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 utilise Python to enrich their understanding of mathematics through:Calculation: performing complex calculations and numerical simulations instantlyVisualisation: demonstrating key theorems with graphs, interactive plots and animationsExtension: 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, Linear Algebra, Calculus, Abstract Algebra and Number Theory, Vector Calculus and Geometry, Probability, Differential Equations and Dynamical Systems, 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.Based on a taught university course, this book will also benefit mathematics lecturers who want to incorporate programming into their teaching, using only basic programming.