Applied and Computational Mathematics MS

Applied and Computational Mathematics (thesis option), MS degree, typical course sequence

Course Sem. Cr. Hrs.
First Year
Choose three of the following core courses: 9
   MATH-601
   Methods of Applied Mathematics 
This course is an introduction to classical techniques used in applied mathematics. Models arising in physics and engineering are introduced. Topics include dimensional analysis, scaling techniques, regular and singular perturbation theory, and calculus of variations. (Prerequisites: MATH-221 and MATH-231 or equivalent courses or students in the ACMTH-MS or MATHML-PHD programs.) Lecture 3 (Spring).
 
   MATH-602
   Numerical Analysis I 
This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and matrix algebra. (Prerequisites: ((MATH-241 or MATH-241H) and MATH-431) or equivalent courses or graduate standing in ACMTH-MS or MATHML-PHD programs.) Lecture 3 (Fall).
 
   MATH-605
   Stochastic Processes
This course is an introduction to stochastic processes and their various applications. It covers the development of basic properties and applications of Poisson processes and Markov chains in discrete and continuous time. Extensive use is made of conditional probability and conditional expectation. Further topics such as renewal processes, reliability and Brownian motion may be discussed as time allows. (Prerequisites: ((MATH-241 or MATH-241H) and MATH-251) or equivalent courses or graduate standing in ACMTH-MS or MATHML-PHD or APPSTAT-MS programs.) Lecture 3 (Spring).
 
   MATH-622
   Mathematical Modeling I
This course will introduce graduate students to the logical methodology of mathematical modeling. They will learn how to use an application field problem as a standard for defining equations that can be used to solve that problem, how to establish a nested hierarchy of models for an application field problem in order to clarify the problem’s context and facilitate its solution. Students will also learn how mathematical theory, closed-form solutions for special cases, and computational methods should be integrated into the modeling process in order to provide insight into application fields and solutions to particular problems. Students will study principles of model verification and validation, parameter identification and parameter sensitivity and their roles in mathematical modeling. In addition, students will be introduced to particular mathematical models of various types: stochastic models, PDE models, dynamical system models, graph-theoretic models, algebraic models, and perhaps other types of models. They will use these models to exemplify the broad principles and methods that they will learn in this course, and they will use these models to build up a stock of models that they can call upon as examples of good modeling practice. (This course is restricted to students in the ACMTH-MS or MATHML-PHD programs.) Lecture 3 (Fall).
 
   MATH-645
   Graph Theory
This course introduces the fundamental concepts of graph theory. Topics to be studied include graph isomorphism, trees, network flows, connectivity in graphs, matchings, graph colorings, and planar graphs. Applications such as traffic routing and scheduling problems will be considered. (This course is restricted to students with graduate standing in the College of Science or Graduate Computing and Information Sciences.) Lecture 3 (Fall).
 
   MATH-722
   Mathematical Modeling II
This course will continue to expose students to the logical methodology of mathematical modeling. It will also provide them with numerous examples of mathematical models from various fields. (Prerequisite: MATH-622 or equivalent course.) Lecture 3 (Spring).
 
MATH-606
Graduate Seminar I
The course prepares students to engage in activities necessary for independent mathematical research and introduces students to a broad range of active interdisciplinary programs related to applied mathematics. (This course is restricted to students in the ACMTH-MS or MATHML-PHD programs.) Lecture 2 (Fall).
1
MATH-607
Graduate Seminar II
This course is a continuation of Graduate Seminar I. It prepares students to engage in activities necessary for independent mathematical research and introduces them to a broad range of active interdisciplinary programs related to applied mathematics. (Prerequisite: MATH-606 or equivalent course or students in the ACMTH-MS or MATHML-PHD programs.) Lecture 2 (Spring).
1
 
MATH Graduate Electives
9
Second Year
MATH-790
Research & Thesis
Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor. (This course is restricted to students in the ACMTH-MS or MATHML-PHD programs.) Thesis (Fall, Spring, Summer).
7
 
MATH Graduate Elective
3
Total Semester Credit Hours
30

Applied and Computational Mathematics (project option), MS degree, typical course sequence

Course Sem. Cr. Hrs.
First Year
Choose three of the following core courses:
9
   MATH-601
   Methods of Applied Mathematics
This course is an introduction to classical techniques used in applied mathematics. Models arising in physics and engineering are introduced. Topics include dimensional analysis, scaling techniques, regular and singular perturbation theory, and calculus of variations. (Prerequisites: MATH-221 and MATH-231 or equivalent courses or students in the ACMTH-MS or MATHML-PHD programs.) Lecture 3 (Spring).
 
