Overview

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. 

Full Product Details

Author:   Gila Hanna ,  David A. Reid ,  Michael de Villiers
Publisher:   Springer Nature Switzerland AG
Imprint:   Springer Nature Switzerland AG
Edition:   1st ed. 2019
Volume:   14
Weight:   0.911kg
ISBN:  

9783030284824

ISBN 10:   3030284824
Pages:   379
Publication Date:   18 October 2019
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Chapter 1. Proof technology: Implications for teaching.- Chapter 2. A fully automatic theorem prover with human-style output.- Chapter 3. A common type of rigorous proof that resists Hilbert's programme.- Chapter 4. SMTCoq: Mixing automatic and interactive proof technologies.- Chapter 5. Studying algebraic structures using Prover9 and Mace4.- Chapter 6. Didactical issues at the interface of mathematics and computer science.- Chapter 7. Issues and challenges in instrumental proof.- Chapter 8. Reasoning by equivalence: the potential contribution of an automatic proof checker.- Chapter 9. Virtual manipulatives and students’ counterexamples during proving.- Chapter 10. Proof technology and learning in mathematics: Common issues and perspectives.

Reviews

This book is intended for specialists in mathematics education with an interest in computer science advances as well as for researchers in the field of automated reasoning with an interest in the pedagogical and didactic implications of their work. It provides a valuable contribution to mathematics education by initiating a process of in-depth reflection on the educational value of new technological tools such as automatic theorem provers and dynamic geometric environments. (Frederic Morneau-Guerin, MAA Reviews, May 24, 2020)

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