Quaternions and Cayley Numbers: Algebra and Applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | Mathematics and Its Applications
403 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In essence, this text is written as a challenge to others, to discover significant uses for Cayley number algebra in physics. I freely admit that though the reading of some sections would benefit from previous experience of certain topics in physics - particularly relativity and electromagnetism - generally the mathematics is not sophisticated. In fact, the mathematically sophisticated reader, may well find that in many places, the rather deliberate progress too slow for their liking. This text had its origin in a 90-minute lecture on complex numbers given by the author to prospective university students in 1994. In my attempt to develop a novel approach to the subject matter I looked at complex numbers from an entirely geometric perspective and, no doubt in line with innumerable other mathematicians, re-traced steps first taken by Hamilton and others in the early years of the nineteenth century. I even enquired into the possibility of using an alternative multiplication rule for complex numbers (in which argzlz2 = argzl- argz2) other than the one which is normally accepted (argzlz2 = argzl + argz2). Of course, my alternative was rejected because it didn't lead to a 'product' which had properties that we now accept as fundamental (i. e |
| Beschreibung: | 1 Online-Ressource (XI, 242 p) |
| ISBN: | 9789401157681 9789401064347 |
| DOI: | 10.1007/978-94-011-5768-1 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042423998 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1997 |||| o||u| ||||||eng d | ||
| 020 | |a 9789401157681 |c Online |9 978-94-011-5768-1 | ||
| 020 | |a 9789401064347 |c Print |9 978-94-010-6434-7 | ||
| 024 | 7 | |a 10.1007/978-94-011-5768-1 |2 doi | |
| 035 | |a (OCoLC)863704528 | ||
| 035 | |a (DE-599)BVBBV042423998 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 512.46 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Ward, J. P. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quaternions and Cayley Numbers |b Algebra and Applications |c by J. P. Ward |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 1997 | |
| 300 | |a 1 Online-Ressource (XI, 242 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematics and Its Applications |v 403 | |
| 500 | |a In essence, this text is written as a challenge to others, to discover significant uses for Cayley number algebra in physics. I freely admit that though the reading of some sections would benefit from previous experience of certain topics in physics - particularly relativity and electromagnetism - generally the mathematics is not sophisticated. In fact, the mathematically sophisticated reader, may well find that in many places, the rather deliberate progress too slow for their liking. This text had its origin in a 90-minute lecture on complex numbers given by the author to prospective university students in 1994. In my attempt to develop a novel approach to the subject matter I looked at complex numbers from an entirely geometric perspective and, no doubt in line with innumerable other mathematicians, re-traced steps first taken by Hamilton and others in the early years of the nineteenth century. I even enquired into the possibility of using an alternative multiplication rule for complex numbers (in which argzlz2 = argzl- argz2) other than the one which is normally accepted (argzlz2 = argzl + argz2). Of course, my alternative was rejected because it didn't lead to a 'product' which had properties that we now accept as fundamental (i. e | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Matrix theory | |
| 650 | 4 | |a Associative Rings and Algebras | |
| 650 | 4 | |a Non-associative Rings and Algebras | |
| 650 | 4 | |a Linear and Multilinear Algebras, Matrix Theory | |
| 650 | 4 | |a Theoretical, Mathematical and Computational Physics | |
| 650 | 4 | |a Applications of Mathematics | |
| 650 | 4 | |a Mathematik | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-011-5768-1 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027859415 | ||
Datensatz im Suchindex
| _version_ | 1804153100413435904 |
|---|---|
| any_adam_object | |
| author | Ward, J. P. |
| author_facet | Ward, J. P. |
| author_role | aut |
| author_sort | Ward, J. P. |
| author_variant | j p w jp jpw |
| building | Verbundindex |
| bvnumber | BV042423998 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863704528 (DE-599)BVBBV042423998 |
| dewey-full | 512.46 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.46 |
| dewey-search | 512.46 |
| dewey-sort | 3512.46 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-011-5768-1 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02799nmm a2200469zcb4500</leader><controlfield tag="001">BV042423998</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1997 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401157681</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-011-5768-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401064347</subfield><subfield code="c">Print</subfield><subfield code="9">978-94-010-6434-7</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-011-5768-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863704528</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423998</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-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.46</subfield><subfield code="2">23</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">Ward, J. P.