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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

Graph Theory

Graphs are mathematical structures that are used to model pairwise relationships. Graph theory provides a tool to quantify these relationships in a dynamic system. In other words, graphs are ways to represent a network or a collection of interconnected objects. Graph theory is mostly applied in operations research and social sciences. Its history dates back to the 18th century when the Swiss mathematician Leonhard Euler solved the Königsberg bridge problem (Figure 6.1), which served as a precursor to graph theory. The city of Königsberg in Russia was set on both sides of the Pregel river and included two large islands, namely, Kneiphof and Lomse, which were connected by seven bridges. The problem was to devise a walk through the city that would cross each of these bridges only once. Euler drew out the first known visual representation of a modern graph for the city. It is represented (abstractly) by a set of points known as vertices or nodes, connected by a set...

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