Applied Math with Python

Applied Mathematics with Python is an comprenhensive guide that combines mathematical rigor and Python programming. Covering a wide range of topics, from statistics and probability to optimization, numerical methods, and deep learning, the book aims to equip you with the tools to tackle real-world problems that involve both mathematics and Python programming. Each chapter builds a foundation of theoretical concepts and complements them with Python-based implementations and applications, making abstract ideas accessible and applicable for everyone. Whether you’re working on statistical analysis, developing machine learning models, or exploring applications in fields like biology or finance, this book offers a seamless integration of mathematics and computational methods.

Designed for a diverse audience, including students, researchers, and professionals, the book emphasizes practical problem-solving while maintaining academic depth. Further specialized chapters focus on areas such as time series analysis, Bayesian methods, and stochastic processes, alongside multiple applications in science. By illustrating concepts through Python, we expect that readers can directly apply their learning to real-world scenarios. With this book we aim to provide not only a textbook compendium but also a bridge between theory and practice.

We are both trained mathematicians and work as data science/data engineering professionals. Here you can find more information about us:

• Jimmy Calvo-Monge

• Michael Abarca

These are the contents for Applied Mathematics with Python. You can see the wide depth of topics and applications. We encourage you to use this resource when a particular topic is of interest and you want to explore how to apply it through the means of Python programming. We wish you a fruitful learning journey and please don’t hesitate in contacting us with suggestions, comments, corrections or perhaps gifts (?).

San José, Costa Rica, 2024.

Table of Contents

General Statistics

• 1. General Statistics

General Probability

• 2. General Probability

Time Series Analysis

• 3. Time Series Analysis

Bayesian Analysis

• 4. Bayesian Analysis

Stochastic Processes

• 5. Stochastic Processes

Non-Parametric Statistics

• 6. Non-Parametric Statistics

General Numerical Methods

• 7. General Numerical Methods

Numerical Linear Algebra

• 8. Numerical Linear Algebra

Optimization

• 9. Optimization in Mathematics and Computer Science
• 10. Linear Programming
• 11. Gradient Descent

Ordinary Differential Equations

• 12. Ordinary Differential Equations (ODEs)

Partial Differential Equations

• 13. Partial Differential Equations (PDEs)

Classification Models in Machine Learning

• 14. Classification Models in Machine Learning

Regression Models in Machine Learning

• 15. Regression Models in Machine Learning

Deep Learning

• 16. Deep Learning

Reinforcement Learning

• 17. Reinforcement Learning

Clustering Theory

• 18. Clustering Theory in Data Science

Dimensionality Reduction Techniques

• 19. Dimensionality Reduction Techniques

Information Theory

• 20. Information Theory

Graph Theory and Network Analysis

• 21. Graph Theory and Network Analysis

Game Theory

• 22. Game Theory

Fourier Analysis

• 23. Fourier Analysis

Natural Language Processing

• 24. Natural Language Processing

Generative Artificial Intelligence

• 25. Generative Artificial Intelligence

Operations Research

• 26. Operations Research

Scientific Computing

• 27. Scientific Computing

Applications to Biology and Epidemiology

• 28. Applications to Biology and Epidemiology

Applications to Finance

• 29. Applications to Finance

Applications to Material Science and Physics

• 30. Applications to Material Science and Physics