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

This course covers probabilistic aspects of risk management intended for those familiar with probability theory. Games of chance are used as models of real-world situations of decision-making under uncertainty. Students will gain a deeper understanding of the mathematical foundations of probability theory and stochastic processes. They will apply concepts in game theory and probability theory to real-world problems in risk management.

This course is an introduction to knot theory. Knot theory is currently an active area of research in low-dimensional topology, with all kinds of connections to other mathematical fields, including geometry, algebra, physics, combinatorics, and number theory.

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.

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.

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.

This is a rigorous introduction to some topics in mathematics that underlie areas in computer science and computer engineering, including: graphs and trees, spanning trees, colorings and matchings, the pigeonhole principle, induction and recursion, generating functions, and (if time permits) combinatorial geometry. The course integrates mathematical theories with applications to concrete problems from other disciplines using discrete modeling techniques.

Foundational material in mathematical finance. Course covers interest rates, annuities, bonds, forwards, futures, options and other derivative securites. (Basis of actuarial exam in financial math exam fm/2).