Groups /:
This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always mo...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Oxford :
Newnes,
1994.
|
| Schriftenreihe: | Modular mathematics series.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic. |
| Beschreibung: | "Transferred to digital printing 2004"--Title page verso. |
| Beschreibung: | 1 online resource (xi, 207 pages :) : illustrations. |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9780080571652 0080571654 034061045X 9780340610459 1283587394 9781283587396 9786613899842 6613899844 |
Internformat
MARC
| LEADER | 00000cam a2200000Ma 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn811406072 | ||
| 003 | OCoLC | ||
| 005 | 20240705115654.0 | ||
| 006 | m o d | ||
| 007 | cr cn||||||||| | ||
| 008 | 120912s1994 enka ob 001 0 eng d | ||
| 040 | |a E7B |b eng |e pn |c E7B |d N$T |d OCLCF |d OCLCQ |d AGLDB |d OCLCQ |d VTS |d STF |d M8D |d VLY |d OCLCO |d OCLCQ |d OCLCO |d OCLCL | ||
| 019 | |a 1162228686 |a 1241909064 |a 1300481161 | ||
| 020 | |a 9780080571652 |q (electronic bk.) | ||
| 020 | |a 0080571654 |q (electronic bk.) | ||
| 020 | |a 034061045X |q (electronic bk.) | ||
| 020 | |a 9780340610459 |q (electronic bk.) | ||
| 020 | |a 1283587394 | ||
| 020 | |a 9781283587396 | ||
| 020 | |a 9786613899842 | ||
| 020 | |a 6613899844 | ||
| 035 | |a (OCoLC)811406072 |z (OCoLC)1162228686 |z (OCoLC)1241909064 |z (OCoLC)1300481161 | ||
| 050 | 4 | |a QA174.2 |b .J67 1994eb | |
| 072 | 7 | |a MAT |x 014000 |2 bisacsh | |
| 082 | 7 | |a 512.2 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Jordan, C. R. |q (Camilla R.) |1 https://id.oclc.org/worldcat/entity/E39PCjvTkYjJyXjm8pMkwgvq43 |0 http://id.loc.gov/authorities/names/nr95015140 | |
| 245 | 1 | 0 | |a Groups / |c C.R. Jordan & D.A. Jordan. |
| 260 | |a Oxford : |b Newnes, |c 1994. | ||
| 300 | |a 1 online resource (xi, 207 pages :) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Modular mathematics series | |
| 500 | |a "Transferred to digital printing 2004"--Title page verso. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Online resource; title from PDF information screen (Ebsco, viewed December 11, 2012). | |
| 505 | 0 | |a Front Cover; Groups; Copyright Page; Series Preface; Preface; Table of Contents; Chapter 1. Squares and Circles; 1.1 Symmetries of a square; 1.2 Symmetries of a circle; 1.3 Further exercises on Chapter 1; Chapter 2. Permutations; 2.1 The symmetric group S4; 2.2 Functions; 2.3 Permutations; 2.4 Basic properties of cycles; 2.5 Cycle decomposition; 2.6 Transpositions; 2.7 The 15-puzzle; 2.8 Further exercises on Chapter 2; Chapter 3. Linear Transformations and Matrices; 3.1 Matrix multiplication; 3.2 Linear transformations; 3.3 Orthogonal matrices; 3.4 Further exercises on Chapter 3 | |
| 505 | 8 | |a Chapter 4. The Group Axioms4.1 Number systems; 4.2 Binary operations; 4.3 Definition of a group; 4.4 Examples of groups; 4.5 Consequences of the axioms; 4.6 Direct products; 4.7 Further exercises on Chapter 4; Chapter 5. Subgroups; 5.1 Subgroups; 5.2 Examples of subgroups; 5.3 Groups of symmetries; 5.4 Further exercises on Chapter 5; Chapter 6. Cyclic Groups; 6.1 Cyclic groups; 6.2 Cyclic subgroups; 6.3 Order of elements; 6.4 Orders of products; 6.5 Orders of powers; 6.6 Subgroups of cyclic groups; 6.7 Direct products of cyclic groups; 6.8 Further exercises on Chapter 6 | |
| 505 | 8 | |a Chapter 7. Group Actions7.1 Groups acting on sets; 7.2 Orbits; 7.3 Stabilizers; 7.4 Permutations arising from group actions; 7.5 The alternating group; 7.6 Further exercises on Chapter 7; Chapter 8. Equivalence Relations and Modular Arithmetic; 8.1 Partitions; 8.2 Relations; 8.3 Equivalence classes; 8.4 Equivalence relations from group actions; 8.5 Modular arithmetic; 8.6 Further exercises on Chapter 8; Chapter 9. Homomorphisms and Isomorphisms; 9.1 Comparing D3 and S3; 9.2 Properties of homomorphisms; 9.3 Homomorphisms arising from group actions; 9.4 Cayley's theorem; 9.5 Cyclic groups | |
