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

The Art of Cryptography

By: Nia Beverly, Makayla McDaniel, Yuanyuan Matherly, and Tyler Deegan

Introduction

Cryptography is defined as the art of writing and solving codes. Upon first thought, many people picture codes as an antiquated war time communication technique. However, the field of cryptography is alive and well,  and it has become pervasive in our everyday lives. The world is becoming more and more connected through technology, and with this, there is a greater need to protect information. Encryption is probably the most widely used application of cryptography, and it is used to protect information by making it so only one person with a key can understand what is transmitted. In the following paragraphs we will walk through the steps to mathematically understanding one widely used type of encryption.

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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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Quantum Mechanics

By Izzy Cox, Divya Iyer, Wgoud Mansour, Ashleigh Sico, and Elizabeth Whetzel.

Quantum Mechanics is the physics of molecular and microscopic particles. However, it has applications in everyday life as well. If someone asked you if a human was a particle or a wave, what would you think? What about a ball? What about light? Not so easy now, is it? It turns out that all of those things, and in fact, everything around us, can be expressed in physics as both a particle and a wave. This might seem a little unbelievable, but for now, let’s start with the basics.

 

Classical Physics

Although Classical Physics sounds like a complicated idea, it’s the most simple branch of physics. It’s what you think of when someone says “physics”. Classical Physics lays the basic foundation to Quantum Physics with a few basic laws.

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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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Mathematical Epidemiology

by Jillian Byrnes, La’Ziyah Henry, Delphine Liu, Sophie Ussery, and Elizabeth Whetzel.

What is Mathematical Epidemiology?

What is mathematical epidemiology? Well, mathematical epidemiology is when mathematicians use math to predict outcomes in various statistical problems. These problems include growth in infectious bacteria, change in population, and even the effects of climate change. Why is this used? It is used because it doesn’t need a complete set of data to figure out a solution, as long as you can create an equation and plug in the values.

Who uses it? Mathematicians and scientists use it in fields such as biotechnology, medical science, civil engineering, and as public health professionals.

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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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Special Relativity

By Katie Clark, Tori Dunston, Kelly Fan, Abrianna Macklin, and McKenna Vernon

Picture a hummingbird. At any moment, it can go in any of the three dimensions it is a part of. So, it could go up and down, forwards and backwards, or left and right. But, one thing that is not taken into account is time. As it moves through space, it is also occupying time. However, we’re not used to thinking about our world in a four dimensional sense. But, as the movement of the pigeon progresses, so does time. This is known as the relationship between space and time, and it is the primary foundation that special relativity is built on. So, at any given moment, it actually can move in four dimensions at once. This can be simply modeled using a spacetime diagram.

lightcone3

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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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Number Systems

by Alysia Davis, Alyssa Drumgold, Pascale Gomez, Delaney Washington, and Auden Wolfe.

 

Intro to Number Systems

As children we grew up counting in the base ten system (1, 2, 3, etc). However, base ten is only one of many numerical systems. Over these past to weeks at Girls Talk Math at UNC, our  task was to explore other number systems that are not as frequently used as the base 10 system, specifically binary and hexadecimal number systems.

 

Binary

The exact definition of binary is related to using a system of numerical notation that has 2 rather than 10 as a base. This means only two single digits are used, 0 and 1. 

Binary is used for data storage. Binary basically makes it easier for computer processors to understand and interpret incoming information/instructions.

Binary was first discussed by Gottfried Leibniz in 1689 but binary numerical systems were not put to use until a binary converter was created hundreds of years later. The binary system was officially implemented just before the beginning of the nineteenth century.

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