Possible topics include cryptography, primes and factoring, computer passwords, networking problems, shortest paths, scheduling problems, building circuits, modeling computation, and correctness of algorithms. This course is an extension of Math 233 and focuses on applications of systems of differential equations including linearization and equilibrium analysis, partial differential equations, underpinnings of linear algebra, and probability and statistics. Computer labs using Mathematica are a fundamental part of the course with one class session each week held in the lab. This course covers the traditional topics from abstract algebra, including groups, rings, integral domains, fields, and homomorphic and isomorphic relationships, as well as standard topics from geometry, including axiomatic systems in both Euclidean and Non-Euclidean geometrics and transformational geometry with vectors and matrices. The focus for the class is the contemporary applications of the concepts presented, together with the weaving together of geometric and algebraic themes.
Linear algebra is the integrating theme.
This course focuses on student-led explorations and discussions of application projects from a variety of disciplines. As a senior-level capstone course, it will give students the opportunity to both use and extend much of the mathematics they have learned in their first three years, and it will deepen and broaden their insights regarding the applications of mathematics. This course in the history of mathematics is intended to give students an insight into some of the great masterpieces of mathematics, as seen in their historical contexts. Developing an understanding of the individuals who were the creators of mathematics helps one better appreciate their creations. Since mathematics is an ever-growing discipline in which new ideas are built upon the old, half the semester is dedicated to 20th century developments in mathematics.