| 505 | 8 | |a 9.6 Further exercises on Chapter 9Chapter 10. Cosets and Lagrange's Theorem; 10.1 Left cosets; 10.2 Left cosets as equivalence classes; 10.3 Lagrange's theorem; 10.4 Consequences of Lagrange's theorem; 10.5 Applications to number theory; 10.6 Right cosets; 10.7 Further exercises on Chapter 10; Chapter 11. The Orbit-Stabilizer Theorem; 11.1 The orbit-stabilizer theorem; 11.2 Fixed subsets; 11.3 Counting orbits; 11.4 Further exercises on Chapter 11; Chapter 12. Colouring Problems; 12.1 Colouring problems; 12.2 Groups of symmetries in three dimensions; 12.3 Three-dimensional colouring problems | |
| 505 | 8 | |a 12.4 Further exercises on Chapter 12Chapter 13. Conjugates, Centralizers and Centres; 13.1 Conjugates; 13.2 Conjugacy classes; 13.3 Conjugacy classes in Sn; 13.4 Centralizers; 13.5 Centres; 13.6 Conjugates and centralizers; 13.7 Further exercises on Chapter 13; Chapter 14. Towards Classification; 14.1 An action of S3 on three-dimensional space; 14.2 Cauchy's theorem; 14.3 Direct products; 14.4 Further exercises on Chapter 14; Chapter 15. Kernels and Normal Subgroups; 15.1 Kernels of homomorphisms; 15.2 Kernels of actions; 15.3 Conjugates of a subgroup; 15.4 Normal subgroups | |
| 520 | |a This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Group theory. |0 http://id.loc.gov/authorities/subjects/sh85057512 | |
| 650 | 6 | |a Théorie des groupes. | |
| 650 | 7 | |a MATHEMATICS |x Group Theory. |2 bisacsh | |
| 650 | 7 | |a Group theory |2 fast | |
| 700 | 1 | |a Jordan, D. A. |q (David A.) |1 https://id.oclc.org/worldcat/entity/E39PCjD3xF9dDdrwv8dKxxMMKb |0 http://id.loc.gov/authorities/names/nr95015142 | |
| 758 | |i has work: |a Groups (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFxhxdBHbXrWFXRR4vhVhb |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | |z 0-340-61045-X | ||
| 830 | 0 | |a Modular mathematics series. |0 http://id.loc.gov/authorities/names/no96016632 | |
| 856 | 1 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=480358 |3 Volltext | |
| 856 | 1 | |l CBO01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=480358 |3 Volltext | |
| 938 | |a ebrary |b EBRY |n ebr10597045 | ||
| 938 | |a EBSCOhost |b EBSC |n 480358 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn811406072 |
|---|---|
| _version_ | 1813903587721347073 |
| adam_text | |
| any_adam_object | |
| author | Jordan, C. R. (Camilla R.) |
| author2 | Jordan, D. A. (David A.) |
| author2_role | |
| author2_variant | d a j da daj |
| author_GND | http://id.loc.gov/authorities/names/nr95015140 http://id.loc.gov/authorities/names/nr95015142 |
| author_facet | Jordan, C. R. (Camilla R.) Jordan, D. A. (David A.) |
| author_role | |
| author_sort | Jordan, C. R. |
| author_variant | c r j cr crj |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA174 |
| callnumber-raw | QA174.2 .J67 1994eb |
| callnumber-search | QA174.2 .J67 1994eb |
| callnumber-sort | QA 3174.2 J67 41994EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Front Cover; Groups; Copyright Page; Series Preface; Preface; Table of Contents; Chapter 1. Squares and Circles; 1.1 Symmetries of a square; 1.2 Symmetries of a circle; 1.3 Further exercises on Chapter 1; Chapter 2. Permutations; 2.1 The symmetric group S4; 2.2 Functions; 2.3 Permutations; 2.4 Basic properties of cycles; 2.5 Cycle decomposition; 2.6 Transpositions; 2.7 The 15-puzzle; 2.8 Further exercises on Chapter 2; Chapter 3. Linear Transformations and Matrices; 3.1 Matrix multiplication; 3.2 Linear transformations; 3.3 Orthogonal matrices; 3.4 Further exercises on Chapter 3 Chapter 4. The Group Axioms4.1 Number systems; 4.2 Binary operations; 4.3 Definition of a group; 4.4 Examples of groups; 4.5 Consequences of the axioms; 4.6 Direct products; 4.7 Further exercises on Chapter 4; Chapter 5. Subgroups; 5.1 Subgroups; 5.2 Examples of subgroups; 5.3 Groups of symmetries; 5.4 Further exercises on Chapter 5; Chapter 6. Cyclic Groups; 6.1 Cyclic groups; 6.2 Cyclic subgroups; 6.3 Order of elements; 6.4 Orders of products; 6.5 Orders of