Algorithmic adventures: from knowledge to magic by Juraj Hromkovič

By Juraj Hromkovič

The ?rst and superior aim of this lecture sequence used to be to teach the sweetness, intensity and usability of the foremost principles in desktop technology. whereas engaged on the lecture notes, we got here to appreciate that one could realize the genuine spirit of a scienti?c self-discipline basically via viewing its contributions within the framework of technology as an entire. We current desktop technology right here as a primary technology that, interacting with different scienti?c disciplines, replaced and alterations our view at the global, that contributes to our figuring out of the elemental ideas of technology and that sheds new mild on and brings new aspiring to a number of of those ideas. We convey that computing device technological know-how is a self-discipline that discovers dazzling, unforeseen proof, that ?nds methods out in doubtless unsolvable s- uations, and which can do real wonders. The message of this e-book is that machine technological know-how is an engaging study zone with a huge impact at the genuine global, jam-packed with dazzling rules and nice ch- lenges. it really is an essential component of technological know-how and engineering with an above-average dynamic during the last 30 years and a excessive measure of interdisciplinarity. The objective of this booklet isn't usual for well known technology writing, whichoftenrestrictsitselftooutliningtheimportanceofaresearch quarter. at any time when attainable we attempt to carry complete knowing of the innovations and effects presented.

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Extra info for Algorithmic adventures: from knowledge to magic

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If somebody designs a method for a special purpose and this method corresponds to our intuitive image of an algorithm, but is not an algorithm with respect to our definition, then the definition was not good enough and we have to revise it. In spite of many attempts to revise the definition of an algorithm since 1936, each attempt only confirmed Turing’s definition and so the belief in this axiom grew. After proving that the class of problems algorithmically solvable by quantum computers is the same as the class of problems solvable by Turing’s algorithms, almost nobody sees any possibility of a violation of this axiom.

In this way, a computer as a machine without any intelligence can solve quadratic equations by applying this method. 22 1 The Development of Computer Science Therefore, one associates the existence of a mathematical method for solving a problem to the possibility of calculating solutions in an automatic way. Today, we do not use the notion “method” in this context, because this term is used in many different areas with distinct meanings. Instead, we use the term algorithm. The choice of this new term as a synonym for a solution method was inspired by the name of the Arabic mathematician al-Khwarizmi, who wrote a book about algebraic methods in Baghdad in the ninth century.

Consider, for instance, the problem of solving a quadratic equation. ax2 + bx + c = 0. The input data are the numbers a, b, and c and the task is to find all x that satisfy this equation. For instance, a concrete problem instance is to solve the following equation: 46 2 What Programming and Baking Have in Common x2 − 5x + 6 = 0. Here, we have a = 1, b = −5, and c = 6. The solutions are x1 = 2 and x2 = 3. By substituting these values, one can easily verify that 22 − 5 · 2 + 6 = 4 − 10 + 6 = 0 32 − 5 · 3 + 6 = 9 − 15 + 6 = 0 and so verify that x1 and x2 are really the solutions of the quadratic equation x2 − 5x + 6 = 0.

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