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020 _a9783030284831
024 7 _a10.1007/978-3-030-28483-1
_2doi
040 _cМУБИС
050 4 _aLC8-6691
072 7 _aJNU
_2bicssc
072 7 _aEDU029010
_2bisacsh
072 7 _aJNU
_2thema
072 7 _aPB
_2thema
082 0 4 _a370
_223
245 1 0 _aProof Technology in Mathematics Research and Teaching
_h[electronic resource] /
_cedited by Gila Hanna, David A. Reid, Michael de Villiers.
250 _a1st ed. 2019.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2019.
300 _aVIII, 379 p. 137 illus., 83 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematics Education in the Digital Era,
_x2211-8136 ;
_v14
505 0 _aChapter 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 _aThis 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 _aMathematics—Study and teaching .
650 0 _aEducational technology.
650 0 _aProof theory.
650 0 _aCritical Thinking.
650 0 _aTeaching.
650 1 4 _aMathematics Education.
_0https://scigraph.springernature.com/ontologies/product-market-codes/O25000
650 2 4 _aTechnology and Digital Education.
_0https://scigraph.springernature.com/ontologies/product-market-codes/O47000
650 2 4 _aStructures and Proofs.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M24010
650 2 4 _aCritical Thinking.
_0https://scigraph.springernature.com/ontologies/product-market-codes/O53030
650 2 4 _aTeaching and Teacher Education.
_0https://scigraph.springernature.com/ontologies/product-market-codes/O31000
700 1 _aHanna, Gila.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aReid, David A.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _ade Villiers, Michael.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030284824
776 0 8 _iPrinted edition:
_z9783030284848
776 0 8 _iPrinted edition:
_z9783030284855
830 0 _aMathematics Education in the Digital Era,
_x2211-8136 ;
_v14
856 4 0 _uhttps://doi.org/10.1007/978-3-030-28483-1
942 _2ddc
_cEBOOK