Algorithmic Mathematics

Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++.

This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this “Algorithmic Mathematics” course at the University of Bonn several times in recent years.

Table of Contents

Chapter 1 Introduction
Chapter 2 Representations of the Integers
Chapter 3 Computing with Integers
Chapter 4 Approximate Representations of the Real Numbers
Chapter 5 Computing with Errors
Chapter 6 Graphs
Chapter 7 Simple Graph Algorithms
Chapter 8 Sorting Algorithms
Chapter 9 Optimal Trees and Paths
Chapter 10 Matchings and Network Flows
Chapter 11 Gaussian Elimination