【Springer 数学】Algorithmic Mathematics (2016)

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Algorithmic Mathematics

Authors: Stefan Hougardy, Jens Vygen



Textbook covering basic mathematical lecture course

Allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation

Provides an introduction to programming and demonstrates in detail how to implement algorithms in C++

Suitable for students who are new to the subject

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

Front Matter

Introduction

Representations of the Integers

Computing with Integers

Approximate Representations of the Real Numbers

Computing with Errors

Graphs

Simple Graph Algorithms

Sorting Algorithms

Optimal Trees and Paths

Matchings and Network Flows

Gaussian Elimination

Back Matter

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