Titlebook: Algorithmic Mathematics; Stefan Hougardy,Jens Vygen Textbook 2016 Springer International Publishing Switzerland 2016 algorithms.algorithmi

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Introduction,In this chapter we will define a number of basic concepts and present several simple algorithms which we will analyze and implement in C++. We will also see that not everything is computable.

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Graphs,Numerous discrete structures can best be described using graphs. Furthermore, in countless applications graphs appear naturally. Thus graphs can well be considered to be the most important structure in discrete mathematics.

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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..978-3-319-39558-6

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Representations of the Integers,ore all occurring natural numbers in the data type .. This, however, is in fact not the case. A variable of type . usually corresponds to a sequence of 4 bytes. This clearly enables us to represent no more than 2. different numbers. In this chapter we will learn how integers are stored.

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Computing with Integers,e this assumption, although it is clearly by no means a realistic one for arbitrarily large numbers. Here we will investigate how fast one can actually compute with integers. Here, in a narrower sense, elementary operations only include operations and comparisons restricted to integers in some bound

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Computing with Errors,not only when inputting data (the number 0.1, for example, has no exact binary representation with finitely many digits; cf. Example .), but also when using the elementary operations +, −, ⋅ and ∕. Moreover, the desired answer may be a nonrepresentable number.