Proof Technology in Mathematics Research and Teaching by Gila Hanna (English) Pa

Description: Proof Technology in Mathematics Research and Teaching by Gila Hanna, David A. Reid, Michael de Villiers 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Back Cover 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 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 Hilberts 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. Review "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." (Frédéric Morneau-Guérin, MAA Reviews, May 24, 2020) Review Quote "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." (Fr Feature 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 Description for Sales People 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 Details ISBN3030284859 Pages 379 Series Mathematics Education in the Digital Era Language English Year 2020 ISBN-10 3030284859 ISBN-13 9783030284855 Format Paperback Series Number 14 Publication Date 2020-10-18 Publisher Springer Nature Switzerland AG Edition 1st Imprint Springer Nature Switzerland AG Place of Publication Cham Country of Publication Switzerland UK Release Date 2020-10-18 Author Michael de Villiers Illustrations 83 Illustrations, color; 54 Illustrations, black and white; VIII, 379 p. 137 illus., 83 illus. in color. Edited by Michael de Villiers Edition Description 1st ed. 2019 Alternative 9783030284824 DEWEY 370 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:134249952;

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