and Gloria Su.

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

Number systems are how we represent numbers like 1, 32, and 75. We use the base ten (decimal) system for our numbers most of the time. It’s called base ten because it uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. But what if I told you that 1001101 and 4D both mean seventy-seven? Crazy, right? There are countless number systems, but today we will be focusing on two: hexadecimal (base sixteen) and binary (base two)!

As we’ve said before, the binary system is base two; it only uses 0 and 1. Since only 1 or 0 can be used, the placement of each digit is important. Computers use binary to store and transfer information. It is used in communication (Morse code, braille) and everything electronic like computers, lights, calculators, MP3s, MIDI, JPEG, etc. 

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RSA Encryption Cryptography

By Divya Aikat, Helena Harrison, Annie Qin, and Quinn Shanahan

The definition of cryptography is the art of writing and solving code. However, over the last two weeks, we learned so much more than just this textbook explanation. While working together within our team, we explored many different aspects behind cryptography. By building off our individual strengths, we prepared ourselves for higher level mathematics. The following is a synopsis of the progress we’ve made over the past two weeks.

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Knot Theory

By Jillian Byrnes, Monique Dacanay, Kaycee DeArmey,  Alana Drumgold, Ariyana Smith*, and Wisdom Talley*.

*Ariyana and Wisdom helped the group work through the problem set but were unfortunately unable to attend camp during the blog writing.

A mathematical knot is a loop in three-dimensional space that doesn’t intersect itself, and knot theory is the topological study of these knots. Two knots are considered to be equivalent if they can be stretched or bent into each other without cutting or passing  through themselves. The simplest of these knots is known as the unknot, which is just a circle or its equivalence. Similar to a knot is a link, which is multiple knots intersecting each other. Both knots and links are often described in the form of knot diagrams, which are two-dimensional representations of the three-dimensional shape. There are an infinite number of both knots and links, but here are a few examples in diagram form:

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Network Science

By Cameron Farrar, Elizabeth Gross, Shiropa Noor, and Rebecca Rozansky

Girls Talk Math was an eyeopening experience to a brand new world of mathematics. Over the past two weeks, we have been introduced to multiple topics and related professions. We learned about: quantum mechanics, surface classification, knot theory, computing & dynamics, elliptic curve cryptography, RSA encryption, special relativity and the most interesting of them all- NETWORK SCIENCE!

During our time at Girls Talk Math, we learned about the wonders of network science and graph theory. The difficult part of this otherwise enjoyable journey? Mathematica. Mathematica is a software created to make you suffer, especially if you already know computer science (AHEM BECKY). Basically, we created graphs, did calculations and got confused on Mathematica. Typing out all the commands took ages. We’ll show you some examples as we go through the different concepts we explored. Don’t worry- once you spend some time on Mathematica, you’ll get used to it.

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