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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

Optimization use case

Graphs can be used to model relations and processes in physical, biological, and information systems. They have a wide range of applications, such as ranking hyperlinks in search engines, the study of biomolecules, computer network security, GPS in maps to find the shortest route, and social network analysis. There are knowledge graphs for information mining as well. In the following subsection, we pick a dataset and formulate the problem in a way that is solved using graph theory.

Optimization problem

There can be multiple paths between origin and destination airports. An airline seeks the shortest possible path between airports, wherein the shortest path can be defined in terms of either distance or airtime. If the city airports are represented as nodes and the flight routes between them as edges, we convert the problem into a graph (Figure 6.8a). The dataset can be found in the GitHub repository: https://github.com/ranja-sarkar/graphs.

Figure 6.8a: Network (flight routes) between origin (city) airport and destination (city) airport...

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