Number Theory Commons^™

Symmetric Presentations Of Finite Groups And Related Topics, Samar Mikhail Kasouha

Electronic Theses, Projects, and Dissertations

A progenitor is an infinite semi-direct product of the form m∗n : N, where N ≤ Sn and m∗n : N is a free product of n copies of a cyclic group of order m. A progenitor of this type, in particular 2∗n : N, gives finite non-abelian simple groups and groups involving these, including alternating groups, classical groups, and the sporadic group. We have conducted a systematic search of finite homomorphic images of numerous progenitors. In this thesis we have presented original symmetric presentations of the sporadic simple groups, M12, J1 as homomorphic images of the progenitor 2∗12 : …

An Integration Of Art And Mathematics, Henry Jaakola

Undergraduate Honors Theses

Mathematics and art are seemingly unrelated fields, requiring different skills and mindsets. Indeed, these disciplines may be difficult to understand for those not immersed in the field. Through art, math can be more relatable and understandable, and with math, art can be imbued with a different kind of order and structure. This project explores the intersection and integration of math and art, and culminates in a physical interdisciplinary product. Using the Padovan Sequence of numbers as a theoretical basis, two artworks are created with different media and designs, yielding unique results. Through these pieces, the order and beauty of number …

Collaboration (Reacting To The Past/Math/History/Writing), James Hayashi

Q2S Enhancing Pedagogy

This is an assignment for a Freshman level course in the College of Natural Science. By the end students will have an understanding of valid research, collaboration and communication skills. Faculty that chooses to use this assignment will be preparing students for an active learning environment, and understanding a “Big Idea”, valid research, technology and communication skills.

Faculty should give an example of what is valid research. As students are completing this assignment mini deadlines (check-ins) shall be set. With the check-ins for this assignment focus on how the group will communicate the check point and the collaboration.

The focus …

The Kronecker-Weber Theorem: An Exposition, Amber Verser

Lawrence University Honors Projects

This paper is an investigation of the mathematics necessary to understand the Kronecker-Weber Theorem. Following an article by Greenberg, published in The American Mathematical Monthly in 1974, the presented proof does not use class field theory, as the most traditional treatments of the theorem do, but rather returns to more basic mathematics, like the original proofs of the theorem. This paper seeks to present the necessary mathematical background to understand the proof for a reader with a solid undergraduate background in abstract algebra. Its goal is to make what is usually an advanced topic in the study of algebraic number …

Prove It!, Kenny W. Moran

Journal of Humanistic Mathematics

A dialogue between a mathematics professor, Frank, and his daughter, Sarah, a mathematical savant with a powerful mathematical intuition. Sarah's intuition allows her to stumble into some famous theorems from number theory, but her lack of academic mathematical background makes it difficult for her to understand Frank's insistence on the value of proof and formality.

Mathematical Card Tricks, Sarah Zimmermann

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.