The goal of this program is to produce generalized problem solvers of great versatility, capable of moving within an organization from task to task. The graduate will have studied not only the standard mathematical and statistical tools, but also the basic ideas of engineering and business, and will have received training in project development and in modes of industrial communication.
This program consists of six components:- Survey of Industrial Mathematics (Fall semester).
- Projects in Industrial Mathematics (Spring semester).
- Certificate in Business and Communication.
- Four electives in Applied Mathematics.
- Two electives in Statistics.
- Four electives in Engineering, Economics, or Computer Science.
Apply for the program. (Support will automatically be considered).
Request Literature.Contact the director, Peiru Wu at peiruw@math.msu.edu.
Other MSU Mathematics Graduate programs.
MSU Mathematics Department home page.Employers
MTH 843: A Survey of Industrial Mathematics (Fall term)The course has three objectives:
- To survey mathematics of particular importance to industry
- To gain experience in team project report generation
- To gain experience in oral presentation of project results
- 1. Statistical reasoning.
- Random variables, Uniform distributions, Gaussian distributions, The binomial distribution, The Poisson distribution, Taguchi quality control.
- 2. Monte Carlo methods.
- Computing integrals, Mean time between failure (MTBF), Servicing requests, The newsboy problem (reprise).
- 3. Data acquisition and manipulation.
- The z-transform, Linear recursions, Filters, Stability, Polar and Bode plots, Aliasing, Closing the loop, Why decibels?
- 4. The discrete Fourier transform (DFT).
- Realtime processing, Properties of the DFT, Filter design, The fast Fourier transform, Image processing.
- 5. Linear programming.
- Optimization, The Diet Problem, The Simplex Algorithm.
- 6. Regression.
- Best fit to discrete data, Norms on R^n, Hilbert space, Gram's theorem on regression.
- 7. Cost benefit analysis.
- Present value, Life cycle costing.
- 8. Microeconomics.
- Supply and demand, Revenue, cost, and profit, Elasticity of demand, Duopolistic competition, Theory of production.
- 9. Ordinary differential equations.
- Separation of variables, Mechanics, Linear ODEs with constant coefficients, Systems.
- 10. Frequency domain methods.
- The frequency domain, Generalized signals, Plants in cascade, Surge impedance, Stability, Filters, Feedback and root-locus, Nyquist analysis, Control.
- 11. Partial differential equations.
- Lumped versus distributed, The big six PDEs, Separation of variables, Unbounded spatial domains, Periodic steady state, Other distributed models.
- 12. Divided differences.
- Euler's method, Systems, PDEs, Runge-Kutta.
- 13. Galerkin's method.
- Galerkin's requirement, Eigenvalue problems, Steady problems, Transient problems, Finite elements, Why so effective?.
- 14. B-splines.
- Why cubics? m-splines, Cubic splines.
- 15. Report writing.
- The formal technical report, The memo, The progress report, The executive summary, The problem statements, Overhead Projector Presentations, Approaching a writing task, Style, Checklist.
Representatives from Industry or Government will come to campus to pose problems of interest to their unit. Students will divide into teams of 3 or 4 to tackle one of the posed problems. By the end of the term each student team will present both a written and oral report of their findings to the industrial or governmental unit that posed the problem, and to students and faculty in the Industrial Mathematics program.
Teams will be advised by a faculty member plus a liaison from the unit that posed the problem.Often these student/industrial relationships will continue after the project is completed in the form of internships or employment. Projects in Progress.
All of the Professional MS programs of the College of Natural Science require the completion of a Certificate in Basic Business and Communication Skills. This Certificate program will be organized as a series of week-end workshops covering the topics: Marketing Management, Financial Management, Managerial Accounting, The Legal Environment of Business, Micro and Macro Economics, Project Management, Writing for Clarity, Group Communication, Presentation Skills, Negotiation and Consensus Building. The Certificate offered by faculty from the Colleges of Business and of Communication Arts and Sciences will include a case study approach.
- Industrial Mathematics 843
- Industrial Mathematics 844
- Certificate in Basic Business and Communication Skills
- Mathematics (at least 4 courses)
- 841, 842 Boundary Value Problems I and II
- 848, 849 ODE, PDE
- 850, 851 Numerical Analysis I and II
- 852 Numerical Methods for Odes
- 810, 880, 881 Error-correcting codes, Combinatorics, Graph theory
-
Statistics (at least 2 courses)
- 455 Actuarial Models
- 461 Computations in Probability and Statistics
- 471 Quality and Productivity
- 801 Design of Experiments
- 818 Introduction to Econometrics
- 820A Econometrics IA
- 821, 822 Econometrics I and II
- 825 Sample Surveys
- 843 Multivariate Analysis
- 844 Time Series Analysis
- 847 Analysis of Survival Data
- 861, 862 Theory of Probability and Statistics I and II
- 863, 864 Applied Statistics Methods I and II
- 888 Stochastic Models in Finance
-
and at least 4 courses chosen from
- Civil and Environmental Engineering
- 811 Advanced Hydrogeology
- 821 Groundwater Hydraulics
- 829 Mixing and Transport in Surface Water
- 841 Traffic Flow Theory
- 843 Simulation/Optimization of Urban Traffic Flow
- 844 Highway and Traffic
- 846 Transport Policies and Decision Making
- 850 Intelligent Transport Systems (ITS)
- Computer Science and Engineering
- 471 Media Processing and Multimedia Computing
- 472 Computer Graphics
- 802 Pattern Recognition and Analysis
- 803 Computer Vision
- 830 Design and Theory of Algorithms
- 835 Algorithmic Graph Theory
- 841 Artificial Intelligence
- 847 Machine Learning
- 848 Evolutionary Computation
- 872 Advanced Computer Graphics
- 881 Data Mining
- Economics
- 801 Mathematical Applications in Economics
- 805 Microeconomic Analysis
- 807 Applied Microeconomic Analysis
- 809 Macroeconomic Analysis
- 811A Mathematical Applications in Economics
- 811B Structure of Economic Analysis
- 812A, 812B Microeconomics I and II
- 813A, 813B Macroeconomics I and II
- 816 Economic Thought II
- 818 Introduction to Econometrics
- Electrical and Computer Engineering
- 816 Cryptography and Network Security
- 826 Linear Control Systems
- 829 Optimal Multivariable Control
- 851 Linear Systems and Control
- 853 Optimal Control
- 854 Robust Control
- 856 Adaptive Control
- 859 Nonlinear Control
- 863 Analysis of Stochastic Systems
- 864 Detection and Estimation Theory
- 865 Analog and Digital Communications
- 885 Artificial Neural Networks
- Environmental Engineering
- 801 Dynamics of Environmental Engineering
- 802 Physicochemical Processes in Environmental Engineering
- 804 Biological Processes in Environmental Engineering
- 827 Integrated Risk Assessment of Environmental Hazards
- Marketing and Supply Chain Management
- 800 Supply Chain Management
- 801 Materials Management
- 803 Operations Management Strategy
- 805 Marketing Management
- Mechanical Engineering
- 830 Fluid Mechanics I
- 851 Linear Systems and Control
- 852 Intermediate Control Systems
- 853 Optimal Control
- 854 Robust Control
- 855 Digital Data Acquisition and Control
- 856 Adaptive Control
- 859 Nonlinear Systems and Control
- 860 Theory of Vibrations
- 861 Advanced Dynamics
- 863 Nonlinear Vibrations
- Civil and Environmental Engineering
Other Links
College of Natural Science Professional Masters ProgramsThe Sloan Foundation statement of professional Science degrees