This course is based on the first examination of the Society of Actuaries. Its content is largely dependent on that examination.

The course will cover the following topics: Introduction to and classification of second-order partial differential equations, wave equation, heat equation and Laplace equation, D'Alembert solution to the wave equation, solution of the heat equation, maximum principle, energy methods, separation of variables, Fourier series, Fourier transform methods and operator eigenvalue problems. Time-permitting, we will briefly examine numerical methods for partial differential equations, as well as some select examples of nonlinear partial differential equations.

Topology of the euclidean space and functions of several variables (implicit function theorem), introduction to Fourier analysis, metric spaces and normed spaces. Applications to differential equations, calculus of variations, and others.

This course is an introduction to mathematical analysis. A rigorous treatment of the topics covered in calculus will be presented with a particular emphasis on proofs. Topics include: properties of real numbers, sequences and series, continuity, Riemann integral, differentiability, sequences of functions and uniform convergence.

Cross-listed with CompSci 575. A basic introduction to combinatorics and graph theory for advanced students in computer science, mathematics, and related fields. Topics include elements of graph theory, Euler and Hamiltonian circuits, graph coloring, matching, basic counting methods, generating functions, recurrences, inclusion-exclusion, Polya's theory of counting. Prerequisites: mathematical maturity, calculus, linear algebra, discrete mathematics course such as CompSci 250 or Math 455. Math 411 recommended but not required.

The Commonwealth Honors College thesis or project is intended to provide students with the opportunity to work closely with faculty members to define and carry out in-depth research or creative endeavors. It provides excellent preparation for students who intend to continue their education through graduate study or begin their professional careers. The student works closely with their 499Y Honors Research sponsor to pursue research on a topic or question of special interest to them in preparation for writing a 499T Honors Thesis or completing a 499P Honors Project.

Honors Thesis expectations are high. The intended end-product is a traditional research manuscript with accompanying artifact(s), all theses: - are 6 credits or more of sustained research on a single topic, typically conducted over two semesters. - begin with creative inquiry and systematic research. - include documentation of substantive scholarly endeavor. - culminate in an oral defense or other form of public presentation.

Honors Project expectations are high. The intended end-product is a traditional project manuscript with accompanying artifact(s), all projects: - are 6 credits or more of sustained research on a single topic, typically conducted over two semesters. - begin with creative inquiry and systematic research. - include documentation of substantive scholarly endeavor. - culminate in an oral defense or other form of public presentation.

Not available at this time

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.