Chapter 1, Introduction to Mathematical Modeling, provides an introduction to the theory and concepts of mathematical modeling and the areas in which a mathematical model is predominant and useful.

Chapter 2, Machine Learning vis-à-vis Mathematical Modeling, describes with examples how machine learning models serve as predictive tools and classical mathematical models serve as prescriptive tools.

Chapter 3, Principal Component Analysis, provides the method to reduce the dimensionality of very high-dimensional data and examples wherein dimensionality reduction is necessary.

Chapter 4, Gradient Descent, is about an algorithm that lays the foundation for machine learning models. Variants of the gradient descent method are used to train machine learning as well as deep learning models.

Chapter 5, Support Vector Machine, provides mathematical details about an algorithm mostly utilized for data classification.

Chapter 6, Graph Theory, provides a theory that quantifies or models the relationships between interconnected entities in a network.

Chapter 7, Kalman Filter, is about a state estimation and prediction algorithm in the presence of imprecise and uncertain measurements of a dynamic system.

Chapter 8, Markov Chain, provides the theory of modeling a stochastic (random) process. The Markov chain is a class of probabilistic models that determines the next future state from knowledge of only the present state.

Chapter 9, Exploring Optimization Techniques, provides exposure to optimization algorithms used in machine learning models and those used in operations research. It also introduces you to evolutionary algorithms with examples.

Chapter 10, Optimization Techniques for Machine Learning, provides the methods for determining which algorithm to choose for the optimization of a machine learning model fitted to a dataset.