The Math Club
Department of Mathematics and Statistics
Texas Tech University
Polynomials in three variables x, y, and z form an algebraic structure known as a ring.
Just as subspaces are distinguished subsets of a vector space, a ring has its distinguished subsets known as ideals.
All linear combinations - with polynomial coefficients – of $ p_1 = x y^2 z - x^4 $, $ p_2 = xy-xz $, and $ p_3 = xy-xz $ form an ideal.
Does the polynomial $ x^{15} + y^{15} – xz^{14} $ belong to this ideal?
This is not straightforward to decide, but there is a way, and I will illustrate it with some examples from a popular past time.
Communities, groups of nodes in a graph that are closely related among each other but loosely related to the other nodes in the network, exists within the species, gene, and protein networks of a microbiome. Many different algorithms have been developed to detect these communities, two of which include the Girvan-Newman algorithm and the Louvain algorithm. Trials run on assortative planted partiton models assess the accuracy of these algorithms with respect to their computational time. When applying community detection algorithms to dynamic graphs with community structure imposed by the Chinese restaurant stochastic process, initial results show promising use of the Jaccard index as well as the Pointwise Mutual Information index as tracking methods.
Nuclear science is one of the most technologically advanced branches of human knowledge.
Let us walk together through this fascinating world and understand how mathematics can be used to help the design and operation of nuclear systems.
This talk is meant to bring an example of how diverse disciplines such as math, physics, engineering, and computer science meet together in real life.
In the first part of this joint talk, we give a detailed description of Problem Solving (MATH-4000), Fall
2018. The course teaches important skills in problem-solving that are not taught in a systematic way in
any other course. These skills are extremely valuable in preparing students for jobs and for graduatelevel research. The teaching style will be a mixture of a lecture and a problem-solving session. By the
end of this course, students should develop fundamental problem-solving skills, and become
accustomed to concentrating on a problem for an extended period of time. Indeed, this seminar
concentrates on the raw creative problem-solving skills which can serve as an essential ingredient in
almost every field of activity. This course will be offered again this Fall under MATH 4000-Problem
Solving for Putnam and we invite all interested students to register.
Ultimately, this course is designed to train the best math & science undergraduate students at TTU for
the most prestigious competition: The William Lowell Putnam Mathematical Competition.
In the second part of the talk, a Putnam A1-2018 will be presented by Alexander who was a competitor
last year.