Research Opportunities

M.S. and Ph.D. Programs in Applied Mathematics

These degrees are designed to give candidates a contemporary, in-depth education in applied mathematics and to provide research opportunities in the special fields of

• computational mathematics
• computational and mathematical biology
• discrete mathematics
• mathematics of science and engineering
• optimization
• probability
• statistics

Ideas for research could come from working with a faculty on a research project

Faculty are involved in a wide array of research projects.  Here are just a few:

• Image processing and radiation therapy: A variety of optimization methods are used to develop methods of delivering radiation to tumors with minimal damage to healthy tissue; the same research has led to improvements in image understanding and diagnosis.
• Molecular biology: Linear programming methods, once applied to problems in business and management, are now used to understand metabolic pathways and the regulation of genes.
  
• Population genetics: Mathematical models relying on differential equations are used to predict the evolution of multiple traits in a selective gene pool.
  
• Graph theory applications: Algorithms being designed to handle problems in DNA mapping and quantum random walks.
• Operations research:  modeling, analysis and computation of solutions to a wide variety of problems in government, industry, and science.

Ideas for research could come from a Mathematics Clinic

This is a project-driven course designed to illustrate the applicability and utility of mathematics in many problem areas in private and public sectors.  Students apply their analytical skills to various problems in business and government. Past clinics have included medial image processing and radiation therapy, biomedical modeling, survivability of Mars landers, genetic algorithms, cancer models and detection, calibration of water distribution networks, mobile robot planning, and many more.   See our Clinic home at http://www-math.cudenver.edu/clinic/.

• Oil reservoir recovery: Partial differential equations are used to model the recovery of oil from reservoirs and the underground flow of contaminants.
  
• Environmental issues: Multivariate spatial models are used to assess environmental equity (the association between locations of toxic facilities and local population demographics) and to aid the U.S. Environmental Protection Agency in siting decisions for new facilities.
  
• Weather and climate: Spatio-temporal statistical models for rainfall, weather conditions, and soil characteristics are used to assess uncertainty in crop models.
  
• Computational mechanics and fluid dynamics: State of the art software and parallel computers are used to model sound propagation in fluids and solids, and the deformation of solid bodies.