powers; 6.6 Subgroups of cyclic groups; 6.7 Direct products of cyclic groups; 6.8 Further exercises on Chapter 6 Chapter 7. Group Actions7.1 Groups acting on sets; 7.2 Orbits; 7.3 Stabilizers; 7.4 Permutations arising from group actions; 7.5 The alternating group; 7.6 Further exercises on Chapter 7; Chapter 8. Equivalence Relations and Modular Arithmetic; 8.1 Partitions; 8.2 Relations; 8.3 Equivalence classes; 8.4 Equivalence relations from group actions; 8.5 Modular arithmetic; 8.6 Further exercises on Chapter 8; Chapter 9. Homomorphisms and Isomorphisms; 9.1 Comparing D3 and S3; 9.2 Properties of homomorphisms; 9.3 Homomorphisms arising from group actions; 9.4 Cayley's theorem; 9.5 Cyclic groups 9.6 Further exercises on Chapter 9Chapter 10. Cosets and Lagrange's Theorem; 10.1 Left cosets; 10.2 Left cosets as equivalence classes; 10.3 Lagrange's theorem; 10.4 Consequences of Lagrange's theorem; 10.5 Applications to number theory; 10.6 Right cosets; 10.7 Further exercises on Chapter 10; Chapter 11. The Orbit-Stabilizer Theorem; 11.1 The orbit-stabilizer theorem; 11.2 Fixed subsets; 11.3 Counting orbits; 11.4 Further exercises on Chapter 11; Chapter 12. Colouring Problems; 12.1 Colouring problems; 12.2 Groups of symmetries in three dimensions; 12.3 Three-dimensional colouring problems 12.4 Further exercises on Chapter 12Chapter 13. Conjugates, Centralizers and Centres; 13.1 Conjugates; 13.2 Conjugacy classes; 13.3 Conjugacy classes in Sn; 13.4 Centralizers; 13.5 Centres; 13.6 Conjugates and centralizers; 13.7 Further exercises on Chapter 13; Chapter 14. Towards Classification; 14.1 An action of S3 on three-dimensional space; 14.2 Cauchy's theorem; 14.3 Direct products; 14.4 Further exercises on Chapter 14; Chapter 15. Kernels and Normal Subgroups; 15.1 Kernels of homomorphisms; 15.2 Kernels of actions; 15.3 Conjugates of a subgroup; 15.4 Normal subgroups |
| ctrlnum | (OCoLC)811406072 |
| dewey-full | 512.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06057cam a2200637Ma 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn811406072</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20240705115654.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cn|||||||||</controlfield><controlfield tag="008">120912s1994 enka ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">E7B</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">E7B</subfield><subfield code="d">N$T</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">STF</subfield><subfield code="d">M8D</subfield><subfield code="d">VLY</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">1162228686</subfield><subfield code="a">1241909064</subfield><subfield code="a">1300481161</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780080571652</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0080571654</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">034061045X</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780340610459</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1283587394</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781283587396</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9786613899842</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">6613899844</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)811406072</subfield><subfield code="z">(OCoLC)1162228686</subfield><subfield code="z">(OCoLC)1241909064</subfield><subfield code="z">(OCoLC)1300481161</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA174.2</subfield><subfield code="b">.J67 1994eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">014000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">512.2</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Jordan, C. R.</subfield><subfield code="q">(Camilla R.)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjvTkYjJyXjm8pMkwgvq43</subfield><subfield code="0">http://id.loc.gov/authorities/names/nr95015140</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Groups /</subfield><subfield code="c">C.R. Jordan & D.A. Jordan.