Approximation in Math Problems

Approximations predict market trends and changes in demand for goods and services.

Harmonic analysis of the digital approximation of wave signals inspired Emmanuel J. Candes to improve methods, which translate analog signals into digital forms. Candes teaches applied mathematics at Vanderbuilt University, where he won a $500,000 National Science Foundation award for solving problems of digital approximation of signals in electronic devices, medical technology, aircraft safety and DNA analysis. Vanderbuilt University's "Journal of Constructive Approximations" ranks 8th out of 207 journals of mathematics and science.

Geography Hydrocarbon Reservoir

At Carnegie Mellon University in 2011, numerical approximations of incompressible fluid with specific density and viscosity approximate hydrocarbon reservoirs. Hydrocarbon reservoirs, detected with ultraviolet lasers, can be differentiated from water, oil and gas at varied temperatures and pressures. Nuclear magnetic resonance helps researchers distinguish ethane, propane, methane, carbon dioxide and nitrogen by viscosity, diffusion rate, density, pressure and hydrogen index. Seismic readings, 50 meters apart, help the United States Geological Survey map the three-dimensional geometry of petroleum or hydrocarbon reservoirs. The USGS also maps the locations of aquifers, reservoirs of water, which can undermine mining operations by filling the mineshaft with water.

Exploration Algorithms Robotics

Applied mathematics, statistics and bio-statistics at Old Dominion University yield analytical and numerical approximations, probability and statistical inference in oceanography and meteorology. Approximations in applied mathematics explain biological, geological, ecological, business, banking and medical statistics. The American Society of Mechanical Engineering on the University of California Los Angeles campus researches robotic microsurgery in USC's Advanced Surgical and Interventional Technology classroom. Motors, 1.5 mm long, are used in minimally invasive medical microsurgery. Since 1979, the Carnegie Mellon Robotics Institute has created robots equipped with sensors, data and algorithms to explore uncertain areas and transmit data to researchers.

Market Trend Analysis

Strategies for success include resiliency. Successful enterprise requires recognizing opportunities and strategic marketing. Daily monitoring of profit and loss with the ability to change direction if profits or stock prices fall, is a necessary characteristic of a successful resilient business. Financial markets are approximated by theoretical models for decision making. Network analysis of projected sales yield production information for management. For example, network analysis of seasonal summer sales tells merchants when they must receive delivery of merchandise, how much they iare likely to sell and the number in their inventory. Basic mathematical approximations tell merchants when to order more of an inventoried part.

Actuarial Approximations

Actuarial science is based on probabilistic approximations of age and mortality factors, but actuarial ages are usually given in years and half-years, with no months or days considered. Mortality rates are based on diverse aggregate sums, not mixed factors in unique individuals. Financial and insurance actuarial models consider collections of contracts or policies. Investors approximations are based on a portfolio of investments. Central tendency is an approximation of distribution. Statistical models of pension plans, risk estimation and modeling of investment options. The "Journal of Financial and Actuarial Statistics" addresses mortality adjustment factors, time-trend regression adjustments and simulation of stochastic models.

References

• Vanderbuilt University International Journal of Approximations and Expansions
• Vanderbuilt University Center for Constructive Approximations
• Carnegie Mellon University: Convergence of Numerical Approximations Density and Viscosity
• University of Waterloo, Canada: Approximation Algorithms for Network Problems
• Oxford University: Practical Applied Mathematics
• Old Dominion Univeristy: Department of Mathematics and Statistics

Resources

• Ohio State University: Journal of Approximation Theory
• Financial and Actuarial Statistics: An Introduction; Dale S. Borowiak; 2003
• Penn State: International Center for Actuators and Transducers
• Pennsylvania State University: Radiation and Science Engineering Center
• UCLA: Center for Advanced Surgical and Interventional Technology
• UCLA: Henry Samueli School of Engineering and Applied Science
• Carnegie Mellon: The Robotics Institute
• Massachusetts Institute of Technology: Field and Space Robotics Laboratory
• University of California Los Angeles: American Society Mechanical Engineering Robotics
• Massachusetts Institute of Technology: Field and Space Robotics Laboratory
• Massachusetts Institute of Technology: Graduate Study in Mechanical Engineering
• Carnegie Mellon Robotic Institute: Academic Programs