Book Image

A Handbook of Mathematical Models with Python

By : Dr. Ranja Sarkar
Book Image

A Handbook of Mathematical Models with Python

By: 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)
1
Part 1:Mathematical Modeling
4
Part 2:Mathematical Tools
11
Part 3:Mathematical Optimization

Types of graphs

The primary graph types are undirected, directed, and weighted graphs, as illustrated in Figure 6.4. Social networks can be undirected as well as directed graphs. In the former, edges end up being unordered pairs, for example, Facebook. In the latter, edges are ordered pairs, for example, Twitter, in which one node is an origin and the other a destination.

Figure 6.4: Three standard graph types

Figure 6.4: Three standard graph types

We will explore each of these graphs in the following subsections.

Undirected graphs

While solving a problem using graph theory, the first step is to determine the type of graph we are dealing with. In undirected graphs, there is no particular direction of the edges between nodes, in other words, the edge is bidirectional. An edge connecting node 1 to node 2 (Figure 6.5) would be identical to the edge connecting node 2 to node 1.

Figure 6.5: Directed and undirected graphs

Figure 6.5: Directed and undirected graphs

Directed graphs

In directed graphs,...