Mathematical Logic through Python

Erscheinungsjahr 2022
ISBN: 978-1-108-84507-6
Verlag: Cambridge University Press

Buch, Englisch, 280 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 734 g

Using a unique pedagogical approach, this text introduces mathematical logic by guiding students in implementing the underlying logical concepts and mathematical proofs via Python programming. This approach, tailored to the unique intuitions and strengths of the ever-growing population of programming-savvy students, brings mathematical logic into the comfort zone of these students and provides clarity that can only be achieved by a deep hands-on understanding and the satisfaction of having created working code. While the approach is unique, the text follows the same set of topics typically covered in a one-semester undergraduate course, including propositional logic and first-order predicate logic, culminating in a proof of Gödel's completeness theorem. A sneak peek to Gödel's incompleteness theorem is also provided. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. Familiarity with proofs and basic proficiency in Python is assumed.

Autoren/Hrsg.

Gonczarowski, Yannai A.

Nisan, Noam

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Software Engineering
• Mathematik | Informatik EDV | Informatik Informatik Rechnerarchitektur
• Mathematik | Informatik EDV | Informatik EDV & Informatik Allgemein

Inhaltsverzeichnis

Preface; Introduction and Overview; Part I. Propositional Logic: 1. Propositional Logic Syntax; 2. Propositional Logic Semantics; 3. Logical Operators; 4. Proof by Deduction; 5. Working with Proofs; 6. The Tautology Theorem and the Completeness of Propositional Logic; Part II. Predicate Logic: 7. Predicate Logic Syntax and Semantics; 8. Getting Rid of Functions and Equality; 9. Deductive Proofs of Predicate Logic Formulas; 10. Working with Predicate Logic Proofs; 11. The Deduction Theorem and Prenex Normal Form; 12. The Completeness Theorem; 13. Sneak Peek at Mathematical Logic II: Godel's Incompleteness Theorem; Cheatsheet Axioms and Axiomatic Inference Rules Used in this Book; Notes; Index.

Über Autor(innen)

Gonczarowski, Yannai A.
Yannai A. Gonczarowski is Assistant Professor of both Economics and Computer Science at Harvard University, and is the first faculty at Harvard to be appointed to both of these departments. He received his PhD in Mathematics and Computer Science from The Hebrew University of Jerusalem. Among his research awards are the ACM SIGecom Dissertation Award and INFORMS AMD Junior Researcher Paper Prize. He is also a professionally trained opera singer.

Nisan, Noam
Noam Nisan is Professor of Computer Science and Engineering at The Hebrew University of Jerusalem, serving as Dean of the School of Computer Science and Engineering during 2018-2021. He received his PhD in Computer Science from the University of California, Berkeley. Among the awards for his research on computational complexity and algorithmic game theory are the Gödel Prize and Knuth Award. This is his fifth book.