Course Descriptions

MATH-S 261 - Honors Multivariate Calculus

Credits:

4

Description:

This is an honors level version of third semester calculus (MATH-I 261). It is intended for students who have strong motivation and a desire for additional challenge. The theory of multivariate calculus is developed as rigorously as possible and studied in greater depth than in MATH-I 261.

Prerequisite:

MATH-I 166 or MATH-S 166 with a minimum grade of B and MATH-I 171 and permission of the instructor.

MATH-I 266 - Ordinary Differential Equations

Credits:

3

Description:

First order equations, second and n-th order linear equations, series solutions, solution by Laplace transform, systems of linear equations.

Prerequisite:

MATH-I 165, MATH-I 166 and MATH-I 171 taken within the last 3 terms with grades of C- or better.

MATH-I 276 - Discrete Math

Credits:

3

Description:

Logic, sets, functions, integer algorithms, applications of number theory, mathematical induction, recurrence relations, permutations, combinations, finite probability, relations and partial ordering, and graph algorithms.

Prerequisite:

or C: MATH-I 165.

MATH-I 290 - Topics in Mathematics for Sophomores

Credits:

1-3

Description:

Treats topics in mathematics at the sophomore level.

Prerequisite:

Prerequisites and course material vary with the topics.

MATH-I 300 - Logic and the Foundations of Algebra

Credits:

3

Description:

Logic and the rules of reasoning, theorem proving. Applications to the study of the integers; rational, real, and complex numbers; and polynomials. Bridges the gap between elementary and advanced courses. This is a prerequisite for 300-level and 400-level pure mathematics courses.

Prerequisite:

or C: MATH-I 166 and MATH-I 171.

MATH-M 303 - Linear Algebra for Undergraduates

Credits:

3

Description:

Introduction to the theory of real vector spaces. Coordinate systems, linear dependence, bases. Linear transformations and matrix calculus. Determinants and rank. Eigenvalues and eigenvectors.

Prerequisite:

MATH-M 230 or MATH-M 216 or equivalent.

MATH-I 321 - Elementary Topology

Credits:

3

Description:

Introduction to topology, including metric spaces, abstract topological spaces, continuous functions, connectedness, compactness, curves, Cantor sets, continua, and the Baire Category Theorem. Also, an introduction to surfaces, including spheres, tori, the Mobius band, the Klein bottle and a description of their classification.

Prerequisite:

MATH-I 261.

MATH-I 333 - Chaotic Dynamical Systems

Credits:

3

Description:

The goal of the course is to introduce some of the spectacular new discoveries that have been made in the past twenty years in the field of mathematics known as dynamical systems. It is intended for undergraduate students in mathematics, science, or engineering. It will include a variety of computer experiments using software that is posted on the Web.

Prerequisite:

MATH-I 166 or MATH-I 222 or MATH-I 232.

MATH-I 351 - Elementary Linear Algebra

Credits:

3

Description:

Not open to students with credit in MATH-I 511. Systems of linear equations, matrices, vector spaces, linear transformations, determinants, inner product spaces, eigenvalues, and applications.

Prerequisite:

MATH-I 166 and MATH-I 171.

MATH-I 353 - Linear Algebra II with Applications

Credits:

3

Description:

This course involves the development of mathematics with theorems and their proofs. This course also includes several important applications, which will be used to create a mathematical model, prove theorems that lead to the solution of problems in the model, and interpret the results in terms of the original problem.

Prerequisite:

MATH-I 351 or MATH-I 511.

MATH-I 354 - Linear Algebra II for Data Science

Credits:

3

Description:

In this course, we will explore a number of contemporary applications of linear algebra (all of which have arisen since the dawn of the Internet Age and most are still under development) in information retrieval, website ranking, text processing, community detection, pattern recognition, and recommender systems for e-commerce, all largely based on matrix factorizations, that should be of interest to students in pure and applied mathematics, actuarial science, computer & information science, and engineering.

Prerequisite:

MATH-I 351 or MATH-I 511 or consent of instructor.

MATH-I 366 - Ordinary Differential Equations

Credits:

3

Description:

Introduction to differential equations for students majoring in Mathematics.  Ordinary differential equations, first and second order equations, linear systems, series solutions, existence and uniqueness, numerical methods, applications to physical problems.  Will be required of majors in Pure and Applied Mathematics Concentrations starting Fall 2024.

Prerequisite:

Prerequisites: MATH-I 165 and MATH-I 166 and MATH-I 171 with a grade of C or better in each course.

Corequisite:

Corequisite: MATH-I 351.

MATH-I 373 - Financial Mathematics

Credits:

3

Description:

Fundamental concepts of financial mathematics and economics, and their application to business situations and risk management. Valuing investments, capital budgeting, valuing contingent cash flows, modified duration, convexity, immunization, financial derivatives. Provides preparation for the SOA/CAS Exam FM/2.

Prerequisite:

MATH-I 261.

MATH-I 390 - Topics in Mathematics for Juniors

Credits:

1-3

Description:

Treats topics in mathematics at the junior level.

Prerequisite:

Prerequisites and course material vary with the topics.

MATH-I 398 - Internship in Professional Practice

Credits:

0-3

Description:

Professional work experience involving significant use of mathematics or statistics. Evaluation of performance by employer and Department of Mathematical Sciences. May count toward major requirements with approval of the Department of Mathematical Sciences for a total of 6 credits.

Prerequisite:

Approval of Department of Mathematical Sciences.

MATH-I 414 - Numerical Methods

Credits:

3

Description:

Error analysis, solution of nonlinear equations, direct and iterative methods for solving linear systems, approximation of functions, numerical differentiation and integration, and numerical solution of ordinary differential equations.

Prerequisite:

MATH-I 266 and a course in a high-level programming language.

MATH-I 421 - Linear Programming and Optimization Techniques

Credits:

3

Description:

This course covers a variety of topics in operations research, including solution of linear programming problems by the simplex method, duality theory, transportation problems, assignment problems, network analysis, dynamic programming.

Prerequisite:

MATH-I 261 and MATH-I 351.

MATH-I 423 - Discrete Modeling

Credits:

3

Description:

Linear programming, mathematical modeling of problems in economics, management, urban administration, and the behavioral sciences.

Prerequisite:

MATH-I 266 and MATH-I 351 or MATH-I 511 or consent of instructor.

MATH-I 425 - Elements of Complex Analysis

Credits:

3

Description:

Complex numbers and complex-valued functions; differentiation of complex functions; power series, uniform convergence; integration, contour integrals; elementary conformal mapping.

Prerequisite:

MATH-I 261.

MATH-I 426 - Introduction to Applied Mathematics and Modeling

Credits:

3

Description:

Introduction to problems and methods in applied mathematics and modeling. Formulation of models for phenomena in science and engineering, their solutions, and physical interpretation of results. Examples chosen from solid and fluid mechanics, mechanical systems, diffusion phenomena, traffic flow, and biological processes.

Prerequisite:

MATH-I 266 and PHYS-I 152.