M.S. and Ph.D. in Computational Mathematical and Statistical Sciences
The Department of Mathematical and Statistical Sciences offers both M.S. and Ph.D. study in Computational Mathematical and Statistical Sciences. Computational mathematical and statistical sciences is a field of study that emphasizes the discovery, implementation, and use of computational tools to solve problems in mathematics and statistics that are both applied and pure. Commonly, these efforts involve the development of new computational methodologies, computer software, or computer systems to solve large-scale problems.
Our program is designed to equip graduates with a distinctive blend of theoretical and computational skills, for employment in industry, research laboratories and institutions of higher education. While the bulk of their coursework will be undertaken in this Department, their research topics may range across the computational aspects of a broad spectrum of disciplines.
A relatively small number of programs with the same overall goals exist in this country. Most have a similar title, although their focus varies, quite naturally, according to the resources with which they are blessed. Nonetheless, each offers students the opportunity to work within an interdisciplinary setting wherein the ultimate goal is the solution of a scientific problem using state-of-the-art computational techniques.
Students that excel in the M.S. program that decide to apply for Ph.D. program and are accepted may seamlessly enter the doctoral studies since both share the same core courses. Our doctoral program is designed for individuals of outstanding ability who show promise as a researcher in an interdisciplinary environment. The diverse research opportunities in our naturally interdisciplinary department are enhanced by the research programs of associated faculty on the Marquette campus in the sciences and engineering and Milwaukee area research laboratories and clinics. For a listing of department research and research laboratories, please consult the Faculty section of this web site.
What is Computational Mathematical and Statistical Sciences?
Computational mathematical and statistical sciences (CMPS) is a field of study that emphasizes the discovery, implementation, and use of computational tools to solve problems in mathematics and statistics that are both applied and pure. For instance, in the NSF Program Description for Computational Mathematics, this program "supports mathematical research in areas of science where computing plays a central and essential role, emphasizing algorithms, numerical methods, and symbolic methods. The prominence of computation in the research is a hallmark of the program."
Since the advent of the computer, its potential to advance scientific investigation has been recognized. From the design and application of early computers to aid in the cracking of codes during WWII and the simulations leading to the hydrogen bomb in 1952, the use of computers and the development of algorithms and systems in the service of science, “computational science,” was born. Since that time, the computer has become an indispensable appliance of business and an essential facet of science. From the statistical analysis of the mutations of HIV to the simulations describing the evolution of the universe or the flow of traffic on the freeway; from information extracted in a meaningful way from large databases to the transfer of money when an ATM card is used, the computer, sophisticated algorithms, large networks and databases are central to our life – and in science, essential. In science, as problems become more complicated and datasets larger, the techniques needed to design the experiments and make sense of it all requires both the computer and algorithms for the development of the necessary systems, simulations, and analysis. The activity which enables this accomplishment – using the computer as a research tool – is the field of computational science. It clearly involves mathematics, applied mathematics, computer science, and statistics, along with an understanding of the science of the applications. This activity involves original thought and discovery, the ability to design and use tools and systems, and a facility for communicating with those from other fields.
The need for these programs
The need for these programs, as part of STEM (Science, Technology, Engineering and Mathematics) education has been recognized by several influential groups. The most powerful statement is the report from the President’s Information Technology Advisory Committee (PITAC) in 2005 entitled “Computational Science: Ensuring America’s Competitiveness.” In this report, the Principal Finding was:
- Computational science is now indispensable to the solution of complex problems in every sector, from traditional science and engineering domains to such key areas as national security, public health, and economic innovation. Advances in computing and connectivity make it possible to develop computational models and capture and analyze unprecedented amounts of experimental and observational data to address problems previously deemed intractable or beyond imagination. Yet, despite the great opportunities and needs, universities and the Federal government have not effectively recognized the strategic significance of computational science in either their organizational structures or their research and educational planning. These inadequacies compromise U.S. scientific leadership, economic competitiveness, and national security.
The principal recommendation of special interest to this proposal, is:
- Universities and the Federal government’s R&D agencies must make coordinated, fundamental, structural changes that affirm the integral role of computational science in addressing the 21st century’s most important problems, which are predominantly multidisciplinary, multi-agency, multi sector, and collaborative. To initiate the required transformation, the Federal government, in partnership with academia and industry, must also create and execute a multi-decade roadmap directing coordinated advances in computational science and its applications in science and engineering disciplines.
- Traditional disciplinary boundaries within academia and Federal R&D agencies severely inhibit the development of effective research and education in computational science. The paucity of incentives for longer-term multidisciplinary, multi-agency, or multi-sector efforts stifles structural innovation. To confront these issues, universities must significantly change their organizational structures to promote and reward collaborative research that invigorates and advances multidisciplinary science. They must also implement new multidisciplinary structures and organizations that provide rigorous, multifaceted educational preparation for the growing ranks of computational scientists the Nation will need to remain at the forefront of scientific discovery.
