Название: Algorithmics and Optimization
Автор: Andreas de Vries
Издательство: University of Applied Sciences of Hagen
Год: 2015
Формат: pdf
Страниц: 123
Размер: 1,24 mb.
Язык: English

Why mathematics in a book about algorithmics? Algorithms are, in essence, applied mathematics. Even if they deal with apparently “unmathematical” subjects such as manipulating strings or searching objects, mathematics is the basis. To mention just a few examples: the classical algorithmic concept of recursion is very closely related to the principle of mathematical induction; rigorous proofs are needed for establishing the correctness of given algorithms; running times have to be computed.
The contents of these lecture notes spread a wide range. On the one hand they try to give the basic knowledge about algorithmics, such that you will learn the following questions: What is an algorithm and what are its building blocks? How can an algorithm be analyzed? How do standard well-known algorithms work? On the other hand, these lecture notes introduce into the wide and important field of optimization. Optimization is a basic principle of human activity and thinking, it is involved in the sciences and in practice. It mainly deals with the question: How can a solution to a given problem under certain constraints be achieved with a minimum cost, be it time, money, or machine capacity? Optimization is a highly economical principle. However, any solution of an optimization problem is a list of instructions, such as “do this, then do that, but only under the condition that . . . ,” i.e., an algorithm — the circle is closed.

So we think optimization to be one of the basic subjects for you as a student of business information systems, for it will be one of your main business activities in the future. Surely, no lecture can give an answer to all problems which you will be challenged, but we think that it is important to understand that any optimization problem has a basic structure — it is the structure of a given optimization problem that you should understand, because then you may solve it in a more efficient way (you see, another optimization problem).