The science of learning mathematical proofs: an introductory course
"College students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduct...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2021]
|
| Schlagworte: | |
| Zusammenfassung: | "College students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduction utilizes recent research in neuroscience regarding how the brain learns best. Rather than jumping right into proofs, students are first taught how to change their mindset about learning, how to persevere through difficult problems, how to work successfully in a group, and how to reflect on their learning. With these tools in place, students then learn logic and problem solving as a further foundation. Next various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, and mathematical induction are introduced. These proof techniques are introduced using the context of number theory. The last chapter uses Calculus as a way for students to apply the proof techniques they have learned"-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xvi, 226 Seiten Illustrationen |
| ISBN: | 9789811225512 9789811227677 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV047074326 | ||
| 003 | DE-604 | ||
| 005 | 20210917 | ||
| 007 | t | ||
| 008 | 201223s2021 a||| |||| 00||| eng d | ||
| 010 | |a 2020044703 | ||
| 020 | |a 9789811225512 |c Pb.: £ 35.00 |9 978-981-1225-51-2 | ||
| 020 | |a 9789811227677 |c (hardcover): £ 75.00 |9 978-981-1227-67-7 | ||
| 035 | |a (OCoLC)1240400454 | ||
| 035 | |a (DE-599)OBVAC16105826 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-706 |a DE-91G | ||
| 082 | 0 | |a 511.3/6 |2 23 | |
| 084 | |a MAT 036 |2 stub | ||
| 100 | 1 | |a Reiser, Elana |d 1979- |e Verfasser |0 (DE-588)1228138494 |4 aut | |
| 245 | 1 | 0 | |a The science of learning mathematical proofs |b an introductory course |c Elana Reiser, St. Joseph's College, USA |
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo |b World Scientific |c [2021] | |
| 300 | |a xvi, 226 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 520 | |a "College students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduction utilizes recent research in neuroscience regarding how the brain learns best. Rather than jumping right into proofs, students are first taught how to change their mindset about learning, how to persevere through difficult problems, how to work successfully in a group, and how to reflect on their learning. With these tools in place, students then learn logic and problem solving as a further foundation. Next various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, and mathematical induction are introduced. These proof techniques are introduced using the context of number theory. The last chapter uses Calculus as a way for students to apply the proof techniques they have learned"-- | ||
| 650 | 4 | |a Proof theory | |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Beweis |0 (DE-588)4132532-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | 1 | |a Beweis |0 (DE-588)4132532-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-981-1225-52-9 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-981-1225-53-6 |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-032481297 | ||
Datensatz im Suchindex
| _version_ | 1804182080096043008 |
|---|---|
| adam_txt | |
| any_adam_object | |
| any_adam_object_boolean | |
| author | Reiser, Elana 1979- |
| author_GND | (DE-588)1228138494 |
| author_facet | Reiser, Elana 1979- |
| author_role | aut |
| author_sort | Reiser, Elana 1979- |
| author_variant | e r er |
| building | Verbundindex |
| bvnumber | BV047074326 |
| classification_tum | MAT 036 |
| ctrlnum | (OCoLC)1240400454 (DE-599)OBVAC16105826 |
| dewey-full | 511.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/6 |
| dewey-search | 511.3/6 |
| dewey-sort | 3511.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02579nam a2200421 c 4500</leader><controlfield tag="001">BV047074326</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210917 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">201223s2021 a||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2020044703</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789811225512</subfield><subfield code="c">Pb.: £ 35.00</subfield><subfield code="9">978-981-1225-51-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789811227677</subfield><subfield code="c">(hardcover): £ 75.00</subfield><subfield code="9">978-981-1227-67-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1240400454</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)OBVAC16105826</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-706</subfield><subfield code="a">DE-91G</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3/6</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 036</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Reiser, Elana</subfield><subfield code="d">1979-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1228138494</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The science of learning mathematical proofs</subfield><subfield code="b">an introductory course</subfield><subfield code="c">Elana Reiser, St. Joseph's College, USA</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo</subfield><subfield code="b">World Scientific</subfield><subfield code="c">[2021]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xvi, 226 Seiten</subfield><subfield code="b">Illustrationen</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">"College students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduction utilizes recent research in neuroscience regarding how the brain learns best. Rather than jumping right into proofs, students are first taught how to change their mindset about learning, how to persevere through difficult problems, how to work successfully in a group, and how to reflect on their learning. With these tools in place, students then learn logic and problem solving as a further foundation. Next various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, and mathematical induction are introduced. These proof techniques are introduced using the context of number theory. The last chapter uses Calculus as a way for students to apply the proof techniques they have learned"--</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Proof theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Beweis</subfield><subfield code="0">(DE-588)4132532-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Beweis</subfield><subfield code="0">(DE-588)4132532-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-981-1225-52-9</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-981-1225-53-6</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-032481297</subfield></datafield></record></collection> |
| id | DE-604.BV047074326 |
| illustrated | Illustrated |
| index_date | 2024-07-03T16:14:33Z |
| indexdate | 2024-07-10T09:01:51Z |
| institution | BVB |
| isbn | 9789811225512 9789811227677 |
| language | English |
| lccn | 2020044703 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032481297 |
| oclc_num | 1240400454 |
| open_access_boolean | |
| owner | DE-706 DE-91G DE-BY-TUM |
| owner_facet | DE-706 DE-91G DE-BY-TUM |
| physical | xvi, 226 Seiten Illustrationen |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Reiser, Elana 1979- Verfasser (DE-588)1228138494 aut The science of learning mathematical proofs an introductory course Elana Reiser, St. Joseph's College, USA New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2021] xvi, 226 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index "College students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduction utilizes recent research in neuroscience regarding how the brain learns best. Rather than jumping right into proofs, students are first taught how to change their mindset about learning, how to persevere through difficult problems, how to work successfully in a group, and how to reflect on their learning. With these tools in place, students then learn logic and problem solving as a further foundation. Next various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, and mathematical induction are introduced. These proof techniques are introduced using the context of number theory. The last chapter uses Calculus as a way for students to apply the proof techniques they have learned"-- Proof theory Mathematik (DE-588)4037944-9 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Mathematik (DE-588)4037944-9 s Beweis (DE-588)4132532-1 s DE-604 Erscheint auch als Online-Ausgabe 978-981-1225-52-9 Erscheint auch als Online-Ausgabe 978-981-1225-53-6 |
| spellingShingle | Reiser, Elana 1979- The science of learning mathematical proofs an introductory course Proof theory Mathematik (DE-588)4037944-9 gnd Beweis (DE-588)4132532-1 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4132532-1 |
| title | The science of learning mathematical proofs an introductory course |
| title_auth | The science of learning mathematical proofs an introductory course |
| title_exact_search | The science of learning mathematical proofs an introductory course |
| title_exact_search_txtP | The science of learning mathematical proofs an introductory course |
| title_full | The science of learning mathematical proofs an introductory course Elana Reiser, St. Joseph's College, USA |
| title_fullStr | The science of learning mathematical proofs an introductory course Elana Reiser, St. Joseph's College, USA |
| title_full_unstemmed | The science of learning mathematical proofs an introductory course Elana Reiser, St. Joseph's College, USA |
| title_short | The science of learning mathematical proofs |
| title_sort | the science of learning mathematical proofs an introductory course |
| title_sub | an introductory course |
| topic | Proof theory Mathematik (DE-588)4037944-9 gnd Beweis (DE-588)4132532-1 gnd |
| topic_facet | Proof theory Mathematik Beweis |
| work_keys_str_mv | AT reiserelana thescienceoflearningmathematicalproofsanintroductorycourse |