<p>“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)</p>“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)<p></p>

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.

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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.
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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
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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.

Les mer
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 Includes supplementary material: sn.pub/extras
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GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
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Produktdetaljer

ISBN
9783319395579
Publisert
2016-10-24
Utgiver
Vendor
Springer International Publishing AG
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Lower undergraduate, UU, 05
Språk
Product language
Engelsk
Format
Product format
Innbundet
Orginaltittel
Algorithmische Mathematik

Oversetter

Om bidragsyterne

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.