Undergraduate Courses

(3 Credits)

This course will reveal the key role played by number theory in the development of mathematics. Some applications of number theory will be covered in the course.

Syllabus Example

Topics covered include the binomial theorem, inclusion exclusion principle, recurrence relations, generating functions, and coloring problems.

(3 Credits)

This course is an introduction to numerical linear algebra which addresses numerical methods for solving linear algebraic systems and matrix Eigen problems and applications to partial differential equations. Although the course will stress a computational viewpoint, analysis of the convergences and stability of the algorithms will be investigated.

Syllabus Example

(3 Credits)

This course introduces students to the techniques of optimization. Applications will be emphasized, but some theory will be addressed and proofs will be discussed. As well, students will be taught how to use available software to answer questions. Course topics will include linear programming, integer programming, nonlinear programming, convex and affine sets, convex and concave functions, unconstrained optimization, and combinatorial optimization (i.e. Network flow problems). 

Syllabus Example

(3 Credits)

This course is concerned with the approximate numerical solution of problems which arise in an industrial environment. Topics covered include physical interpretation of a mathematical model, use of library software, preparation of software, analysis of results, and reporting on findings. 

(3 Credits)

Life Contingencies

Syllabus Example

(3 Credits)

This course stresses the theoretical and rigorous development of linear algebra. Major topics include the theory of vector spaces, linear transformations, matrices, characteristic polynomials, bases and canonical forms. Other topics may be covered as time permits. 

Syllabus Example

(3 Credits)

The "big ideas" course is intended to provide a capstone type experience for math majors. It will integrate the student's current math knowledge into a coherent whole via the adoption of a historical perspective. It is particularly aimed at math majors with an interest in math education or the history, philosophy and psychology of mathematics. Students opting for the optional internship, MATH 1231, will explore how the historical development of math relates to the math in the secondary school. The capstone experience will culminate with a research project and presentation.

(3 Credits)

In this course the basic algebraic systems, groups and rings are studied in some detail. Topics include: subgroups, permutation groups, homomorphism's, subrings, ideals and quotient rings. The emphasis is on theory with examples.

Syllabus Example

(3 Credits)

This course provides a more thorough mathematical treatment of the theory than is possible in the non-honors course (MATH 1270), and also covers some more recent applications. In addition to basic material on exact solutions, mathematical proofs will be given of the existence and uniqueness theorems, leading to a better understanding of such important topics as phase plane behavior and stability theory. In addition, more topics will be covered, including a more extensive discussion of series solutions and special functions than is possible in MATH 1270. Finally, a course project, usually done in pairs, on a topic to be chosen by the students with guidance and approval from the instructor, will be a key feature.

Syllabus Example

(3 Credits)

A course intended to give a "modern" view of geometry. Possible approaches include (1) the connection of geometries to abstract algebraic systems and (2) the deductive, synthetic development of Euclidean and non-Euclidean geometry. 

Syllabus Example

(3 Credits)

This course introduces some of the fundamental approaches of applied mathematics. The emphasis is on the model-building process and on developing an understanding of some of the unifying themes of applied mathematics such as equilibria, stability, conservation laws, etc. The material is presented in the form of case studies. 

Syllabus Example

(3 Credits)

This course will provide a broad introduction to mathematical methods typically applied to problems in biology. Models using calculus, ordinary differential equations, partial differential equations, discrete dynamical systems, stochastic dynamics, or a cellular automata framework will be presented and principal methods for their analysis will be described. Computational methods will also be covered, including computing platforms such as XPPAUT. Throughout the course, students will have extensive opportunities to practice the development and analysis of mathematical biology models.

Syllabus Example

(3 Credits)

This is the first term of a two-term sequence in elementary PDE's. The objectives of the course are to provide students with the techniques necessary for the formulation and solution of problems involving PDE's and to prepare for further study in PDE's. The three main types of second order linear PDE's - parabolic, elliptic, and hyperbolic are studied. In addition the tools necessary for the solution of PDE's such as Fourier series and Laplace transforms are introduced.

(3 Credits)

This course contains a rigorous development of the calculus of functions of a single variable, including compactness on the real line, continuity, differentiability, integration, and the uniform convergence of sequences and series of functions. Other topics may be included, such as the notion of limits and continuity in metric spaces.

(3 Credits)

This course covers the following topics: elementary operations with complex numbers, derivatives, integrals, Cauchy's theorem and consequences such as the integral formula, power series, residue theorem, applications to real integrals and series.

(3 Credits)

The topology of r1, as well as that of general metric spaces, will be studied. Basic notions will be applied to obtain the fundamental existence theorem for first order ordinary differential equations. The course will be run on a theorem proving and problem solving basis.