Mathematical modeling is a powerful craft that requires practice.
The more practice the better one will become in executing the art.
The authors wrote this book to develop the craft of mathematical
modeling and to foster a desire for lifelong learning, habits of
mind and develop competent and confident problem solvers and
decision makers for the 21st century. This book offers a
problem-solving approach. The authors introduce a problem to help
motivate the learning of a particular mathematical modeling topic.
The problem provides the issue or what is needed to solve using an
appropriate modeling technique. Then principles are applied to the
problem and present the steps in obtaining an appropriate model to
solve the problem. Modeling Change and Uncertainty: Covers both
linear and nonlinear models of discrete dynamical systems.
Introduces statistics and probability modeling. Introduces critical
statistical concepts to handle univariate and multivariate data.
Establishes a foundation in probability modeling. Uses ordinary
differential equations (ODEs) to develop a more robust solution to
problems. Uses linear programming and machine learning to support
decision making. Introduces the reality of uncertainty and
randomness that is all around us. Discusses the use of linear
programing to solve common problems in modern industry. Discusses
he power and limitations of simulations. Introduces the methods and
formulas used in businesses and financial organizations. Introduces
valuable techniques using Excel, MAPLE, and R. Mathematical
modeling offers a framework for decision makers in all fields. This
framework consists of four key components: the formulation process,
the solution process, interpretation of the solution in the context
of the actual problem, and sensitivity analysis. Modeling Change
and Uncertainty will be of interest to mathematics departments
offering advanced mathematical modeling courses focused on decision
making or discrete mathematical modeling and by undergraduate,
graduate students and practitioners looking for an opportunity to
develop, practice, and apply the craft of mathematical modeling.
Table of Contents 1. Perfect Partners: Combining Models of Change
and Uncertainty with Technology 2. Modeling Change: Discrete
Dynamical Systems (DDS) and Modeling Systems of DDS 3. Statistical
and Probabilistic Models 4. Modeling with Probability 5.
Differential Equations 6. Forecasting with Linear Programming and
Machine Learning 7. Stochastic Models and Markov Chains 8. Linear
Programming 9. Simulation of Queueing Models 10. Modeling of
Financial Analysis 11. Reliability Models 12. Machine Learning and
Unconstrained Optimal Process Dr. William P. Fox is currently a
visiting professor of Computational Operations Research at the
College of William and Mary. He is an emeritus professor in the
Department of Defense Analysis at the Naval Postgraduate School and
teaches a three-course sequence in mathematical modeling for
decision making. He received his Ph.D. in Industrial Engineering
from Clemson University. He has taught at the United States
Military Academy for twelve years until retiring and at Francis
Marion University where he was the chair of mathematics for eight
years. He has many publications and scholarly activities including
twenty plus books and one hundred and fifty journal articles.
Colonel (R) Robert E. Burks, Jr., Ph.D. is an Associate Professor
in the Defense Analysis Department of the Naval Postgraduate School
(NPS) and the Director of the NPS' Wargaming Center. He holds a
Ph.D. in Operations Research from the Air Force Institute of
Technology. He is a retired logistics Army Colonel with more than
thirty years of military experience in leadership, advanced
analytics, decision modeling, and logistics operations who served
as an Army Operations Research analyst at the Naval Postgraduate
School, TRADOC Analysis Center, United States Military Academy, and
the United States Army Recruiting Command. Other book by William P.
Fox and Robert E. Burks: Advanced Mathematical Modeling with
Technology, 2021, CRC Press. Other books by William P. Fox from CRC
Press: Mathematical Modeling in the Age of the Pandemic, 2021, CRC
Press. Advanced Problem Solving Using Maple: Applied Mathematics,
Operations Research, Business Analytics, and Decision Analysis
(w/William Bauldry), 2020, CRC Press. Mathematical Modeling with
Excel (w/Brian Albright), 2020, CRC Press. Nonlinear Optimization:
Models and Applications, 2020, CRC Press. Advanced Problem Solving
with Maple: A First Course (w/William Bauldry), 2019. CRC Press.
Mathematical Modeling for Business Analytics, 2018, CRC Press.
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