Algorithmic mathematics
type: Item
instance of: scholarly article
title: Algorithmic mathematics
zbMATH Open document ID: 1382.68001
DOI: 10.1007/978-3-662-47014-5
author: Stefan Hougardy
author: Jens Vygen
published in: Springer-Lehrbuch
publication date: 2015-09-08T00:00:00Z
review text: This book is the textbook that accompanies the homonymous module at the University of Bonn, Germany, which, alongside modules on analysis and linear algebra, forms the basis of the first semester. Its highlight is the overview of algorithms with an emphasis on their mathematical component, but not neglecting the implementation aspect (numerous examples of implementations in C++ are included, accompanied by comments on their respective complexities; the examples can be further studied on the webpages of the authors). \newline The book is structured in eleven chapters; it commences with a general overview of algorithms and an example on prime numbers. The second chapter is focused on the b-adic representation of integers, on b-complements and on handling large integers (not representable using the standard Integer data type). The third chapter follows on counting operations with integers and includes a discussion on Euclid's algorithm and Fibonacci numbers. The fourth and fifth chapters present operations on real numbers and analyse the rounding errors, machine precision and the effect of error propagation. The three other topics discussed are elements of graph theory, sorting algorithms and operations on matrices. The sorting algorithms are presented in Chapter 8 and include key-sorting, merge sort, quicksort, binary heaps and heapsort. The chapters on graph theory overview introductory notions (Chapter 6, e.g., graph, tree definitions, paths and cycles, graph representations) and algorithms (Chapter 7, e.g., breadth-first search, approaches on acyclic digraphs). In the ninth chapter methods on the identification of optimal trees and paths are presented, including the Prim and the Dijkstra algorithms. In the tenth chapter the authors focus on networks and flows and describe the matching problem, the max-flow-min-cut theorem and algorithms for finding the maximal flow. The eleventh chapter presents algorithms on matrices such as the Gauss elimination, the LU factoriza…
reviewed by: Irina Ioana Mohorianu
Mathematics Subject Classification ID: 68-01
Mathematics Subject Classification ID: 65-01
Mathematics Subject Classification ID: 05C85
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65G99
Mathematics Subject Classification ID: 65Y04
Mathematics Subject Classification ID: 68P10
Mathematics Subject Classification ID: 68R10
Mathematics Subject Classification ID: 90C27
Mathematics Subject Classification ID: 90C35
zbMATH DE Number: 6479526
zbMATH Keywords: algorithms
zbMATH Keywords: pseudocode
zbMATH Keywords: C++
zbMATH Keywords: b-adic representation of integers
zbMATH Keywords: b-adic representation of real numbers
zbMATH Keywords: binary search
zbMATH Keywords: representation error
zbMATH Keywords: graph theory
zbMATH Keywords: trees
zbMATH Keywords: Dijkstra algorithm
zbMATH Keywords: matching on graphs
zbMATH Keywords: bipartite matching
zbMATH Keywords: flows
zbMATH Keywords: sorting algorithms
zbMATH Keywords: matrices
zbMATH Keywords: Gauss elimination
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-662-47014-5
OpenAlex ID: W4250620569
description: scientific article; zbMATH DE number 6479526