Course Search Results

Computer arithmetic, root finding, polynomial approximation, numerical integration, numerical linear algebra, numerical solution of differential equations; use of a higher-level computer language such as Matlab, Python, or Julia.

This course examines numerical methods for finding solutions of nonlinear equations, polynomial interpolation and approximation of functions, numerical integration, 

numerical solution of simultaneous linear algebraic equations, and numerical solution of differential equations.  Homework requires the use of a computer.  The system and

the language used will be taught in the course. The current choices Matlab, or Python, or Julia.

 

 

 

Basic theory of optimization, use of numerical algorithms in solution of optimization problems; linear and nonlinear programming, sensitivity analysis, convexity, optimal control theory, dynamic programming, calculus of variations.

Partial derivatives, max-min problems, integrals along curves, surfaces and solids, vector fields and conservation of energy; curl, divergence, Stokes' theorem and the divergence theorem; the classical partial differential equations and qualitative behavior of their solutions.

Topics include partial derivatives, max-min problems, integrals along curves, surfaces and solids, Stokes' Theorem and the Divergence Theorem and classical partial differential equations. There are usually two or three hour-long exams and a comprehensive final exam. Depending on the instructor, part of the grade may also depend on homework or quizzes. Although the course is part of the engineering sequence, it is not restricted to engineering students. The course is taught by faculty.

First-order ordinary differential equations; second-order linear differential equations; series solutions; higher-order linear and matrix differential equations; existence and uniqueness theorems; may include introduction to basic partial differential equations (PDE) or Laplace Transforms.

Topics include first-order ordinary differential equations, second-order linear differential equations, series solutions, higher order linear and matrix differential equations, and existence and uniqueness theorems. Optional Topics: Introduction to basic PDE or Laplace Transforms. Not recommended for students who have taken MATH:2560, since there is considerable overlap. Requirements include in-class exams and a comprehensive final exam; homework involving problem solving is emphasized. Quizzes and/or homework may be collected. The course is taught by a faculty member.

 

Vector algebra and geometry of three-dimensional Euclidean space and extensions to n-space and vector spaces; lines and planes, matrices, linear transformations, systems of linear equations, reduction to row-echelon form, dimension, rank, determinants, eigenvalues and eigenvectors, diagonalization, Principal Axis Theorem.

This course is for graduate students in a department other than mathematics and covers the basics of linear algebra. It covers the same material as MATH:2700; undergraduates should register for MATH:2700. Requirements include homework, quizzes, one or more midterms, and a final exam. The course is taught by a faculty member.

Basic logic, proof methods, sets, functions, relations, mathematical induction; gradual transition from familiar number systems to abstract structures—division algorithm, unique factorization theorems; groups, subgroups, quotient groups, homomorphisms. This course introduces students to basic logic, proof methods, sets, functions, relations, and mathematical induction, through a gradual transition from familiar systems to abstract structures. Topics include the division algorithm and unique factorization theorems for integers and polynomials, the construction of integers, rationals and reals, and an introduction to algebraic systems such as groups, rings, and fields. Particular attention is given to solving problems and writing proofs; regular written assignments are required. Students are expected to attain a more exact knowledge of theoretical concepts than in previous courses. Consequently, students may find this course rather demanding and time consuming. Grades are based on problem sets, one or more midterms, and a comprehensive final exam. The course is taught by faculty members and complemented by a discussion section led by a TA.

Elementary topological and analytic properties of real numbers; emphasis on ability to handle definitions, theorems, proofs.

This course starts with a discussion of the real number system, especially the completeness axiom, covers convergence of sequences, and explains the basic theory underlying the differential and integral calculus. Particular attention is given to solving problems and writing proofs; regular written assignments are required. Students are expected to attain a more exact knowledge of theoretical concepts than in previous courses. Consequently, students may find this course rather demanding and time consuming. The course is taught by a faculty member and complemented by a discussion section led by a TA.

Research experience; students study an elementary topic of active research, then work in groups under faculty supervision.

Elementary topological and analytical properties of real numbers; emphasis on ability to handle definitions, theorems, proofs; same material as MATH:3770 for non-mathematics graduate students.

This course is for graduate students in departments other than mathematics and covers the same material as MATH:3770; undergraduates should register for MATH:3770. Requirements include homework, quizzes, one or more midterms, and a final exam. The course is taught by a faculty member with a discussion section taught by a TA.

Vector spaces, linear transformations, matrices, equivalence of matrices, eigenvalues and eigenvectors, canonical forms, similarity, orthogonal transformations, bilinear and quadratic forms.

Basic combinatorics and graph theory, their applications (which may include scheduling, matching, optimization); Eulerian and Hamiltonian paths, spanning trees. Offered spring semesters.

May include numerical systems; Babylonian, Egyptian, and Greek mathematics; mathematics of other cultures; calculus; 19th- and 20th-century mathematics.