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Oxford :</subfield><subfield code="b">Newnes,</subfield><subfield code="c">1994.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xi, 207 pages :) :</subfield><subfield code="b">illustrations.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Modular mathematics series</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">"Transferred to digital printing 2004"--Title page verso.</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Online resource; title from PDF information screen (Ebsco, viewed December 11, 2012).</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Front Cover; Groups; Copyright Page; Series Preface; Preface; Table of Contents; Chapter 1. Squares and Circles; 1.1 Symmetries of a square; 1.2 Symmetries of a circle; 1.3 Further exercises on Chapter 1; Chapter 2. Permutations; 2.1 The symmetric group S4; 2.2 Functions; 2.3 Permutations; 2.4 Basic properties of cycles; 2.5 Cycle decomposition; 2.6 Transpositions; 2.7 The 15-puzzle; 2.8 Further exercises on Chapter 2; Chapter 3. Linear Transformations and Matrices; 3.1 Matrix multiplication; 3.2 Linear transformations; 3.3 Orthogonal matrices; 3.4 Further exercises on Chapter 3</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Chapter 4. The Group Axioms4.1 Number systems; 4.2 Binary operations; 4.3 Definition of a group; 4.4 Examples of groups; 4.5 Consequences of the axioms; 4.6 Direct products; 4.7 Further exercises on Chapter 4; Chapter 5. Subgroups; 5.1 Subgroups; 5.2 Examples of subgroups; 5.3 Groups of symmetries; 5.4 Further exercises on Chapter 5; Chapter 6. Cyclic Groups; 6.1 Cyclic groups; 6.2 Cyclic subgroups; 6.3 Order of elements; 6.4 Orders of products; 6.5 Orders of powers; 6.6 Subgroups of cyclic groups; 6.7 Direct products of cyclic groups; 6.8 Further exercises on Chapter 6</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Chapter 7. Group Actions7.1 Groups acting on sets; 7.2 Orbits; 7.3 Stabilizers; 7.4 Permutations arising from group actions; 7.5 The alternating group; 7.6 Further exercises on Chapter 7; Chapter 8. Equivalence Relations and Modular Arithmetic; 8.1 Partitions; 8.2 Relations; 8.3 Equivalence classes; 8.4 Equivalence relations from group actions; 8.5 Modular arithmetic; 8.6 Further exercises on Chapter 8; Chapter 9. Homomorphisms and Isomorphisms; 9.1 Comparing D3 and S3; 9.2 Properties of homomorphisms; 9.3 Homomorphisms arising from group actions; 9.4 Cayley's theorem; 9.5 Cyclic groups</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">9.6 Further exercises on Chapter 9Chapter 10. Cosets and Lagrange's Theorem; 10.1 Left cosets; 10.2 Left cosets as equivalence classes; 10.3 Lagrange's theorem; 10.4 Consequences of Lagrange's theorem; 10.5 Applications to number theory; 10.6 Right cosets; 10.7 Further exercises on Chapter 10; Chapter 11. The Orbit-Stabilizer Theorem; 11.1 The orbit-stabilizer theorem; 11.2 Fixed subsets; 11.3 Counting orbits; 11.4 Further exercises on Chapter 11; Chapter 12. Colouring Problems; 12.1 Colouring problems; 12.2 Groups of symmetries in three dimensions; 12.3 Three-dimensional colouring problems</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">12.4 Further exercises on Chapter 12Chapter 13. Conjugates, Centralizers and Centres; 13.1 Conjugates; 13.2 Conjugacy classes; 13.3 Conjugacy classes in Sn; 13.4 Centralizers; 13.5 Centres; 13.6 Conjugates and centralizers; 13.7 Further exercises on Chapter 13; Chapter 14. Towards Classification; 14.1 An action of S3 on three-dimensional space; 14.2 Cauchy's theorem; 14.3 Direct products; 14.4 Further exercises on Chapter 14; Chapter 15. Kernels and Normal Subgroups; 15.1 Kernels of homomorphisms; 15.2 Kernels of actions; 15.3 Conjugates of a subgroup; 15.4 Normal subgroups</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">English.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Group theory.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85057512</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Théorie des groupes.