M.S. in Computational Mathematics & Statistics

2023-2024 Graduate Catalog

Our MS in Mathematical and Computational Statistics program equips students with the essential knowledge and skills to tackle real-world problems in computational mathematics. Through a comprehensive curriculum, students will develop the ability to analyze, synthesize, and evaluate solutions to complex challenges using advanced statistical techniques. Moreover, students will gain proficiency in modern computational tools, enabling them to effectively leverage technology in their problem-solving endeavors. Prepare to excel in the ever-evolving field of statistical analysis and contribute to innovative solutions in diverse industries.

Curriculum

Requirements

Requirements for the MS Program

The MS in Computational Mathematics & Statistics is a multidisciplinary program. With a total of 36 credits, this program combines the expertise and resources from the Department of Mathematics and Computer Science, drawing on the strengths of mathematics, computer science, and statistics. Benefit from our faculty's commitment to teaching and their active research programs in computational fields, which often transcend traditional disciplinary boundaries.

Additional Information:

As part of the Computational Mathematics & Statistics program, students have the flexibility to enhance their education through the following options, subject to approval by the program director:

Taking graduate courses outside the program: With the program director's consent, students can enroll in graduate courses offered by other departments within Duquesne University. Furthermore, students have the opportunity to cross-register at renowned local institutions, including Carnegie Mellon University and the University of Pittsburgh. Up to six credits earned from outside the program can be applied towards the degree.
Independent study: Students have the option to engage in an independent study under the guidance and evaluation of a faculty member. This personalized educational experience allows students to delve into material that may have been previously offered as a course but is not expected to be available again before the student completes the program. This tailored approach fosters individualized learning and research opportunities.

These additional opportunities expand the academic horizons of students in the Computational Mathematics & Statistics program, enabling them to explore interdisciplinary coursework and engage in unique educational experiences.

Core

Core Requirements

Our program offers a comprehensive core curriculum comprising twelve 1.5-credit mini-courses, with four courses each in mathematics, computer science, and statistics. This foundational component ensures a shared knowledge base across the three disciplines. Students may have the opportunity to waive certain core courses based on prior knowledge, in consultation with the program director, and substitute them with elective courses. The core curriculum integrates computational components, utilizing relevant software packages and programming languages specific to each discipline. By completing the entire core curriculum, students will gain proficiency in essential tools such as computer algebra software, the Python programming language, the Linux operating system, and statistical software packages.

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

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

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

Electives

Elective Requirements

Every semester, a diverse range of elective courses is available in the fields of mathematics, statistics, and computer science. The selection of electives takes into account student interests and preferences, ensuring a customized learning experience. Notably, all elective courses emphasize the integration of computational methods, providing students with valuable hands-on experience in applying computational techniques to solve complex problems.

Electives:

鈼� CPMA 550 Computer Networks
鈼� CPMA 555 Web-based Systems
鈼� CPMA 560 Algorithms/Graph Theory
鈼� CPMA 563 Numerical Differential Equations
鈼� CPMA 566 Operations Research
鈼� CPMA 573 Statistical Computing
鈼� CPMA 574 Prediction and Classification Modeling
鈼� CPMA 575 Data Mining and Data Science Analytics
鈼� CPMA 580 Artificial Intelligence/Cognitive Science
鈼� CPMA 582 Machine Learning
鈼� CPMA 590 Advanced Operating Systems (FA20)
鈼� CPMA 590 Data Compression (SP21)
鈼� CPMA 591 Database Management Systems (FA20)

Internship

The Computational Mathematics & Statistics program places a strong emphasis on real-life problem-solving and practical experiences. As part of this commitment, all students are required to register for and successfully complete CPMA 599 Internship. The internship requirement can be satisfied through two options: prior or current employment experience related to computational mathematics, or a supervised internship in a position that involves computational mathematics.

To fulfill the requirement, students must provide a supervisor's written report verifying their employment experience or supervised internship, which will then be reviewed and approved by the program director. Students who wish to fulfill the requirement without receiving elective credit toward their degree can register for zero credits of CPMA 599. For the zero-credit course, a Pass grade is earned by accumulating a minimum of 40 hours of relevant employment or internship experience.

Alternatively, students can register for up to three credits of CPMA 599 per semester, with a maximum of six credits overall, if they have or anticipate having experience beyond the minimum 40-hour requirement. This allows students to further deepen their practical expertise in computational mathematics through extended internship opportunities.

By incorporating the internship component, the Computational Mathematics & Statistics program ensures that students gain valuable real-world exposure, strengthening their problem-solving skills and preparing them for successful careers in their chosen field.

Thesis/Project

Under the guidance and approval of a Computational Mathematics & Statistics faculty advisor, first reader, and the Graduate Studies Committee, students have the option to undertake a thesis or project as part of their degree. This endeavor carries six credits, contributing towards the total of 36 credits required for graduation. Tailored to the student's background and interests, this phase of the program allows for the design of a project or the pursuit of research with a substantial computational focus. The culmination of the thesis or project involves both written documentation and oral presentations to showcase the outcomes and findings.

Computational Component

In the M.S. in Computational Mathematics & Statistics program, nearly all courses integrate a computational component that necessitates the utilization of discipline-specific tools. While these tools evolve continuously in the rapidly advancing fields, some common examples include: 鈥� Mathematics: Maple, MATLAB庐鈥� Computer Science: Python, C++, Linux, Windows 鈥� Statistics: SAS庐, R, JMP庐, SPSS庐 Through the application of these tools, students gain hands-on experience and proficiency in employing the appropriate computational resources within their respective disciplines.

BS/MS Degree

BS/MS Degree Program

The Mathematics and Computer Science Department adheres to University policy by offering a combined B.S./M.S. program tailored to academically-strong majors. Students admitted to this program have the unique opportunity to apply graduate credits earned during their undergraduate studies towards the requirements of both their B.S. degree and the Computational Mathematics & Statistics M.S. degree. Upon completing the B.S. degree, a portion or all of these graduate credits can potentially be applied towards the attainment of the Computational Mathematics & Statistics M.S. degree as well.

To earn both the B.S. and M.S. degrees, students must accumulate a minimum of 156 credits, with at least 36 of those credits being graduate-level (500-level or above) courses that fulfill the requirements of the Computational Mathematics & Statistics master's program. Of these 36 graduate credits, a maximum of 15 can be taken during the student's undergraduate years. Additionally, a minimum of 114 credits earned for the B.S. must be undergraduate credits (400-level or below). Admitted students must closely collaborate with their undergraduate advisor and the program director to ensure appropriate course selection and registration.

By participating in the combined B.S./M.S. program, students can optimize their academic journey, accelerate their progress towards an advanced degree, and gain a competitive edge in the field of Computational Mathematics & Statistics.

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Master of Science in Computational Mathematics & Statistics