Foundations of Mathematics: A Preparatory Course
Description
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!"
The authors have succeeded in writing a mathematics book for students of all disciplines and continuing professional education that is easy to read from cover to cover without getting lost in formalism or humorless dryness, but that nevertheless left you with the necessary knowledge and technical confidence after reading it.
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, 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 German language 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
Reviews / Votes
"The book is one of the more comprehensive works that seek to accompany the transition from school to college. It spans a wide range: from school material below middle school (fractions) to beyond the first year of college (probability and statistics). ... The appearance of the book is excellent. Essentials are clearly highlighted. Exercises are included. Solutions are found in the appendix. A removable collection of formulas facilitates use of the book." Of particular note: "Removable collection of formulas." (Dr. Bruno Riedmüller, Chair of Mathematical Optimization, Technical University of Munich)
"Finally, an engaging, well-done prep course that highlights the elementary but essential basic concepts in just the right way."
Priv.-Doz. Dr. Frank Hettlich, University of Karlsruhe
"Easy-to-read and work-out work that is very convincing because of its entertaining nature."
Prof. Dr. Sax Kreutz, University of Applied Sciences, Hamburg
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Persons
Guido Walz is professor for applied mathematics at the Wilhelm-Büchner-Hochschule, Darmstadt, and lecturer at the Baden-Württemberg Cooperative State University in Mannheim. He is editor oft he six-volume Lexikon der Mathematik and author of numerous publications and textbooks, including Mathematik für Hochschule und Duales Studium .
Thomas Rießinger studied mathematics at the University of Mannheim and received his doctorate there in 1987. After working as a research assistant and systems analyst, he became a professor of mathematics and computer science at the University of Applied Sciences in Frankfurt am Main in 1992. He is the author of several textbooks about mathematics.
Frank Zeilfelder received his PhD (mathematics) in 1996 and his habilitation in 2002. In addition to various research stays abroad, he worked at the MPI for Computer Science in Saarbrücken, the University of Duisburg-Essen and the TU Darmstadt. Currently, he holds a position as "Fachberater Mathematik" at the RP Karlsruhe and works as a teacher for mathematics and computer science at the Carl-Benz-Schule in Mannheim.