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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By Ayanna Blake, Lisa Oommen*, Myla Marve, Tamarr Moore, Caylah Vickers, and Lily Zeng.

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

The Girls Talk Math camp is about female high school students from different places who discuss mathematics, mathematicians, and theories. We were split up into groups and were assigned different math topics to learn. Our topic was classification of surfaces, which is listed under the umbrella topic of abstract geometry.

We thought the surfaces project was very interesting and cool to learn about, because it introduced us to college level math and allowed us to understand different parts of geometry. Along with gaining knowledge of surfaces, we also got to learn about other groups topics. Campers presented their topics on the last day and helped us to perceive the significance of the different subjects.

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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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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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