# Program Details

The program in Computational Mathematics leading to a Master of Science degree is a 36 credit multidisciplinary program combining the mathematics, computer science, and statistics resources found in the Department of Mathematics and Computer Science. The degree takes advantage of faculty strengths: a strong commitment to teaching and active research programs in computational fields, often crossing discipline lines.

### CORE

The core of the program consists of twelve 1.5 credit mini-courses, four each in mathematics, computer science, and statistics. This portion of the program is designed to ensure a common knowledge base in the three disciplines. Incoming students can, in consulatation with the program director, choose to waive one or more core courses based on prior knowledge. Any core courses that are waived are replaced by elective courses. Most courses in the core curriculum have a computational component using a software package or programming language related to that particular core topic. Students who complete the entire core will have facility with at least a computer algebra software package, the Python programming language, the Linux operating system, and a statistical software package.

The core courses are:

- Mathematics (prerequisites: Calculus I and II)
- CPMA 511 Logic and Proof
- CPMA 512 Linear Algebra
- CPMA 515 Advanced Discrete Math
- CPMA 518 Vector Calculus

- Statistics (prerequisites: a calculus-based Probability and Statistics course, such as Duquesne's MATH 301, or equivalent knowledge)
- CPMA 521 Probability/Markov Chains
- CPMA 522 Statistical Inference
- CPMA 525 Linear Models
- CPMA 526 Experimental Design

- Computer Science (prerequisities: a major's level introductory programming course, such as Duquesne's COSC 160, or equivalent knowledge)
- CPMA 530 Programming Language: Python
- CPMA 532 Data Structures
- CPMA 535 Intro to Computer Systems
- CPMA 536 Software Engineering

See the graduate catalog for course descriptions. Incoming students who do not have the appropriate prerequisite background for a core sequence will be advised by the program director on acquiring the requisite knowledge prior to beginning the program.

### ELECTIVES

Each semester, at least one elective is offered in each of mathematics, statistics, and computer science. Student interest is considered in deciding what electives will be offered. Generally speaking, each elective includes a significant computational component.

Elective offerings in recent years have included:

- CPMA 550 Computer Networks
- CPMA 560 Algorithms/Graph Theory
- CPMA 563 Numerical Differential Equations
- CPMA 566 Operations Research
- CPMA 573 Statistical Computing
- CPMA 574 Prediction and Classification Modeling
- CPMA 580 Aritificial Intelligence/Cognitive Science
- CPMA 582 Machine Learning
- CPMA 583 Principles of Programming Languages
- CPMA 584 Formal Languages and Automata
- CPMA 585 Computer Security
- CPMA 59x Special Topics: Fundamentals of Clinical Trials

Other options for earning credit beyond the core include:

- Internship.
- Project or thesis.
- Taking graduate courses outside the Computational Mathematics program, with the approval of the program director. In addition to taking graduate courses offered by other Duquesne departments, students can potentially cross-register at other local institutions, including Carnegie Mellon and the University of Pittsburgh. At most six credits earned outside the program can be applied to the degree.
- Independent study. This can be an option if a faculty member is willing to provide an individualized educational experience for a student, for instance supervising and evaluating the student's independent study of material that has been offereed as a course in a previous semester but that is not expected to be offered again before the student completes the program.

### INTERNSHIP

The Computational Mathematics program stresses real-life problems and real-life experiences. To that end, all students in the Computational Mathematics program must register for and complete CPMA 599 Internship. The internship requiement can be fulfilled in one of two ways:

- Prior or current employment experience related to computational mathematics, or
- A supervised internship in a position involving computational mathematics.

The employment experience or supervised internship must be verified by a supervisor's written report and approved by the program director. Students wishing to fulfill the requirement without receiving elective credit toward their degree for the experience may register for zero credits of CPMA 599. At least 40 hours of appropriate employment/internship experience is required to earn a Pass grade for the 0-credit course. Alternatively, students may register for up to three credits of CPMA 599 per semester (and a maximum of six credits overall) if they have or anticipate having experience beyond the minimum 40-hour requirement.

### THESIS/PROJECT

With the approval of a Computational Mathematics faculty advisor, a first reader, and the Graduate Studies Committee, a student may write a thesis/project--worth six credits toward the 36 required for a degree--to be begun after completion of 18 credit hours. Depending on the student's background and interests, this portion of the program provides an opportunity to design a project or conduct research with a significant computational component. Written and oral presentations of the results are required for both thesis and project.

### COMPUTATIONAL COMPONENT

Virtually every course in the M.S. in Computational Mathematics includes a computational component requiring the use of tools appropriate to the discipline. Although tools change frequently in these rapidly developing areas, typical examples might include:

- Mathematics: Maple, MATLAB®
- Computer Science: Python, C++, Linux, Windows
- Statistics: SAS®, R, JMP®, SPSS®

### COMBINED B.S./M.S. DEGREES PROGRAM

The Mathematics and Computer Science Department offers a combined B.S./M.S. program to its academically-strong majors. Students admitted to the program have the opportunity to apply graduate credits earned while undergraduates toward fulfilling requirements of both their departmental B.S. degree and the Computational Mathematics M.S. degree. A student in the program could potentially complete both the B.S. and M.S. degrees in as little as five years--four years to earn the B.S. degree and to begin earning graduate credits, one additional year to complete earning the M.S.--rather than the six years that would typically be required to earn both degrees separately. In addition to saving time, there is also potentially a significant savings financially, since a number of graduate credits can be earned while the student is paying flat-rate undergraduate tuition.

The program description page provides more details on this program along with a link for applying.

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