Fundamental Concepts of Mathematics

This book provides essential foundations of mathematics, covering set theory, algebra, the theory of real and complex numbers, and topology. It serves as the basis for further exploration of mathematics. Not only are the necessary concepts introduced, but also essential – including deeper – statements are proven. The material is illustrated and supplemented by unusual examples and diverse exercises. The book is suitable for self-study, but primarily designed as companion reading from the beginning for a study in mathematics, physics, and computer science. Its coherent approach makes it highly readable and comparatively easy to understand. The Authors Uwe Storch and Hartmut Wiebe gained extensive experience in lecturing at the Faculty of Mathematics at the Ruhr-University Bochum, particularly for students of physics and computer science. Their mathematical research area was algebra, focusing primarily on its connections to algebraic and analytic geometry. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content (by the author Hartmut Wiebe only, as Uwe Storch is no longer with us). This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.