The Math Club
Department of Mathematics and Statistics
Texas Tech University
In the first part of this talk, we give a detailed description of the course Problem Solving for Putnam (MATH 4000), Fall 2019. 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 graduate-level 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 course concentrates on the raw creative problem-solving skills which can serve as an essential ingredient in almost every field of activity. The second part of the talk will be Jack's presentation of the Putnam A6-2018 problem. This is considered to be one of the most difficult problems from the Putnam contest. The solution relies mostly on analytic geometry techniques.Mathematical Medicine is a relatively new and expanding area of Applied Mathematics research with a growing number of mathematicians, experimentalists, biomedical engineers, and research physicians involved in collaborative efforts on a global scale. Mathematical models are playing an increasing role in our understanding of such complex biological processes as the onset, progression, and mitigation of various diseases. In the talk, I lay out the disease paradigm and the assumptions upon which the mathematical model is constructed. This is followed by a presentation of the general model in the form of a system of nonlinear, primarily parabolic partial differential equations with mixed third type boundary conditions. I will perform stability analyses of the model under two different assumptions regarding the source of inflammatory components. Two stability theorems are given along with a bio-medical interpretation of the criteria derived. Also included is a discussion of the existence of unstable equilibrium with a focus on the role of an antioxidant presence and the competing processes of macrophages motility (unrelated to chemotaxis) and chemotaxis. The chapter closes with a brief conclusion.I will first give a construction of the Rational numbers given the integers using an equivalence relation. Then I will demonstrate why the way we traditionally think of the real numbers doesn't quite work as a definition. Finally, I will use a different equivalence relation to construct the real numbers given the rational numbers.Modern classification and regression tasks depend on powerful techniques and models from machine learning. Despite their predictive power on live inputs, these models exhibit remarkable vulnerability to small perturbations. Indeed, a smart �adversary�, perhaps just nature behaving mischievously, can usually contort images, sounds, or other data in a small, human imperceptible fashion that causes a machine learner to incorrectly predict or classify it. Salient yet surprising examples of this phenomenon include pedestrians suddenly crossing the street in front of a self-driving car, anomalous defects in manufactured goods, and tricking iPhone�s facial recognition. In this talk, we�ll introduce the basics of neural networks then discuss the mathematics of generating and defending against adversarial examples. The defense portion will emphasize adversarial training, the training time robustification of learners against adversarial examples.