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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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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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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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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Knot Theory

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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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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RSA Encryption Cryptography

By Camille Clark, Layke Jones, Isabella Lane, Aza McFadden*, and Lizbeth Otero.

*Aza helped the group work through the problem set but was unfortunately unable to attend camp during the blog writing.

Cryptography is a field of coding and decoding information. It relies on the framework of number theory. Therefore, it can be used to connect theories as well as teaching others the fundamental properties of integers. Relevant number theory topics are modular arithmetic, prime factorization, greatest common divisor, and theorems such as the Chinese Remainder Theorem and Euler’s Theorem. This blog post will focus on the first three topics.

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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.

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Network Science

by Kayla Aguilar, Maris James, and Aynsley Szczesniak.

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:

 

Graph Theory

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.

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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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