Foundations of Mathematics: A Preparatory Course (PDF)

This book spares you the entry-level problems of mathematics by entertainingly building a bridge that gently guides you over any shoals and into the heart of college mathematics. The bridge starts on one side with simple number crunching, as you probably encountered it in middle school, and takes you across to the basics of linear algebra, differential calculus, and probability, which will be the main content of your first few semesters. You will always face this content there, and when dealing with it you can then say with confidence, "I know it already!"

Each chapter is accompanied by exercises that can be used to practice and reinforcethe content taught.

This book is a translation of the original German edition Brückenkurs Mathematik by Guido Walz, Frank Zeilfelder and Thomas Rießinger, 4th edition, published by Springer-Verlag GmbH, DE in 2014. 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.

Voices to the 1st edition

'At last, an engaging, successful preparatory course that accurately highlights the elementary but essential basic concepts.' Priv.-Doz. Dr. Frank Hettlich, University of Karlsruhe

'Easy to read and compile work that is very convincing due to its entertaining nature.' Prof. Dr. Sax Kreutz, University of Applied Sciences, Hamburg