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Proof technology in mathematics rese...

Hanna, Gila.

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Proof technology in mathematics research and teaching

Record Type:	Electronic resources : Monograph/item
Title/Author:	Proof technology in mathematics research and teaching/ edited by Gila Hanna, David A. Reid, Michael de Villiers.
other author:	Hanna, Gila.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	viii, 379 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Proof theory - Study and teaching. -
Online resource:	https://doi.org/10.1007/978-3-030-28483-1
ISBN:	9783030284831

Proof technology in mathematics research and teaching
Proof technology in mathematics research and teaching[electronic resource] /edited by Gila Hanna, David A. Reid, Michael de Villiers. - Cham :Springer International Publishing :2019. - viii, 379 p. :ill. (some col.), digital ;24 cm. - Mathematics education in the digital era,v.142211-8136 ;. - Mathematics education in the digital era ;v.14..

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.

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.

ISBN: 9783030284831

Standard No.: 10.1007/978-3-030-28483-1doiSubjects--Topical Terms:

3502876
Proof theory
--Study and teaching.

LC Class. No.: QA9.54 / .P76 2019

Dewey Class. No.: 511.36

Proof technology in mathematics research and teaching
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245 0 0 $a Proof technology in mathematics research and teaching $h [electronic resource] / $c edited by Gila Hanna, David A. Reid, Michael de Villiers.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a viii, 379 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Mathematics education in the digital era, $x 2211-8136 ; $v v.14
505 0 $a 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.
520 $a 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.
650 0 $a Proof theory $x Study and teaching. $3 3502876
650 1 4 $a Mathematics Education. $3 637497
650 2 4 $a Technology and Digital Education. $3 2181140
650 2 4 $a Structures and Proofs. $3 3459360
650 2 4 $a Critical Thinking. $3 3275118
650 2 4 $a Teaching and Teacher Education. $3 1001835
700 1 $a Hanna, Gila. $3 1066784
700 1 $a Reid, David A. $3 867960
700 1 $a De Villiers, Michael. $3 3502874
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Mathematics education in the digital era ; $v v.14. $3 3502875
856 4 0 $u https://doi.org/10.1007/978-3-030-28483-1
950 $a Education (SpringerNature-41171)