The Ph.D. in Biological Sciences program exemplifies the interdisciplinary approach that has become an essential feature of modern biomedical science. A low student-to-faculty ratio ensures individual attention and advising. Our program emphasizes new technologies, analytical thinking skills and creative approaches to problem solving. Health-related areas of focus include biotechnology, genetics/genomics, computational biology, microbiology, and neuroscience.
Computational Biology [with SCS]—M.S.
The emerging field of computational biology represents the application of modern computer science to solving biological problems. Carnegie Mellon’s world-class strengths in computer science and strong tradition of interdisciplinary research combine to provide training in this new discipline. Program goals include meeting the growing need for computational biologists in the biotechnology and pharmaceutical industries and at universities and research institutes, and allowing nontraditional and reentering students to establish credentials that enable acceptance into Ph.D. programs in computational biology. Students complete the program in three to four semesters.
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This program is noted for research at the interface of chemistry with biology, physics and engineering, including polymer science, materials, green and environmental, bioorganic, bioinorganic, biophysical, spectroscopy, theoretical and computational chemistry. The Ph.D. program’s goal is to prepare students for an academic or research career in chemistry. The M.S. in Chemistry is available only to students who are in the process of pursuing the Ph.D. Except in special circumstances, Chemistry does not admit students seeking only the M.S.
Colloids, Polymers and Surfaces [with CIT]—M.S.
This program focuses on the engineering of complex fluids, which consist of nanoparticles (colloids), macromolecules and interfaces. Topics are relevant to industrial technology and the manufacture of products based on complex fluids; examples include pharmaceuticals, coatings and paint, cosmetics, surfactant-based products and biotech materials. The program can be completed in nine months with coursework only, or in 1.5 years with a research project.
This program provides the basic background for scientists and engineers to pursue technical careers in industries that manufacture, process and use polymeric materials.
Students with these interests may also want to consider the interdisciplinary M.S. in Colloids, Polymers and Surfaces, a joint program with Chemical Engineering designed for professionals working in the polymer field. The M.S. in Polymer Science is available only to students who are in the process of pursuing the Ph.D.
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Algorithms, Combinatorics and Optimization [with SCS and Tepper]—Ph.D.
The focus of this program is on the design of efficient algorithms for problems arising in computer science and operations research, and on the mathematics required to analyze these algorithms and problems. The program brings together the study of the mathematical structure of discrete objects and the design and analysis of algorithms in areas such as graph theory, combinatorial optimization, integer programming, polyhedral theory, computational algebra, geometry and number theory.
Applied Mathematics - Ph.D.
The requirements for this program are the same as for the Ph.D. in Mathematical Sciences, but students also take courses in applied mathematics, such as ordinary differential equations, partial differential equations, advanced topics in analysis, Sobolev spaces, methods of optimization, and numerical analysis.
The PhD. Dissertation will usually be in the area of calculus of variations, continuum mechanics, numerical analysis, partial differential equations, or scientific computing, often involving applications to materials science, engineering, biology, computer vision, etc.
Students interested in Applied Mathematics should apply to the Ph.D. in Mathematical Sciences and indicate their interest on the application.
Computational Finance [with Heinz, DC and Tepper]—M.S.
This 18-month full-time degree (in Pittsburgh or New York) or three-year part-time (in New York) MSCF program focuses on the use of quantitative methods and information technology in the field of finance. The curriculum provides an in-depth understanding of the mathematics used to model security prices, the statistical tools needed to summarize and predict the behavior of financial data, the computer science and e-commerce skills needed to understand the technology used in the financial industry, and the corporate finance needed to employ these skills in finding innovative solutions to business needs.
The requirements for this program are the same as for the Ph.D. in Mathematical Sciences, but students also take courses in probability, statistics, stochastic processes, microeconomics and finance. Normally, the Ph.D. dissertation is on some aspect of stochastic processes applied to finance. The breadth of the curriculum opens up a variety of career opportunities, including research positions in the finance industry and faculty positions in mathematics. Students interested in mathematical finance should apply to the Ph.D. program in mathematical sciences and indicate their interest on the application.
Students seeking a Ph.D. are expected to show a broad grasp of mathematics and demonstrate a genuine ability to do mathematical research. The Ph.D. in Mathematical Sciences is a traditional degree, and its requirements are representative of all doctoral programs in mathematics. The primary intent of the graduate program is to train mathematical scientists for a variety of career opportunities including traditional university settings, industry and work in the finance industry. As part of their Ph.D. training, students may elect to earn a Masters degree. (Please note that the Department does not offer a terminal Masters program.)
Pure and Applied Logic [with DC and SCS]—Ph.D.
This interdisciplinary program is jointly sponsored by the departments of Computer Science, Mathematical Sciences and Philosophy. Each of these departments administers a track of the program, and students are admitted directly to one of these three departments, which will serve as their home base. Carnegie Mellon’s large and active Logic Community has a particularly strong concentration in foundational aspects of computing and has an established record of collaborations in pursuing theoretical research, conducting major implementation projects, and running colloquia and workshops. The program builds on these strengths to educate new generations of scientists who will pursue research in Pure and/or Applied Logic.
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The Ph.D. in Physics and Applied Physics offers advanced training to students at the leading edge of physics research and prepares them to become the next generation of leaders in academia and industry. The program is rigorous as well as practical. In particular, the first two years of the graduate curriculum is designed to provide students with the solid foundation necessary to start research in their chosen area of specialization. Graduate students have the opportunity to study traditional core physics areas of astrophysics, biophysics, condensed matter physics, high energy and medium energy particle physics, or perform interdisciplinary work at the boundaries of chemistry, biology, materials science, or engineering.
The M.S. in Physics is awarded to those who have demonstrated a mastery of advanced topics in physics beyond the B.S. degree level. The M.S. degree is usually offered only to students enrolled in the Ph.D. degree program.
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