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Quaternions and Cayley Numbers</subfield><subfield code="b">Algebra and Applications</subfield><subfield code="c">by J. P. Ward</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XI, 242 p)</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="490" ind1="0" ind2=" "><subfield code="a">Mathematics and Its Applications</subfield><subfield code="v">403</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">In essence, this text is written as a challenge to others, to discover significant uses for Cayley number algebra in physics. I freely admit that though the reading of some sections would benefit from previous experience of certain topics in physics - particularly relativity and electromagnetism - generally the mathematics is not sophisticated. In fact, the mathematically sophisticated reader, may well find that in many places, the rather deliberate progress too slow for their liking. This text had its origin in a 90-minute lecture on complex numbers given by the author to prospective university students in 1994. In my attempt to develop a novel approach to the subject matter I looked at complex numbers from an entirely geometric perspective and, no doubt in line with innumerable other mathematicians, re-traced steps first taken by Hamilton and others in the early years of the nineteenth century. I even enquired into the possibility of using an alternative multiplication rule for complex numbers (in which argzlz2 = argzl- argz2) other than the one which is normally accepted (argzlz2 = argzl + argz2). Of course, my alternative was rejected because it didn't lead to a 'product' which had properties that we now accept as fundamental (i. e</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">Matrix theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Associative Rings and Algebras</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Non-associative Rings and Algebras</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linear and Multilinear Algebras, Matrix Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Theoretical, Mathematical and Computational Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Applications of Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-011-5768-1</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859415</subfield></datafield></record></collection> |
| id | DE-604.BV042423998 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401157681 9789401064347 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859415 |
| oclc_num | 863704528 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XI, 242 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer Netherlands |
| record_format | marc |
| series2 | Mathematics and Its Applications |
| spelling | Ward, J. P. Verfasser aut Quaternions and Cayley Numbers Algebra and Applications by J. P. Ward Dordrecht Springer Netherlands 1997 1 Online-Ressource (XI, 242 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 403 In essence, this text is written as a challenge to others, to discover significant uses for Cayley number algebra in physics. I freely admit that though the reading of some sections would benefit from previous experience of certain topics in physics - particularly relativity and electromagnetism - generally the mathematics is not sophisticated. In fact, the mathematically sophisticated reader, may well find that in many places, the rather deliberate progress too slow for their liking. This text had its origin in a 90-minute lecture on complex numbers given by the author to prospective university students in 1994. In my attempt to develop a novel approach to the subject matter I looked at complex numbers from an entirely geometric perspective and, no doubt in line with innumerable other mathematicians, re-traced steps first taken by Hamilton and others in the early years of the nineteenth century. I even enquired into the possibility of using an alternative multiplication rule for complex numbers (in which argzlz2 = argzl- argz2) other than the one which is normally accepted (argzlz2 = argzl + argz2). Of course, my alternative was rejected because it didn't lead to a 'product' which had properties that we now accept as fundamental (i. e Mathematics Algebra Matrix theory Associative Rings and Algebras Non-associative Rings and Algebras Linear and Multilinear Algebras, Matrix Theory Theoretical, Mathematical and Computational Physics Applications of Mathematics Mathematik https://doi.org/10.1007/978-94-011-5768-1 Verlag Volltext |
| spellingShingle | Ward, J. P. Quaternions and Cayley Numbers Algebra and Applications Mathematics Algebra Matrix theory Associative Rings and Algebras Non-associative Rings and Algebras Linear and Multilinear Algebras, Matrix Theory Theoretical, Mathematical and Computational Physics Applications of Mathematics Mathematik |
| title | Quaternions and Cayley Numbers Algebra and Applications |
| title_auth | Quaternions and Cayley Numbers Algebra and Applications |
| title_exact_search | Quaternions and Cayley Numbers Algebra and Applications |
| title_full | Quaternions and Cayley Numbers Algebra and Applications by J. P. Ward |
| title_fullStr | Quaternions and Cayley Numbers Algebra and Applications by J. P. Ward |
| title_full_unstemmed | Quaternions and Cayley Numbers Algebra and Applications by J. P. Ward |
| title_short | Quaternions and Cayley Numbers |
| title_sort | quaternions and cayley numbers algebra and applications |
| title_sub | Algebra and Applications |
| topic | Mathematics Algebra Matrix theory Associative Rings and Algebras Non-associative Rings and Algebras Linear and Multilinear Algebras, Matrix Theory Theoretical, Mathematical and Computational Physics Applications of Mathematics Mathematik |
| topic_facet | Mathematics Algebra Matrix theory Associative Rings and Algebras Non-associative Rings and Algebras Linear and Multilinear Algebras, Matrix Theory Theoretical, Mathematical and Computational Physics Applications of Mathematics Mathematik |
| url | https://doi.org/10.1007/978-94-011-5768-1 |
| work_keys_str_mv | AT wardjp quaternionsandcayleynumbersalgebraandapplications |