Summing It Up: From One Plus One to Modern Number Theory
We use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numer...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2016]
|
| Schlagworte: | |
| Online-Zugang: | DE-1046 DE-859 DE-860 DE-739 DE-1043 DE-858 Volltext |
| Zusammenfassung: | We use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series—long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms—the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem.Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Mar. 30, 2016) |
| Beschreibung: | 1 online resource |
| ISBN: | 9781400880539 |
| DOI: | 10.1515/9781400880539 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV045928716 | ||
| 003 | DE-604 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 190612s2016 xx o|||| 00||| eng d | ||
| 020 | |a 9781400880539 |9 978-1-4008-8053-9 | ||
| 024 | 7 | |a 10.1515/9781400880539 |2 doi | |
| 035 | |a (ZDB-23-DGG)9781400880539 | ||
| 035 | |a (OCoLC)1165551100 | ||
| 035 | |a (DE-599)BVBBV045928716 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 |a DE-739 |a DE-860 |a DE-859 |a DE-1043 |a DE-858 | ||
| 082 | 0 | |a 512.7 |2 23 | |
| 100 | 1 | |a Ash, Avner. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Summing It Up |b From One Plus One to Modern Number Theory |c Robert Gross, Avner Ash |
| 264 | 1 | |a Princeton, N.J. |b Princeton University Press |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a 1 online resource | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed Mar. 30, 2016) | ||
| 520 | |a We use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series—long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms—the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem.Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers | ||
| 546 | |a In English | ||
| 650 | 4 | |a Mathematics |v Popular works | |
| 650 | 4 | |a Number theory | |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Gross, Robert |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 9780691170190 |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9781400880539 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 912 | |a ZDB-23-DGG | ||
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-031311152 | |
| 966 | e | |u https://doi.org/10.1515/9781400880539?locatt=mode:legacy |l DE-1046 |p ZDB-23-DGG |q FAW_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400880539?locatt=mode:legacy |l DE-859 |p ZDB-23-DGG |q FKE_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400880539?locatt=mode:legacy |l DE-860 |p ZDB-23-DGG |q FLA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400880539?locatt=mode:legacy |l DE-739 |p ZDB-23-DGG |q UPA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400880539?locatt=mode:legacy |l DE-1043 |p ZDB-23-DGG |q FAB_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400880539?locatt=mode:legacy |l DE-858 |p ZDB-23-DGG |q FCO_PDA_DGG |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1824507514012565504 |
|---|---|
| adam_text | |
| any_adam_object | |
| author | Ash, Avner |
| author_facet | Ash, Avner |
| author_role | aut |
| author_sort | Ash, Avner |
| author_variant | a a aa |
| building | Verbundindex |
| bvnumber | BV045928716 |
| collection | ZDB-23-DGG |
| ctrlnum | (ZDB-23-DGG)9781400880539 (OCoLC)1165551100 (DE-599)BVBBV045928716 |
| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400880539 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000zc 4500</leader><controlfield tag="001">BV045928716</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">190612s2016 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400880539</subfield><subfield code="9">978-1-4008-8053-9</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400880539</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-23-DGG)9781400880539</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1165551100</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV045928716</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-1046</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-860</subfield><subfield code="a">DE-859</subfield><subfield code="a">DE-1043</subfield><subfield code="a">DE-858</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.7</subfield><subfield code="2">23</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ash, Avner.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Summing It Up</subfield><subfield code="b">From One Plus One to Modern Number Theory</subfield><subfield code="c">Robert Gross, Avner Ash</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, N.J.</subfield><subfield code="b">Princeton University Press</subfield><subfield code="c">[2016]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2016</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource</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="500" ind1=" " ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed Mar. 30, 2016)</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">We use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series—long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms—the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem.Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield><subfield code="v">Popular works</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gross, Robert</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">9780691170190</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400880539</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-031311152</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400880539?locatt=mode:legacy</subfield><subfield code="l">DE-1046</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FAW_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400880539?locatt=mode:legacy</subfield><subfield code="l">DE-859</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FKE_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400880539?locatt=mode:legacy</subfield><subfield code="l">DE-860</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FLA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400880539?locatt=mode:legacy</subfield><subfield code="l">DE-739</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">UPA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400880539?locatt=mode:legacy</subfield><subfield code="l">DE-1043</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FAB_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400880539?locatt=mode:legacy</subfield><subfield code="l">DE-858</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FCO_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV045928716 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-19T17:25:56Z |
| institution | BVB |
| isbn | 9781400880539 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031311152 |
| oclc_num | 1165551100 |
| open_access_boolean | |
| owner | DE-1046 DE-739 DE-860 DE-859 DE-1043 DE-858 |
| owner_facet | DE-1046 DE-739 DE-860 DE-859 DE-1043 DE-858 |
| physical | 1 online resource |
| psigel | ZDB-23-DGG ZDB-23-DGG FAW_PDA_DGG ZDB-23-DGG FKE_PDA_DGG ZDB-23-DGG FLA_PDA_DGG ZDB-23-DGG UPA_PDA_DGG ZDB-23-DGG FAB_PDA_DGG ZDB-23-DGG FCO_PDA_DGG |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Princeton University Press |
| record_format | marc |
| spelling | Ash, Avner. Verfasser aut Summing It Up From One Plus One to Modern Number Theory Robert Gross, Avner Ash Princeton, N.J. Princeton University Press [2016] © 2016 1 online resource txt rdacontent c rdamedia cr rdacarrier Description based on online resource; title from PDF title page (publisher's Web site, viewed Mar. 30, 2016) We use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series—long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms—the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem.Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers In English Mathematics Popular works Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s 1\p DE-604 Gross, Robert Sonstige oth Erscheint auch als Druck-Ausgabe 9780691170190 https://doi.org/10.1515/9781400880539 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ash, Avner Summing It Up From One Plus One to Modern Number Theory Mathematics Popular works Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | Summing It Up From One Plus One to Modern Number Theory |
| title_auth | Summing It Up From One Plus One to Modern Number Theory |
| title_exact_search | Summing It Up From One Plus One to Modern Number Theory |
| title_full | Summing It Up From One Plus One to Modern Number Theory Robert Gross, Avner Ash |
| title_fullStr | Summing It Up From One Plus One to Modern Number Theory Robert Gross, Avner Ash |
| title_full_unstemmed | Summing It Up From One Plus One to Modern Number Theory Robert Gross, Avner Ash |
| title_short | Summing It Up |
| title_sort | summing it up from one plus one to modern number theory |
| title_sub | From One Plus One to Modern Number Theory |
| topic | Mathematics Popular works Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Mathematics Popular works Number theory Zahlentheorie |
| url | https://doi.org/10.1515/9781400880539 |
| work_keys_str_mv | AT ashavner summingitupfromoneplusonetomodernnumbertheory AT grossrobert summingitupfromoneplusonetomodernnumbertheory |