Mathematics Education in the Digital Era

Proof Technology in Mathematics Research and Teaching

Editors: Hanna, Gila, Reid, David, de Villiers, Michael (Eds.)

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  • Provides a much needed update on new developments on proof in the digital era
    Brings new ideas on teaching proof and proving in mathematics education
    Emphasizes interdisciplinary approaches on education, philosophy and technology
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About this book

This book presents chapters exploring the most recent developments in the role of technology in proving. The full range of topics related to this theme are explored, including computer proving, digital collaboration among mathematicians, mathematics teaching in schools and universities, and the use of the internet as a site of proof learning.

Proving is sometimes thought to be the aspect of mathematical activity most resistant to the influence of technological change. While computational methods are well known to have a huge importance in applied mathematics, there is a perception that mathematicians seeking to derive new mathematical results are unaffected by the digital era. The reality is quite different. Digital technologies have transformed how mathematicians work together, how proof is taught in schools and universities, and even the nature of proof itself. Checking billions of cases in extremely large but finite sets, impossible a few decades ago, has now become a standard method of proof. Distributed proving, by teams of mathematicians working independently on sections of a problem, has become very much easier as digital communication facilitates the sharing and comparison of results. Proof assistants and dynamic proof environments have influenced the verification or refutation of conjectures, and ultimately how and why proof is taught in schools. And techniques from computer science for checking the validity of programs are being used to verify mathematical proofs.

Chapters in this book include not only research reports and case studies, but also theoretical essays, reviews of the state of the art in selected areas, and historical studies. The authors are experts in the field. 

Table of contents (17 chapters)

Table of contents (17 chapters)
  • Proof Technology: Implications for Teaching

    Pages 3-9

    Hanna, Gila (et al.)

  • A Fully Automatic Theorem Prover with Human-Style Output

    Pages 13-57

    Ganesalingam, M. (et al.)

  • A Common Type of Rigorous Proof that Resists Hilbert’s Programme

    Pages 59-71

    Bundy, Alan (et al.)

  • SMTCoq: Mixing Automatic and Interactive Proof Technologies

    Pages 73-90

    Keller, Chantal

  • Studying Algebraic Structures Using Prover9 and Mace4

    Pages 91-111

    Arthan, Rob (et al.)

Buy this book

eBook n/a
  • ISBN 978-3-030-28483-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-3-030-28482-4
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Proof Technology in Mathematics Research and Teaching
Editors
  • Gila Hanna
  • David Reid
  • Michael de Villiers
Series Title
Mathematics Education in the Digital Era
Series Volume
14
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-28483-1
DOI
10.1007/978-3-030-28483-1
Hardcover ISBN
978-3-030-28482-4
Series ISSN
2211-8136
Edition Number
1
Number of Pages
VIII, 379
Number of Illustrations
54 b/w illustrations, 83 illustrations in colour
Topics