Mathematics

Katherine Ballentine

Random Walks and the Central Limit Theorem

Imagine a person walking down a straight path, using a coin as her trail guide. Once each second she flips the coin; for heads she takes one step forward, for tails, one step backward. Mathematics can provide insight into such random walks, telling us things like how far the walker is expected to get and the probability she returns to her origin. This project uses computer simulations of random walks to illustrate one of mathematics' big ideas: the Central Limit Theorem.

Session B - 10:15 a.m. - Room 320.

John Feldkamp

Fermat's Last Theorem -- The Search for the Holy Grail in Mathematics

No problem has puzzled mathematicians more over the centuries than Fermat's Last Theorem. The Pythagorian formula for the lengths x, y and z of the sides of a right triangle has been known for at least 2,500 years and has many known proofs. In the early 1600s, Fermat investigated the integer solutions x, y and z to the more general equation for N any positive integer at least 3. Fermat believed he had discovered that this more general equation has NO integer solutions x, y and z where at least one of them is not 0. It took almost 400 years and the effort of dozens of mathematicians to finally prove in the 1990s that Fermat was indeed correct.

Session B - 10 a.m. - Room 320.

Satik Manasyan

RSA Encryption and Decryption

RSA is a public-key cryptographic algorithm which was first published in 1977 by its three discoverers. The RSA cryptosystem is the workhorse of Internet security. It is widely used in E-commerce and secure Internet access. There are two keys -- a public and a private key for each communication participant in the RSA cryptosystem. The public key is open and the private key is hidden. The message is represented as a digit string that is encrypted by the recipient's public key and decrypted by their private key. The security of the RSA system is based on the assumption that factoring very large integers is extremely time consuming. In this work an efficient implementation of the RSA system is done.

Session A - 9:30 a.m. - Room 350.

John Feldkamp

The Effectiveness of PowerPoint and Electronic White Boards in the Mathematics Classroom

A popular method of teaching in today's K-12 classroom is standardizing lessons on Microsoft Office's PowerPoint. Another tool that is starting to become more common in classrooms is electronic white boards, which are similar to smart boards. In attempting to discover the most effective way to teach in the mathematics classroom, a prospective teacher investigates these techniques at a local Ypsilanti school.

Group 2 - 10:45 a.m. to 12:30 p.m.- Room 310A/B .

Elizabeth Heskett

Thinking Outside the Box: An Introspective Look at the Use of Art in Teaching Geometry

The focus of this study is how visual representations of different mathematical concepts can be an effective way to teach children geometry in a meaningful way, especially when the concepts are tied to art.

Group 2 - 10:45 a.m. to 12:30 p.m.- Room 310A/B .

Stacy Hiller

Helping Students to Make Sense of Mathematical Concepts Using Multiple Representations

The focus of this study is the use of multiple representations to model mathematical concepts. Not all models are equal. This study explores the effectiveness of different models and the implications for mathematics instruction.

Group 1 - 8:30 a.m. - 10:15 a.m. - Room 310A/B .