Exploring University Mathematics with Python

This book provides a unique tour of university mathematics with the help of Python. Written in the spirit of mathematical exploration and investigation, the book enables students to utilize Python to enrich their understanding of mathematics through:

• Calculation: performing complex calculations and numerical simulations instantly
• Visualisation: demonstrating key theorems with graphs, interactive plots and animations
• Extension: using numerical findings as inspiration for making deeper, more general conjectures.

This book is for all learners of mathematics, with the primary audience being mathematics undergraduates who are curious to see how Python can enhance their understanding of core university material. The topics chosen represent a mathematical overview of what students typically study in the first and second years at university, namely analysis, calculus, vector calculus and geometry, differential equationsand dynamical systems, linear algebra, abstract algebra and number theory, probability and statistics. As such, it can also serve as a preview of university mathematics for high-school students. The prerequisites for reading the book are a familiarity with standard A-Level mathematics (or equivalent senior high-school curricula) and a willingness to learn programming.For mathematics lecturers and teachers, this book is a useful resource on how Python can be seamlessly incorporated into the mathematics syllabus, assuming only basic knowledge of programming.

Table of Contents

CHAPTER ONE: Analysis

CHAPTER TWO: Calculus

CHAPTER THREE: Vector Calculus and Geometry

CHAPTER FOUR: Differential Equations and Dynamical Systems

CHAPTER FIVE: Linear Algebra

CHAPTER SIX: Abstract Algebra and Number Theory

CHAPTER SEVEN: Probability

CHAPTER EIGHT Statistics

Appendix A: Python 101

About the Author

Siri Chongchitnan is a Reader in mathematics at the University of Warwick. His research is on mathematical cosmology and the use of technology in mathematics education. At Warwick, he is Director of Student Experience.