Not available at this time

Introduction to the fascinating theory of knots, links, and surfaces in 3- and 4-dimensional spaces. This course will combine geometric, algebraic, and combinatorial methods, where the students will learn how to utilize visualization and make rigorous arguments.

This is a stand-alone independent study designed by the student and faculty sponsor that involves frequent interaction between instructor and student. Qualitative and quantitative enrichment must be evident on the proposed contract before consent is given to undertake the study.

Not available at this time

This class is designed to help students review and prepare for the GRE Mathematics subject exam, which is a required exam for entrance into many PhD programs in mathematics. Students should have completed the three courses in calculus, a course in linear algebra, and have some familiarity with differential equations. The focus will be on solving problems based on the core material covered in the exam. Students are expected to do practice problems before each meeting and discuss the solutions in class.

Description not available at this time

Abstract algebra forms a key part of the ideas behind high school mathematics and is the basis for several parts of the Massachusetts Test for Educator Licensure for secondary school math teachers. This course will cover the parts of abstract algebra most important for building a deep understanding of the ideas of high school mathematics and their interconnections. It will focus on the properties of rings (especially the integers and polynomial rings over fields), and fields. During the course, we will be making connections between these topics and high school mathematics.

Basic properties of the positive integers including congruence arithmetic, the theory of prime numbers, quadratic reciprocity, and continued fractions. Theory applied to develop algorithms and computational techniques of computer science and to cryptography. To help learn these materials, students will be assigned computational projects using computer algebra software. Prerequisite: MATH 233 and 235. Math 300 or COMPSCI 250 as a co-requisite is not absolutely necessary but highly recommended.

This course explores various approaches to geometry, as we trace the evolution of mathematical thinking and rigor from ancient to modern: constructions with straight-edge and compass, axiomatic approach of Euclid and Hilbert, analytic geometry via linear algebra, and Klein?s approach using symmetries and transformations. This will open the doors to many non-Euclidean flavors of geometry, where projective geometry will be studied in some detail.

We learn how to build, use, and critique mathematical models. In modeling we translate scientific questions into mathematical language, and thereby we aim to explain the scientific phenomena under investigation. Models can be simple or very complex, easy to understand or extremely difficult to analyze. We introduce some classic models from different branches of science that serve as prototypes for all models. Student groups will be formed to investigate a modeling problem themselves and each group will report its findings to the class in a final presentation.