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A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

By : Ranja Sarkar, Dr. Ranja Sarkar
4.1 (7)
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A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

4.1 (7)
By: Ranja Sarkar, Dr. Ranja Sarkar

Overview of this book

Mathematical modeling is the art of transforming a business problem into a well-defined mathematical formulation. Its emphasis on interpretability is particularly crucial when deploying a model to support high-stake decisions in sensitive sectors like pharmaceuticals and healthcare. Through this book, you’ll gain a firm grasp of the foundational mathematics underpinning various machine learning algorithms. Equipped with this knowledge, you can modify algorithms to suit your business problem. Starting with the basic theory and concepts of mathematical modeling, you’ll explore an array of mathematical tools that will empower you to extract insights and understand the data better, which in turn will aid in making optimal, data-driven decisions. The book allows you to explore mathematical optimization and its wide range of applications, and concludes by highlighting the synergetic value derived from blending mathematical models with machine learning. Ultimately, you’ll be able to apply everything you’ve learned to choose the most fitting methodologies for the business problems you encounter.
Table of Contents (16 chapters)
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1
Part 1:Mathematical Modeling
4
Part 2:Mathematical Tools
11
Part 3:Mathematical Optimization

Markov Chain

The Markov chain is one of the most important stochastic processes and solves real-world problems with probabilities. A Markov chain is a model of random movement in a discrete set of possible locations (states), in other words, a model of transition from one location (state) to another with a certain probability. It is named after Andrey Markov, the Russian mathematician who is best known for his work on stochastic processes. It is a mathematical system describing a sequence of events in which the probability of each event depends only on the previous event.

“The future depends only upon the present, not upon the past.”

The events or states can be written as {, where is the state at time t. The process {} has a property, which is , which depends only on and does not depend on {. Such a process is called a Markovian or Markov chain. It is a random walk to traverse a system of states. A two-state Markov chain is one in which a state can transition...

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