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Group Theory.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Group theory</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Jordan, D. A.</subfield><subfield code="q">(David A.)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjD3xF9dDdrwv8dKxxMMKb</subfield><subfield code="0">http://id.loc.gov/authorities/names/nr95015142</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Groups (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCFxhxdBHbXrWFXRR4vhVhb</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1=" " ind2=" "><subfield code="z">0-340-61045-X</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Modular mathematics series.</subfield><subfield code="0">http://id.loc.gov/authorities/names/no96016632</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=480358</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">CBO01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=480358</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10597045</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">480358</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn811406072 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:21:03Z |
| institution | BVB |
| isbn | 9780080571652 0080571654 034061045X 9780340610459 1283587394 9781283587396 9786613899842 6613899844 |
| language | English |
| oclc_num | 811406072 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xi, 207 pages :) : illustrations. |
| psigel | ZDB-4-EBA |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Newnes, |
| record_format | marc |
| series | Modular mathematics series. |
| series2 | Modular mathematics series |
| spelling | Jordan, C. R. (Camilla R.) https://id.oclc.org/worldcat/entity/E39PCjvTkYjJyXjm8pMkwgvq43 http://id.loc.gov/authorities/names/nr95015140 Groups / C.R. Jordan & D.A. Jordan. Oxford : Newnes, 1994. 1 online resource (xi, 207 pages :) : illustrations. text txt rdacontent computer c rdamedia online resource cr rdacarrier Modular mathematics series "Transferred to digital printing 2004"--Title page verso. Includes bibliographical references and index. Online resource; title from PDF information screen (Ebsco, viewed December 11, 2012). Front Cover; Groups; Copyright Page; Series Preface; Preface; Table of Contents; Chapter 1. Squares and Circles; 1.1 Symmetries of a square; 1.2 Symmetries of a circle; 1.3 Further exercises on Chapter 1; Chapter 2. Permutations; 2.1 The symmetric group S4; 2.2 Functions; 2.3 Permutations; 2.4 Basic properties of cycles; 2.5 Cycle decomposition; 2.6 Transpositions; 2.7 The 15-puzzle; 2.8 Further exercises on Chapter 2; Chapter 3. Linear Transformations and Matrices; 3.1 Matrix multiplication; 3.2 Linear transformations; 3.3 Orthogonal matrices; 3.4 Further exercises on Chapter 3 Chapter 4. The Group Axioms4.1 Number systems; 4.2 Binary operations; 4.3 Definition of a group; 4.4 Examples of groups; 4.5 Consequences of the axioms; 4.6 Direct products; 4.7 Further exercises on Chapter 4; Chapter 5. Subgroups; 5.1 Subgroups; 5.2 Examples of subgroups; 5.3 Groups of symmetries; 5.4 Further exercises on Chapter 5; Chapter 6. Cyclic Groups; 6.1 Cyclic groups; 6.2 Cyclic subgroups; 6.3 Order of elements; 6.4 Orders of products; 6.5 Orders of powers; 6.6 Subgroups of cyclic groups; 6.7 Direct products of cyclic groups; 6.8 Further exercises on Chapter 6 Chapter 7. Group Actions7.1 Groups acting on sets; 7.2 Orbits; 7.3 Stabilizers; 7.4 Permutations arising from group actions; 7.5 The alternating group; 7.6 Further exercises on Chapter 7; Chapter 8. Equivalence Relations and Modular Arithmetic; 8.1 Partitions; 8.2 Relations; 8.3 Equivalence classes; 8.4 Equivalence relations from group actions; 8.5 Modular arithmetic; 8.6 Further exercises on Chapter 8; Chapter 9. Homomorphisms and Isomorphisms; 9.1 Comparing D3 and S3; 9.2 Properties of homomorphisms; 9.3 Homomorphisms arising from group actions; 9.4 Cayley's theorem; 9.5 Cyclic groups 