Limits of Mathematics
A Journey Through the Key Areas of Mathematical Logic
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Beschreibung
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.
About the author
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 Gödel’s Incompleteness Theorems - A Guided Tour Through Kurt Gödel’s Historic Proof.
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.
A well-understandable introduction to the (fundamental) limits of mathematical knowledge Wherever possible, examples and illustrations help to master the high level of abstraction Numerous historical remarks contribute to bringing the topics to life and presenting the material in an engaging way
Autor*in
Dirk W. Hoffmann
Themen in »Limits of Mathematics«
Forcing Gödel Hilbert Chow algorithmic information theory Provability fundaments of mathematics Goedel's incompleteness theorems set theory model theory Turing machines undecidability continuum hypothesis