By Clara, Ceren, Zoe, and Jess
Dr. Candice Price had always been good at math. But when her third-grade teacher presented “Schoolhouse Rock!–Multiplication Rock!” to her class, her passion truly began. The 30-minute multiplication lesson inspired her everlasting enthusiasm for mathematics. It is this inspiration that drove her to be the accomplished female mathematician that she is today.
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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 Mukta Dharmapurikar, Anagha Jandhyala, Savanna Jones, and Ciara Renaud.
Have you ever wondered how your credit card number stays secure after shopping online? Every day millions of people’s personal information is entered online or stored in databases, where it seems like anyone could access it. However, a process called cryptography keeps theft from occurring.
Cryptography is the ancient art of keeping secret messages secure. Elliptic curve cryptography is one type of encryption that we spent the last two weeks learning about. It has some advantages over the more common cryptography method, known as RSA.
RSA relies on the difficulty of factoring very large prime numbers. Despite the current security, it’s feasible that one day a method could be invented that makes factoring large prime numbers realistic. In this blog post, we will be explaining the essential math behind how elliptic curves work and how they are used to encrypt messages.
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.
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.
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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