Limits of Mathematics

A Journey Through the Key Areas of Mathematical Logic
Erscheinungsjahr 2025
ISBN: 978-3-662-70998-6
Verlag: Springer

Buch, Englisch, 422 Seiten, Format (B × H): 189 mm x 226 mm, Gewicht: 763 g

Reihe: Mathematics Study Resources

Is mathematics free of contradictions? Are there truths beyond what can be proven? Is it possible to encode our mathematical knowledge into a single number?

Modern mathematical logic of the twentieth century provides astonishing answers to these questions.

This book takes you on a journey through the core areas of mathematical logic, leading to the limits of mathematics. The covered topics include the history of mathematical logic, formal systems, axiomatic number theory and set theory, proof theory, Gödel's incompleteness theorems, computability theory, algorithmic information theory, and model theory.

The book contains numerous two-color illustrations and more than 70 exercises (with solutions available on the author's website). This translation is based on the third edition of the original German book.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Hoffmann, Dirk W.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik

Inhaltsverzeichnis

1 Historic Notes.- 2 Formal Systems.- 3 Foundations of Mathematics.- 4 Peoof Thory.- 5 Computability Theory.- 6 Algorithmic Information Theory.- Model Theory.

Über Autor(innen)

Prof. Dr. Dirk W. Hoffmann is a professor at the Department of Computer Science and Business Information Systems at Karlsruhe University of Applied Sciences in Germany. He has also authored the book .