Why prove it again?: alternative proofs in mathematical practice
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham [u.a.]
Birkhäuser Springer
2015
|
| Subjects: | |
| Online Access: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 1 Online-Ressource (XI, 204 S.) 54 illus |
| ISBN: | 9783319173689 |
| DOI: | 10.1007/978-3-319-17368-9 |
Staff View
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042730113 | ||
| 003 | DE-604 | ||
| 005 | 20200930 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150803s2015 |||| o||u| ||||||eng d | ||
| 020 | |a 9783319173689 |c Online |9 978-3-319-17368-9 | ||
| 024 | 7 | |a 10.1007/978-3-319-17368-9 |2 doi | |
| 035 | |a (OCoLC)915913829 | ||
| 035 | |a (DE-599)BVBBV042730113 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91 |a DE-19 |a DE-703 |a DE-20 |a DE-739 |a DE-634 |a DE-861 |a DE-83 | ||
| 082 | 0 | |a 510.9 |2 23 | |
| 084 | |a SK 110 |0 (DE-625)143215: |2 rvk | ||
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Dawson, John W. |c Jr. |d 1944- |e Verfasser |0 (DE-588)137446365 |4 aut | |
| 245 | 1 | 0 | |a Why prove it again? |b alternative proofs in mathematical practice |c John W. Dawson, Jr. |
| 264 | 1 | |a Cham [u.a.] |b Birkhäuser Springer |c 2015 | |
| 300 | |a 1 Online-Ressource (XI, 204 S.) |b 54 illus | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Topology | |
| 650 | 4 | |a History of Mathematical Sciences | |
| 650 | 4 | |a Analysis | |
| 650 | 4 | |a Mathematik | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-3-319-17367-2 |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-319-17368-9 |x Verlag |3 Volltext |
| 856 | 4 | 2 | |m Springer Fremddatenuebernahme |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028161144&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Springer Fremddatenuebernahme |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028161144&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Abstract |
| 912 | |a ZDB-2-SMA | ||
| 940 | 1 | |q UBY_PDA_SMA | |
| 940 | 1 | |q ZDB-2-SMA_2015 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028161144 | ||
| 966 | e | |u https://doi.org/10.1007/978-3-319-17368-9 |l BTU01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/978-3-319-17368-9 |l FRO01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/978-3-319-17368-9 |l TUM01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/978-3-319-17368-9 |l UBM01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/978-3-319-17368-9 |l UBT01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/978-3-319-17368-9 |l UBW01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1007/978-3-319-17368-9 |l UPA01 |p ZDB-2-SMA |x Verlag |3 Volltext | |
Record in the Search Index
| _version_ | 1804174941338206208 |
|---|---|
| adam_text | WHY PROVE IT AGAIN?
/ DAWSON, JR., JOHN W.
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PROOFS IN MATHEMATICAL PRACTICE
MOTIVES FOR FINDING ALTERNATIVE PROOFS
SUMS OF INTEGERS
QUADRATIC SURDS
THE PYTHAGOREAN THEOREM
THE FUNDAMENTAL THEOREM OF ARITHMETIC
THE INFINITUDE OF THE PRIMES
THE FUNDAMENTAL THEOREM OF ALGEBRA
DESARGUES S THEOREM
THE PRIME NUMBER THEOREM
THE IRREDUCIBILITY OF THE CYCLOTOMIC POLYNOMIALS
THE COMPACTNESS OF FIRST-ORDER LANGUAGES
OTHER CASE STUDIES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
WHY PROVE IT AGAIN?
/ DAWSON, JR., JOHN W.
: 2015
ABSTRACT / INHALTSTEXT
THIS MONOGRAPH CONSIDERS SEVERAL WELL-KNOWN MATHEMATICAL THEOREMS AND
ASKS THE QUESTION, “WHY PROVE IT AGAIN?” WHILE EXAMINING ALTERNATIVE
PROOFS. IT EXPLORES THE DIFFERENT RATIONALES MATHEMATICIANS MAY
HAVE FOR PURSUING AND PRESENTING NEW PROOFS OF PREVIOUSLY ESTABLISHED
RESULTS, AS WELL AS HOW THEY JUDGE WHETHER TWO PROOFS OF A GIVEN RESULT
ARE DIFFERENT. WHILE A NUMBER OF BOOKS HAVE EXAMINED ALTERNATIVE
PROOFS OF INDIVIDUAL THEOREMS, THIS IS THE FIRST THAT PRESENTS
COMPARATIVE CASE STUDIES OF OTHER METHODS FOR A VARIETY OF DIFFERENT
THEOREMS. THE AUTHOR BEGINS BY LAYING OUT THE CRITERIA FOR
DISTINGUISHING AMONG PROOFS AND ENUMERATES REASONS WHY NEW PROOFS HAVE,
FOR SO LONG, PLAYED A PROMINENT ROLE IN MATHEMATICAL PRACTICE. HE THEN
OUTLINES VARIOUS PURPOSES THAT ALTERNATIVE PROOFS MAY SERVE. EACH
CHAPTER THAT FOLLOWS PROVIDES A DETAILED CASE STUDY OF ALTERNATIVE
PROOFS FOR PARTICULAR THEOREMS, INCLUDING THE PYTHAGOREAN THEOREM, THE
FUNDAMENTAL THEOREM OF ARITHMETIC, DESARGUES’ THEOREM, THE PRIME
NUMBER THEOREM, AND THE PROOF OF THE IRREDUCIBILITY OF CYCLOTOMIC
POLYNOMIALS. WHY PROVE IT AGAIN? WILL APPEAL TO A BROAD RANGE OF
READERS, INCLUDING HISTORIANS AND PHILOSOPHERS OF MATHEMATICS, STUDENTS,
AND PRACTICING MATHEMATICIANS. ADDITIONALLY, TEACHERS WILL FIND IT TO
BE A USEFUL SOURCE OF ALTERNATIVE METHODS OF PRESENTING MATERIAL TO
THEIR STUDENTS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Dawson, John W. Jr. 1944- |
| author_GND | (DE-588)137446365 |
| author_facet | Dawson, John W. Jr. 1944- |
| author_role | aut |
| author_sort | Dawson, John W. Jr. 1944- |
| author_variant | j w d jw jwd |
| building | Verbundindex |
| bvnumber | BV042730113 |
| classification_rvk | SK 110 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)915913829 (DE-599)BVBBV042730113 |
| dewey-full | 510.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.9 |
| dewey-search | 510.9 |
