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The applications of mathematical methods in management and
economics today are so manifold that it is difficult to find a single
person who is aware of their full scope. The following list can only be
incomplete.
- Economists use linear and nonlinear programming, the
theory of variational inequalities, optimal control theory, dynamic
programming, game theory, probability choice models, utility theory,
regression and factor analysis and other techniques to study equilibrium,
optimal investment, competition, consumer behavior, and a host of other
phenomena.
- People in operations management use statistical
sampling and estimation theory, linear and integer programming, network
programming, dynamic programming and optimal control theory, queuing
theory, simulation, artificial intelligence techniques, and combinatorial
optimization methods to solve problems in quality control, allocation of
resources, logistics, project scheduling, labor and machine scheduling,
job shop scheduling and assembly line balancing, and facility layout and
location. The introduction of flexible manufacturing systems, robots and
other automated devices has posed a whole new array of unsolved
mathematical problems.
- People in finance use linear, nonlinear and integer
programming, optimal control theory and dynamic programming, Markov
decision theory, regression and time series to determine optimal resource
allocation, multiperiod investments, capital budgeting, and investment and
loan portfolio design, and to try to forecast market behavior.
- People in marketing use regression and factor
analysis, time series, game theory, Markov decision theory, location
theory, mathematical programming, probability choice models and utility
theory to study consumer preferences, determine optimal location in
product space, allocate advertising resources, design distribution
systems, forecast market behavior, and study competitive strategy.
- People in information systems and decision support
systems use artificial intelligence techniques, propositional and
quantified logic, Bayesian methods, probabilistic logic, data structures
and other computer science techniques, mathematical programming, and
statistical decision theory to design expert and other knowledge-based
systems, develop efficient inference and retrieval methods, and evaluate
the economic and organizational effects of information systems.
The peculiar nature of mathematics unfortunately raises two
obstacles to learning it. One is that students often believe that
mathematics can be learned simply by studying a book. Mathematics is
learned by working through problems. A second obstacle is that students
often believe that they can learn to work problems by studying a book. A
book can get one started, but learning to work problems is like learning
to play basketball or play the piano--it requires practice, practice,
practice. Mathematical skills are very athletic in this sense. (The
phrase ``quant jock'' is appropriate.)
That is why this course assigns a lot of homework problems.
Acknowledgements: We would like to thank John Hooker,
Bill Hrusa, Rick Green and Anuj Mehrotra for their inputs.
Next: Basic Linear Algebra
Up: Mathematical Methods in Business
Previous: History
Michael A. Trick
Mon Aug 24 16:30:59 EDT 1998