The program in Computational Mathematics leading to a Master of Science degree is a 36 (+1) 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.
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. Most students are expected to bypass some core classes. Any core courses that are waived are replaced by elective courses offered within the department and approved graduate courses offered outside the department. Each course in the core curriculum has a computational component using a software package or programming language related to that particular core topic. After completing the core courses, students have a facility with at least two computer algebra software packages, Java, UNIX, and one statistical software package.
|CPMA 511||Logic and Proof|
|CPMA 521||Probability/Markov Chains|
|CPMA 531||Prog Language: Java|
|CPMA 512||Linear Algebra|
|CPMA 522||Statistical Inference|
|CPMA 532||Data Structures|
|CPMA 515||Advanced Discrete Math|
|CPMA 525||Linear Models|
|CPMA 535||Intro Computer Systems|
|CPMA 518||Vector Calculus|
|CPMA 526||Experimental Design|
|CPMA 536||Software Engineering|
Beyond the required core, students take at least fifteen credits from a list of twelve elective courses spanning the three disciplines. They may choose to focus their study in one of the three areas, or they may select an array of courses across disciplines. All elective courses also contain a significant computational component. Students are allowed to include as many as six credits of work in approved courses on the graduate level in disciplines other than computational mathematics within existing programs in the university.
|CPMA 560||Algorithms/Graph Theory|
|CPMA 565||Numerical Methods|
|CPMA 580||Artificial Intelligence|
|CPMA 561||Math of Financial Markets|
|CPMA 573||Statistical Computing|
|CPMA 581||Distributed Computing|
|CPMA 562||Applied Complex Variables|
|CPMA 582||Machine Learning|
|CPMA 563||Numerical Differential Equations|
|CPMA 583||Prog Lang/Category Theory|
|CPMA 584||Formal Lang & Automata|
The Computational Mathematics program stresses real-life problems and real-life experiences. To that end, all students in the Computational Mathematics program must have either:
- Documented prior or current work experience related to computational mathematics, or
- A supervised internship in a position involving computational mathematics.
Documentation for work experience could be, but is not limited, to a letter from the student's employer stating the nature of the work and how the work involves an application of computational mathematics.
The supervised internship must be be approved by the program director and may be taken for one to three credit hours. The internship may done during any semester of the program. These credit hours are in addition to the 36 credits of the program.
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.
All courses in the M.S. in Computational Mathematics include 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: C++, Java, Unix, Windows
- Statistics: SPSS®, SAS®, JMP®,R
4/1 PROGRAM FOR B.S./M.S.
Academically-strong Duquesne undergraduate students have the opportunity to "double-count" graduate credits they earn while still undergraduates toward a graduate degree. Specifically, if you earn graduate credits while you are working on your undergraduate degree, and if your final undergraduate transcript shows that you earned over 120 credits, then you will likely be able to count some or all of the graduate credits shown on your undergraduate transcript toward your graduate degree as well. There are several limitations on the amount of double-counting allowed. First, only courses that you have enrolled in as graduate courses (numbered 500 and above) can be double-counted. Second, any graduate credits you wish to apply to the Computational Mathematics program must be relevant (e.g., a graduate education course would probably not be considered relevant). Third, you can count at most 15 graduate credits toward both degrees. And finally, if you subtract 120 from the number of earned credits on your final undergraduate transcript, the resulting difference is a limit on the number of credits you may double count. For instance, if you earned 128 credits while an undergraduate then even if 12 of these were graduate credits you would be limited to counting at most 8 of those credits toward your graduate degree.
Students can use double-counting either informally or formally. In the informal approach, a student is admitted to the Computational Mathematics program after earning her Duquesne undergraduate degree and requests that applicable graduate credits earned while an undergraduate be applied to the graduate degree as well. Decisions about the extent to which to grant such requests are made on a case-by-case basis. In the formal approach, a student is provisionally admitted to the Computational Mathematics graduate program while still an undergraduate. Applicable graduate credits earned by the student in this case are automatically applied to both programs.
Students wishing to pursue the formal approach with respect to Computational Mathematics can apply for our 4/1 program. Some advantages of the formal approach are:
- student has provisional graduate admission before completion of undergraduate degree
- graduate credits earned are immediately counted toward the M.S. degree as well as the B.S.
- student does not need to request approval for enrolling in graduate courses, as long as the course prerequisites are met
- concerns during senior year about graduate school applications and admission are eliminated
application process is simpler than regular admission (no GRE, two rather than three recommendations required)
Applicants are expected to be enrolled in the mathematics and/or computer science B.S. program and have at least junior standing, a cumulative grade point average of at least 3.25, and grade point averages in mathematics and computer science of at least 3.5. With careful planning and some summer work, it is feasible to complete both degrees in as little as five years--four years to earn the undergraduate degree along with double-counted 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 without double-counting.
Please see the Admissions page for details on applying to the Computational Mathematics 4/1 program. The application deadline is July 1.