| dewey-sort | 3510.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-17368-9 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02661nmm a2200565zc 4500</leader><controlfield tag="001">BV042730113</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200930 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150803s2015 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783319173689</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-319-17368-9</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-319-17368-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)915913829</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042730113</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-861</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510.9</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 110</subfield><subfield code="0">(DE-625)143215:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dawson, John W.</subfield><subfield code="c">Jr.</subfield><subfield code="d">1944-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)137446365</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Why prove it again?</subfield><subfield code="b">alternative proofs in mathematical practice</subfield><subfield code="c">John W. Dawson, Jr.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cham [u.a.]</subfield><subfield code="b">Birkhäuser Springer</subfield><subfield code="c">2015</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XI, 204 S.)</subfield><subfield code="b">54 illus</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">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global analysis (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topology</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">History of Mathematical Sciences</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-3-319-17367-2</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-319-17368-9</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Springer Fremddatenuebernahme</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028161144&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Springer Fremddatenuebernahme</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028161144&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Abstract</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">UBY_PDA_SMA</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_2015</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028161144</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-3-319-17368-9</subfield><subfield code="l">BTU01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-3-319-17368-9</subfield><subfield code="l">FRO01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-3-319-17368-9</subfield><subfield code="l">TUM01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-3-319-17368-9</subfield><subfield code="l">UBM01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-3-319-17368-9</subfield><subfield code="l">UBT01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-3-319-17368-9</subfield><subfield code="l">UBW01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-3-319-17368-9</subfield><subfield code="l">UPA01</subfield><subfield code="p">ZDB-2-SMA</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV042730113 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:08:23Z |
| institution | BVB |
| isbn | 9783319173689 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028161144 |
| oclc_num | 915913829 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-703 DE-20 DE-739 DE-634 DE-861 DE-83 |
| owner_facet | DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-703 DE-20 DE-739 DE-634 DE-861 DE-83 |
| physical | 1 Online-Ressource (XI, 204 S.) 54 illus |
| psigel | ZDB-2-SMA UBY_PDA_SMA ZDB-2-SMA_2015 |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Birkhäuser Springer |
| record_format | marc |
| spelling | Dawson, John W. Jr. 1944- Verfasser (DE-588)137446365 aut Why prove it again? alternative proofs in mathematical practice John W. Dawson, Jr. Cham [u.a.] Birkhäuser Springer 2015 1 Online-Ressource (XI, 204 S.) 54 illus txt rdacontent c rdamedia cr rdacarrier Mathematics Algebra Global analysis (Mathematics) Geometry Topology History of Mathematical Sciences Analysis Mathematik Erscheint auch als Druckausgabe 978-3-319-17367-2 https://doi.org/10.1007/978-3-319-17368-9 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028161144&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028161144&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Dawson, John W. Jr. 1944- Why prove it again? alternative proofs in mathematical practice Mathematics Algebra Global analysis (Mathematics) Geometry Topology History of Mathematical Sciences Analysis Mathematik |
| title | Why prove it again? alternative proofs in mathematical practice |
| title_auth | Why prove it again? alternative proofs in mathematical practice |
| title_exact_search | Why prove it again? alternative proofs in mathematical practice |
| title_full | Why prove it again? alternative proofs in mathematical practice John W. Dawson, Jr. |
| title_fullStr | Why prove it again? alternative proofs in mathematical practice John W. Dawson, Jr. |
| title_full_unstemmed | Why prove it again? alternative proofs in mathematical practice John W. Dawson, Jr. |
| title_short | Why prove it again? |
| title_sort | why prove it again alternative proofs in mathematical practice |
| title_sub | alternative proofs in mathematical practice |
| topic | Mathematics Algebra Global analysis (Mathematics) Geometry Topology History of Mathematical Sciences Analysis Mathematik |
| topic_facet | Mathematics Algebra Global analysis (Mathematics) Geometry Topology History of Mathematical Sciences Analysis Mathematik |
| url | https://doi.org/10.1007/978-3-319-17368-9 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028161144&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028161144&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dawsonjohnw whyproveitagainalternativeproofsinmathematicalpractice |