Quantum Mechanics

by Nya Batson, Monique Dacanay, Emily Gao, and Staci Tranquille.

Hello! And welcome to the realm of quantum mechanics!  First off, what in the world is quantum mechanics? Let’s start with a brief introduction.

What is Quantum Mechanics?

Quantum mechanics is one of the most important branches of physics. It focuses on the laws of nature at three different levels: molecular, atomic, and subatomic. Quantum mechanics has a variety of important concepts; the following are some that we learned through our problem set: Planck’s law, the photoelectric effect, and wave-particle duality.  A crucial element of quantum mechanics is understanding that everything has characteristics of both waves and particles. We will touch on this and many other topics later on.

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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 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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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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RSA Encryption Cryptography

by Lily Taylor, Zoe Tobien, Tehya Weaver, and Tayloir Wiley.

RSA Encryption Cryptography

What is RSA Encryption Cryptography?

RSA was one of the first public-key* cryptosystems and it is widely used for secure data transmission. It was first created by Ron Rivest, Adi Shamir, and Leona Adleman.

*Public key is used to establish a secret key, and the public key is sent in public. We then use the private key method to encrypt and decrypt large amounts of data, but no one knows the private key.

  • To code: U^s=x X(mod N)=Y
  • To decode Y^t=O O(mod N)=U

In computing, the modulo operation finds the remainder after division of one number by another. Given two positive numbers, a and n, a modulo n (in other words a mod n) is the remainder of the a division of a by n, where a is the dividend and n is the divisor.

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Elliptic Curve Cryptography

by Alana Drumgold*, Lauren Flowers, Emily Huang, Tamarr Moore*, and Ashleigh Sico.

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

For years, people have been trying to find a way to send secret messages. This may have been easy to do in the ancient times of the Roman Empire, where you could write a message, and then hand-deliver it to your recipient.  This way, you could be certain that nobody else could intercept it. However, this becomes a lot more difficult in today’s online tech-driven world. People no longer hand-deliver letters; rather, we email or text our friends.  So how do we make sure that nobody else can intercept your text message as it travels the internet before finally landing on your friend’s cell-phone? The answer is found in cryptography, a technology that is becoming more and more important in today’s world.  Today, we are going to focus on one particular form of cryptography: elliptic curve cryptography.

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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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Intro to Relativity

By: Miranda Copenhaver, Chloe Nash, Wanda Wilkins, Lauren Behringer, and Jazmin Santillan C.

 

Throughout this week, we have worked through multiple problems dealing with both classical mechanics and special relativity. We found the main difference between classical mechanics and special relativity to be the assumptions made about time as a constant. This is what we mean:

  • In classical mechanics it is assumed that time is a constant that is observed the same for all viewers.
  • In special relativity time cannot be taken as a constant. Because the speed of light is the same for all observers, time-dilation occurs.

So, if you are getting a little lost it’s completely normal. We have a couple of examples of both classical mechanics and special relativity below:

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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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