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.

Continue reading

Scientific Computing: Recurrence Relations

By: Kathryn Benedict, Kate Allen, Sarai Ross, Rosy Nuam

Girls Talk Math is an all girls camp that introduces new topics that students would not normally see in their everyday math class at school. This camp also brings together many young women to better explore a field that is male dominated. During this camp we were able to research many important women that we able to make their own legacy while facing much adversity along the way. The camp wants to show not only the campers but also other women going into the field of math and science to not be afraid due to the gender difference, but instead use it as motivation to carry on doing what you love and making your own legacy along the way.

Our group consisted of four young women. Kathryn is a rising sophomore at Cedar Ridge High School. Kate is a rising sophomore at Carrboro High School. Sarai is a rising junior at Northern Vance High School. Rosy is a rising senior at East Chapel Hill High School.

Continue reading

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

Continue reading

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

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:

Continue reading

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!

Continue reading

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.

Continue reading

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.

Continue reading

Real World Cryptography

By: Shai Caspin, Natalie Bowers, Bryana Dorsey, Nia Pierce, and Cana Perry

Cryptography is the act of encrypting and decrypting codes. It’s used to pass secret messages and keep outsiders from accessing information. Math is used to help encrypt codes using different methods. One common methods is to use RSA encryptions, which uses prime numbers and mod functions to make deciphering impossible. RSA encryptions are so successful since factoring large numbers into their prime factors is incredibly difficult, and there is yet a way to do so quickly and efficiently. 

We were all very interested in learning more about cryptography since it incorporates everyday math with real-world problems and situations.

Continue reading