Topics In Mathematical Modeling

By Author: Pierce Brosnan
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Introduction to topics in mathematical modelling:

Much of our progress in the last few centuries has made it necessary to apply mathematical methods to real life problems arising from different fields - be it science, finance, management etc. The use of mathematics in solving real life problems has become wide spread especially due to the increasing computational power of digital computers and computing methods, both of which have facilitated the handling of lengthy and complicated problems. The translation process of a real life problem into a mathematical form may give a better representation and solution of some problems. The process of translation is called mathematical modelling.

Some Topics in Mathematical Modelling:

Laws of Life that can be Scaled, Social Networks and the Internet, Modeling Citation Network and the World Wide Web,
Modelling change based on timesteps, The Payments on Mortagage Loans, Interest Compounded Monthly, Interest Compounded on Daily Basis, Various Differential Equation based Modelling eg. Carbon Dating, HIV Modeling,Modeling in the Physical Sciences, Age of the Universe, ...
... Kepler, Newton, and Calculus,Discrete Time Logistic Map, Periodic and Chaotic Solutions,Snowball Earth and Global Warming,Interactions: Predator-Prey, Spraying of Pests, Nonlinear Population Models: An Introduction to Qualitative Analysis Using Phase Planes, Carnivores in a country,Marriage and Divorce

Different Process Followed in Topics of Mathematical Modelling:

There are different process involved in topics of mathematical modelling.They are understanding the problem, Formulation , Finding the solution and interpretation This leads us to an important observation. The real world is too complex to understand and describe completely. We just pick one or two main factors to be completely accurate that may influence the situation. Try to obtain a simplified model which gives some information about the situation.

Validation/Interpretation of a mathematical model:

A mathematical model is an attempt to study, the essential characteristic of a real life problem. Many times model equations are obtained by assuming the situation in an idealised context. The model will be useful only if it explains all the facts that we would like to explain. Otherwise, we will reject it, or else, improve it, and then test again.

Statistics may be defined as a systematic process of collection, classification, tabulation , analysis, interpretation and drawing valid inferences of numerical data in any field of human activity. In almost all the fields of human activity, the question that crops in are the variability of characteristics. The variability which is observed in nature, is the sound footing of statistical analysis which tells with a certain degree of confidence, the relative and absolute risks involved. This helps in management in decision making and planning for the future.

Application of statistics pervade virtually every area of management decision making whether it be production, finance, distribution, marketing or any other activity. In any organisation, the management uses statistical techniques for making valid decisions on the basis of factual data on the current operations. These decisions are of so vital importance that they not only improve the present situation, but also effect the future operations and policies. Statistics plays an important role and is very much in use in production and inventory decisions, marketing decisions, investment and financial decisions and also in planning decisions.

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