by Knot Nerds
What is knot theory?
Have you ever tied your shoes before? I mean, I hope you have! So, what in the world does tying your shoes have to do with math? Here comes knot theory! Knot theory is a sub-topic of topology that studies mathematical knots, links, and their permutations. Knots can be represented by polynomials and can thus be compared to one another.
Continue reading
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.
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.
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.
by Camille Clark, Layke Jones, Aekta Kallepalli, Maya Mukerjee, and Caroline Zhou.
Euler characteristics are defined by the equation V- E + F = 2 where V = number of vertices, E = number of edges or nodes, and F = number of faces. Sometimes though, the equation V – E + F = 2 does not work for all situations because the solution can give various outcomes due to the dimensions and simplicity of the object. If 2 objects are topologically the same, they will have the same Euler characteristics. For all simple polygons, the Euler characteristics equal one. Figures with holes don’t follow these conventions as the holes in these figures add additional faces and edges not proportional to the formulas for simple figures.
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.
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.
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.
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.
by Kayla Aguilar, Maris James, and Aynsley S.
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:
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.
by Alysia Davis, Alyssa Drumgold, Pascale Gomez, Delaney Washington, and Auden Wolfe.
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.
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.