   MATH-602
   Numerical Analysis I
This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and matrix algebra. (Prerequisites: ((MATH-241 or MATH-241H) and MATH-431) or equivalent courses or graduate standing in ACMTH-MS or MATHML-PHD programs.) Lecture 3 (Fall).
 
   MATH-605
   Stochastic Processes
This course is an introduction to stochastic processes and their various applications. It covers the development of basic properties and applications of Poisson processes and Markov chains in discrete and continuous time. Extensive use is made of conditional probability and conditional expectation. Further topics such as renewal processes, reliability and Brownian motion may be discussed as time allows. (Prerequisites: ((MATH-241 or MATH-241H) and MATH-251) or equivalent courses or graduate standing in ACMTH-MS or MATHML-PHD or APPSTAT-MS programs.) Lecture 3 (Spring).
 
   MATH-622
   Mathematical Modeling I
This course will introduce graduate students to the logical methodology of mathematical modeling. They will learn how to use an application field problem as a standard for defining equations that can be used to solve that problem, how to establish a nested hierarchy of models for an application field problem in order to clarify the problem’s context and facilitate its solution. Students will also learn how mathematical theory, closed-form solutions for special cases, and computational methods should be integrated into the modeling process in order to provide insight into application fields and solutions to particular problems. Students will study principles of model verification and validation, parameter identification and parameter sensitivity and their roles in mathematical modeling. In addition, students will be introduced to particular mathematical models of various types: stochastic models, PDE models, dynamical system models, graph-theoretic models, algebraic models, and perhaps other types of models. They will use these models to exemplify the broad principles and methods that they will learn in this course, and they will use these models to build up a stock of models that they can call upon as examples of good modeling practice. (This course is restricted to students in the ACMTH-MS or MATHML-PHD programs.) Lecture 3 (Fall).
 
   MATH-645
   Graph Theory
This course introduces the fundamental concepts of graph theory. Topics to be studied include graph isomorphism, trees, network flows, connectivity in graphs, matchings, graph colorings, and planar graphs. Applications such as traffic routing and scheduling problems will be considered. (This course is restricted to students with graduate standing in the College of Science or Graduate Computing and Information Sciences.) Lecture 3 (Fall).
 
   MATH-722
   Mathematical Modeling II
This course will continue to expose students to the logical methodology of mathematical modeling. It will also provide them with numerous examples of mathematical models from various fields. (Prerequisite: MATH-622 or equivalent course.) Lecture 3 (Spring).
 
MATH-606
Graduate Seminar I
The course prepares students to engage in activities necessary for independent mathematical research and introduces students to a broad range of active interdisciplinary programs related to applied mathematics. (This course is restricted to students in the ACMTH-MS or MATHML-PHD programs.) Lecture 2 (Fall).
1
MATH-607
Graduate Seminar II
This course is a continuation of Graduate Seminar I. It prepares students to engage in activities necessary for independent mathematical research and introduces them to a broad range of active interdisciplinary programs related to applied mathematics. (Prerequisite: MATH-606 or equivalent course or students in the ACMTH-MS or MATHML-PHD programs.) Lecture 2 (Spring).
1
 
MATH Graduate Electives
9
Second Year
MATH-790
Research & Thesis
Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor. (This course is restricted to students in the ACMTH-MS or MATHML-PHD programs.) Thesis (Fall, Spring, Summer).
4
 
MATH Graduate Electives
6
Total Semester Credit Hours
30