Recursion: Mathematics and Python - Yung-Hsiang Lu

Recursion: Mathematics and Python is designed to help readers develop a clear and systematic understanding of recursion as both a mathematical concept and a programming technique. Rather than presenting recursion as a collection of isolated examples, the book emphasizes recursive thinking: how complex problems can be expressed, analyzed, and solved by breaking them into simpler instances of similar structures.

The book adopts a consistent pedagogical approach throughout. Each topic begins with a mathematical or conceptual formulation that highlights the recursive structure of the problem. Readers are guided to identify parameters, base cases, and recursive relationships before translating these ideas into Python programs. Examples are chosen to identify recurring patterns across domains, including integer partitions, Tower of Hanoi, parentheses counting, binary search, quick sort, Sudoku solving, maze traversal, tree structures, and data compression. Code examples are written for clarity. Readers can follow execution flow and understand how recursive calls interact with computer memory. This book also explains how to reduce the recursion time by identifying and removing redundant computation.

This book is intended for undergraduate students in computer science and computer engineering who already have basic Python programming experience and some prior exposure to recursion. It is well suited for courses in programming, discrete mathematics, data structures, or algorithms. This book can also help instructors seek a resource that tightly integrates mathematical reasoning with executable code.