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Cover: 9783031146480 | Exploring Formalisation | Clara Löh | Taschenbuch | vi | Englisch
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Exploring Formalisation
A Primer in Human-Readable Mathematics in Lean 3 with Examples from Simplicial Topology
Taschenbuch von Clara Löh
Sprache: Englisch

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Beschreibung
This primer on mathematics formalisation provides a rapid, hands-on introduction to proof verification in Lean.
After a quick introduction to Lean, the basic techniques of human-readable formalisation are introduced, illustrated by simple examples on maps, induction and real numbers. Subsequently, typical design options are discussed and brought to life through worked examples in the setting of simplicial complexes (a higher-dimensional generalisation of graph theory). Finally, the book demonstrates how current research in algebraic and geometric topology can be formalised by means of suitable abstraction layers.
Informed by the author's recent teaching and research experience, this book allows students and researchers to quickly get started with formalising and checking their proofs. The core material of the book is accessible to mathematics students with basic programming skills. For the final chapter, familiarity with elementarycategory theory and algebraic topology is recommended.
This primer on mathematics formalisation provides a rapid, hands-on introduction to proof verification in Lean.
After a quick introduction to Lean, the basic techniques of human-readable formalisation are introduced, illustrated by simple examples on maps, induction and real numbers. Subsequently, typical design options are discussed and brought to life through worked examples in the setting of simplicial complexes (a higher-dimensional generalisation of graph theory). Finally, the book demonstrates how current research in algebraic and geometric topology can be formalised by means of suitable abstraction layers.
Informed by the author's recent teaching and research experience, this book allows students and researchers to quickly get started with formalising and checking their proofs. The core material of the book is accessible to mathematics students with basic programming skills. For the final chapter, familiarity with elementarycategory theory and algebraic topology is recommended.
Über den Autor
Clara Löh is Professor of Mathematics at the University of Regensburg, Germany. Her research focuses on simplicial volume and the interaction between geometric topology, geometric group theory, and measured group theory. This includes cohomological, geometric, and combinatorial methods. She is also interested in the foundations of mathematics and the formalisation/verification of mathematics in proof assistants.
Zusammenfassung

Example driven: each topic is first presented in pen-and-paper style and then formalised in Lean

Starts at a very elementary level and ends with examples from current research

Aims for human-readable code and includes a variety of exercises

Inhaltsverzeichnis

Introduction.- 1 The Lean Proof Assistant.- 2 Basic Examples.- 3 Design Choices.- 4 Abstraction and Prototyping.

Details
Erscheinungsjahr: 2022
Fachbereich: Grundlagen
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: vi
147 S.
1 s/w Illustr.
147 p. 1 illus.
ISBN-13: 9783031146480
ISBN-10: 3031146484
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Löh, Clara
Auflage: 1st edition 2022
Hersteller: Springer Nature Switzerland
Springer International Publishing
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 9 mm
Von/Mit: Clara Löh
Erscheinungsdatum: 25.09.2022
Gewicht: 0,276 kg
Artikel-ID: 122099864
Über den Autor
Clara Löh is Professor of Mathematics at the University of Regensburg, Germany. Her research focuses on simplicial volume and the interaction between geometric topology, geometric group theory, and measured group theory. This includes cohomological, geometric, and combinatorial methods. She is also interested in the foundations of mathematics and the formalisation/verification of mathematics in proof assistants.
Zusammenfassung

Example driven: each topic is first presented in pen-and-paper style and then formalised in Lean

Starts at a very elementary level and ends with examples from current research

Aims for human-readable code and includes a variety of exercises

Inhaltsverzeichnis

Introduction.- 1 The Lean Proof Assistant.- 2 Basic Examples.- 3 Design Choices.- 4 Abstraction and Prototyping.

Details
Erscheinungsjahr: 2022
Fachbereich: Grundlagen
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: vi
147 S.
1 s/w Illustr.
147 p. 1 illus.
ISBN-13: 9783031146480
ISBN-10: 3031146484
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Löh, Clara
Auflage: 1st edition 2022
Hersteller: Springer Nature Switzerland
Springer International Publishing
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 9 mm
Von/Mit: Clara Löh
Erscheinungsdatum: 25.09.2022
Gewicht: 0,276 kg
Artikel-ID: 122099864
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