The Society for Industrial and Applied Mathematics (SIAM) asked a distinguished group to study recent developments in CSE (Computational Science and Engineering) education and to give recommendations for SIAM’s role in this important effort. The report was published in 2007. It surveyed graduate programs in computational science, M.S. and Ph.D., in the U.S. and worldwide (list in Appendix 2). Besides examining several programs in detail, they state:
- One point we would like to emphasize in this document is that CSE is a legitimate and important academic enterprise, even if it has yet to be formally recognized as such at some institutions. Although it includes elements from computer science, applied mathematics, engineering and science, CSE focuses on the integration of knowledge and methodologies from all of these disciplines, and as such is a subject, which is distinct from any of them.
The study group recognized that common to all successful programs was a foundation in mathematics, applied mathematics, statistics and computer science and an application area involving an interdisciplinary team.
Program Learning Outcomes
The CMPS M.Sc. graduates will be able to:
- Apply advanced concepts related to discipline coursework to solve theoretical or applied problems.
- Synthesize research publications in their area.
- Demonstrate communication skills appropriate for presenting research to peers and interdisciplinary colleagues.
The CMPS Ph.D. graduates will be able to:
- Modify, adapt or construct methods, techniques and software for addressing significant problems in the field of computational science.
- Conduct original research that results in a major written scholarly work in the computational sciences.
- Synthesize research publications in their area of specialization.
- Demonstrate communication skills appropriate for presenting research to peers, teaching college level courses, or collaborating with interdisciplinary colleagues.
apply to the Computational Mathematical and Statistical Sciences program
Student Success Stories
Do you have a success to share with us? We'd love to hear from you. Please fill out this form and tell us about your new job, presentation, publication, or any other award or honor you've recently received. We will post your story here, on the Graduate School website and on the Marquette University Facebook and Twitter pages.
Iain Bruce - Ph.D., Computational Mathematical and Statistical Sciences (Alumni)
It was during the pursuit of his Ph.D. at Marquette University that Iain was first introduced to the field of MRI physics, which has since become the focus of his research career currently at Duke University. The Computational Sciences program exposed him to truly invaluable statistical and computational tools that enabled me to research the statistical impact of image reconstruction and processing algorithms frequently used in the field of functional MRI. The research training that Iain received at Marquette ultimately led him to pursue a postdoctoral associate position in MR Physics at Duke University’s Brain Imaging and Analysis Center, and he has since been promoted to a Medical Instructor position in the Department of Neurology.
As an extension of his prior research, his work at Duke has centered around the development of MRI acquisition and processing techniques for achieving diffusion tensor imaging data with ultra-high spatial resolution and fidelity. Specifically, his research has been applied to patients with intractable epilepsy - where no apparent abnormalities are present in conventional MR scans - and he has been working closely with neurologists and neurosurgeons to develop advanced MR tools for localizing epilepsy foci during presurgical planning.
"The tools and knowledge I gained at Marquette have been applied to every facet of my research here at Duke, and I would certainly not be in the position I am in now without them," says Iain.
Muge Karaman - Ph.D., Computational Mathematical and Statistical Sciences (Alumni)
Muge Karaman is Assistant Director for the Center for Magnetic Resonance Imaging at the University of Illinois College of Medicine at Chicago. Muge completed her PhD degree in 2014 and immediately went on to a postdoctoral fellowship in the Center for Magnetic Resonance Imaging at the University of Illinois College of Medicine. She utilizes the education and training she received at Marquette to develop and validate quantitative diffusion-weighted MRI techniques for the characterization of complex biological tissue in vivo. “I have been able to invent new MRI techniques thanks to the Computational Mathematical and Statistical Sciences program and its amazing faculty," says Muge.
Piyush Saxenaena - Ph.D., Computational Mathematical and Statistical Sciences (Alumni)
Coming from a Civil engineering background Marquette’s was one of the very few programs that allowed me to leverage my experience as an engineer to succeed in an analytical field without excessive coursework. During my time I was exposed to some of the best research labs and industry-academia collaborations. One such collaboration with Direct Supply evolved into what became a significant part of my dissertation. That industry connection took professional development to new heights for me. I was able to do novel research while being empowered by leaders in academia and industry. The Computational Sciences program provides a sound support structure while encouraging the flexibility that drives innovation. I currently work as a Data Scientist at Direct Supply in Milwaukee. Direct Supply is a Senior-Living industry juggernaut. Using Deep Learning to improve the lives for American seniors, that is what the program empowered me to do!
For more information, please contact Dr. Mehdi Maadooliat, the Director of Graduate Studies.