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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.

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).

Complex numbers and functions, analytic functions, complex integration, series, residues, conformal mappings. Applications: computation of real integrals, Dirichlet's boundary value problem and its application to physics and engineering. Prerequisite: MATH 233.

Introduction to groups, rings, fields, vector spaces, and related concepts. Emphasis on development of careful mathematical reasoning. Prerequisites: MATH 235 or 236; MATH 300 or consent of instructor.