Program Details
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.
CORE:
The core of the program consists of twelve 1.5 credit minicourses, 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 
ELECTIVES:
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 571  Optimization 
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 564  Cryptology 
CPMA 584  Formal Lang & Automata 
INTERNSHIP:
The Computational Mathematics program stresses reallife problems and reallife 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.
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/projectworth six credits toward the 36 required for a degreeto 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:
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.
Academicallystrong Duquesne undergraduate students have the opportunity to "doublecount" 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 doublecounting allowed. First, only courses that you have enrolled in as graduate courses (numbered 500 and above) can be doublecounted. 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 doublecounting 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 casebycase 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 yearsfour years to earn the undergraduate degree along with doublecounted 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 doublecounting.
Please see the Admissions page for details on applying to the Computational Mathematics 4/1 program. The application deadline is July 1.