Algorithmic Mathematics

by Stefan Hougardy, Jens Vygen, Rabe von Randow

Overview

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.

Product Details

ISBN-13:	9783319395579
Publisher:	Springer International Publishing
Publication date:	10/15/2016
Edition description:	1st ed. 2016
Pages:	163
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Stefan Hougardy is professor of discrete mathematics at the University of Bonn. His research interests include combinatorial optimization and chip design.

Jens Vygen is professor of discrete mathematics at the University of Bonn. His research interests include combinatorial optimization and chip design.

Table of Contents

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

Editorial Reviews

The book under review contains the lectures the authors have taught at the University of Bonn for beginner students. It includes many worked-out examples, detailed explanations, as well as references for further study. … Alongside the mathematical themes, the authors have included an introduction to the programming language C++.” (Costică Moroşanu, zbMATH 1357.68002, 2017)

“This is a brief introduction to some simple numerical and computer algorithms, including an analysis of their timing. It’s aimed at students with a good high-school math background, but has no specific prerequisites, and has enough material for a one-semester course. … a good choice for a very early introduction to these topics.” (Allen Stenger, MAA Reviews, maa.org, December, 2016)

From the Publisher