Course Descriptions

MATH-I 611 - Methods of Applied Mathematics I

Credits:

3

Description:

Introduction to Banach and Hilbert spaces, linear integral equations with Hilbert-Schmidt kernels, eigenfunction expansions, and Fourier transforms.

Prerequisite:

Consent of instructor.

MATH-I 612 - Methods of Applied Mathematics II

Credits:

3

Description:

Continuation of theory of linear integral equations; Sturm-Liouville and Weyl theory for second-order differential operators, distributions in n dimensions, and Fourier transforms.

Prerequisite:

MATH-I 611.

MATH-I 626 - Mathematical Formulation of Physical Problems I

Credits:

3

Description:

Nature of applied mathematics, deterministic systems and ordinary differential equations, random processes and partial differential equations, Fourier analysis, dimensional analysis and scaling.

Prerequisite:

Advanced calculus or vector calculus, partial differential equations, linear algebra.

MATH-I 627 - Mathematical Formulation of Physical Problems II

Credits:

3

Description:

Theories of continuous fields, continuous medium, field equations of continuum mechanics, inviscid fluid flow, viscous flow, turbulence. Additional topics to be discussed include application of the theory of dynamical systems, methods for analysis of nonlinear ordinary and partial differential equations, and others. This course is an advancement of topics covered in MATH-I 626.

Prerequisite:

MATH-I 626.

MATH-I 646 - Functional Analysis

Credits:

3

Description:

Advanced topics in functional analysis, varying from year to year at the discretion of the instructor.

Prerequisite:

MATH-I 546.

MATH-I 667 - Dynamical Systems II

Credits:

3

Description:

Continuation of MATH-I 567. Topics in dynamics.

Prerequisite:

MATH-I 567.

MATH-I 672 - Algebraic Topology I

Credits:

3

Description:

Continuation of MATH-I 572. Cohomology, homotopy groups, fibrations, and further topics.

Prerequisite:

MATH-I 572.

MATH-I 673 - Algebraic Topology II

Credits:

3

Description:

A sequel to MATH-I 672 covering further advanced topics in algebraic differential topology such as K-theory and characteristic classes.

Prerequisite:

MATH-I 672.

MATH-I 674 - Mathematical Physics II

Credits:

3

Description:

Continuation of MATH-I 574 Mathematical Physics I. Students will learn more advanced notions and theorems of various mathematical theories that have direct applications to physics.

Prerequisite:

MATH-I 574.

MATH-I 692 - Topics in Applied Mathematics

Credits:

1-3

Description:

Research topics of current interest in applied mathematics to be chosen by the instructor.

MATH-I 693 - Topics in Analysis

Credits:

1-3

Description:

Research topics in analysis and their relationships to other branches of mathematics. Topics of current interest will be chosen by the instructor.

Prerequisite:

Department consent required.

MATH-I 694 - Topics in Differential Equations

Credits:

1-3

Description:

Research topics in differential equations related to physics and engineering. Topics of current interest will be chosen by the instructor.

Prerequisite:

MATH-I 554 and MATH-I 530. Department consent required.

MATH-I 697 - Topics in Topology

Credits:

1-3

Description:

Research topics in topology and their relationships to other branches of mathematics. Topics of current interest will be chosen by the instructor.

MATH-I 698 - Research M.S. Thesis

Credits:

1-6

Description:

Students conduct original research under the direction of a member of the graduate faculty leading to a Masters Thesis. This course is eligible for a deferred grade. Course may be repeated for credit.

MATH-I 699 - Research Ph.D. Thesis

Credits:

variable

Description:

STAT-I 190 - Topics in Statistics for Undergraduates

Credits:

1-5

Description:

Supervised reading course or special topics course at the freshman level. Prerequisites and course material vary with the topic.

STAT-I 290 - Topics in Statistics for Undergraduates

Credits:

3

Description:

Supervised reading course or special topics course at the sophomore level. Prerequisites and course material vary with the topic.

STAT-I 301 - Elementary Statistical Methods I

Credits:

3

Description:

Introduction to statistical methods with applications to diverse fields. Emphasis on understanding and interpreting standard techniques. Data analysis for one and several variables, design of samples and experiments, basic probability, sampling distributions, confidence intervals and significance tests for means and proportions, and correlation and regression. Software is used throughout.

Prerequisite:

MATH-I 110 or MATH-I 111, with a grade of C or better, or MATH-M 118 with a grade of C- or better, taken within last 3 terms or an appropriate ALEKS placement score. Not open to students in the Department of Mathematical Sciences.

STAT-I 350 - Introduction to Statistics

Credits:

3

Description:

A data-oriented introduction to the fundamental concepts and methods of applied statistics. The course is intended primarily for majors in the mathematical sciences (mathematics, actuarial sciences, mathematics education). The objective is to acquaint the students with the essential ideas and methods of statistical analysis for data in simple settings. It covers material similar to that of STAT-I 511, but with emphasis on more data-analytic material. Includes a weekly computing laboratory using Minitab.

Prerequisite:

MATH-I 166.

STAT-S 351 - Honors Introduction to Statistics

Credits:

3

Description:

This course introduces the basic concepts and methods of applied statistics in all areas of science and engineering. Three distinctive features of this honors course are: (1) self-learning and discovery of concepts and methods of statistical analysis through guided instructions, literature search, derivation and simulation; (2) classroom participation - both individually and collaboratively - in active learning of difficult concepts; and (3) communicating such learning to general readers. Students will acquire a basic competence in using statistical freeware R, in presenting data visually, in analyzing data appropriately, in interpreting the results in the context of research problems, and in communicating findings in plain but impactful language to readers not trained in Statistics. STAT-S 351 extends all material covered in STAT-I 350 to a deeper level and gives glimpses into some methodologies delegated to advanced courses, thereby motivating and preparing students to take advanced undergraduate statistics courses.

Prerequisite:

MATH-I 166.