9.6 Further exercises on Chapter 9Chapter 10. Cosets and Lagrange's Theorem; 10.1 Left cosets; 10.2 Left cosets as equivalence classes; 10.3 Lagrange's theorem; 10.4 Consequences of Lagrange's theorem; 10.5 Applications to number theory; 10.6 Right cosets; 10.7 Further exercises on Chapter 10; Chapter 11. The Orbit-Stabilizer Theorem; 11.1 The orbit-stabilizer theorem; 11.2 Fixed subsets; 11.3 Counting orbits; 11.4 Further exercises on Chapter 11; Chapter 12. Colouring Problems; 12.1 Colouring problems; 12.2 Groups of symmetries in three dimensions; 12.3 Three-dimensional colouring problems 12.4 Further exercises on Chapter 12Chapter 13. Conjugates, Centralizers and Centres; 13.1 Conjugates; 13.2 Conjugacy classes; 13.3 Conjugacy classes in Sn; 13.4 Centralizers; 13.5 Centres; 13.6 Conjugates and centralizers; 13.7 Further exercises on Chapter 13; Chapter 14. Towards Classification; 14.1 An action of S3 on three-dimensional space; 14.2 Cauchy's theorem; 14.3 Direct products; 14.4 Further exercises on Chapter 14; Chapter 15. Kernels and Normal Subgroups; 15.1 Kernels of homomorphisms; 15.2 Kernels of actions; 15.3 Conjugates of a subgroup; 15.4 Normal subgroups This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic. English. Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Théorie des groupes. MATHEMATICS Group Theory. bisacsh Group theory fast Jordan, D. A. (David A.) https://id.oclc.org/worldcat/entity/E39PCjD3xF9dDdrwv8dKxxMMKb http://id.loc.gov/authorities/names/nr95015142 has work: Groups (Text) https://id.oclc.org/worldcat/entity/E39PCFxhxdBHbXrWFXRR4vhVhb https://id.oclc.org/worldcat/ontology/hasWork 0-340-61045-X Modular mathematics series. http://id.loc.gov/authorities/names/no96016632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=480358 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=480358 Volltext |
| spellingShingle | Jordan, C. R. (Camilla R.) Groups / Modular mathematics series. Front Cover; Groups; Copyright Page; Series Preface; Preface; Table of Contents; Chapter 1. Squares and Circles; 1.1 Symmetries of a square; 1.2 Symmetries of a circle; 1.3 Further exercises on Chapter 1; Chapter 2. Permutations; 2.1 The symmetric group S4; 2.2 Functions; 2.3 Permutations; 2.4 Basic properties of cycles; 2.5 Cycle decomposition; 2.6 Transpositions; 2.7 The 15-puzzle; 2.8 Further exercises on Chapter 2; Chapter 3. Linear Transformations and Matrices; 3.1 Matrix multiplication; 3.2 Linear transformations; 3.3 Orthogonal matrices; 3.4 Further exercises on Chapter 3 Chapter 4. The Group Axioms4.1 Number systems; 4.2 Binary operations; 4.3 Definition of a group; 4.4 Examples of groups; 4.5 Consequences of the axioms; 4.6 Direct products; 4.7 Further exercises on Chapter 4; Chapter 5. Subgroups; 5.1 Subgroups; 5.2 Examples of subgroups; 5.3 Groups of symmetries; 5.4 Further exercises on Chapter 5; Chapter 6. Cyclic Groups; 6.1 Cyclic groups; 6.2 Cyclic subgroups; 6.3 Order of elements; 6.4 Orders of products; 6.5 Orders of powers; 6.6 Subgroups of cyclic groups; 6.7 Direct products of cyclic groups; 6.8 Further exercises on Chapter 6 Chapter 7. Group Actions7.1 Groups acting on sets; 7.2 Orbits; 7.3 Stabilizers; 7.4 Permutations arising from group actions; 7.5 The alternating group; 7.6 Further exercises on Chapter 7; Chapter 8. Equivalence Relations and Modular Arithmetic; 8.1 Partitions; 8.2 Relations; 8.3 Equivalence classes; 8.4 Equivalence relations from group actions; 8.5 Modular arithmetic; 8.6 Further exercises on Chapter 8; Chapter 9. Homomorphisms and Isomorphisms; 9.1 Comparing D3 and S3; 9.2 Properties of homomorphisms; 9.3 Homomorphisms arising from group actions; 9.4 Cayley's theorem; 9.5 Cyclic groups 9.6 Further exercises on Chapter 9Chapter 10. Cosets and Lagrange's Theorem; 10.1 Left cosets; 10.2 Left cosets as equivalence classes; 10.3 Lagrange's theorem; 10.4 Consequences of Lagrange's theorem; 10.5 Applications to number theory; 10.6 Right cosets; 10.7 Further exercises on Chapter 10; Chapter 11. The Orbit-Stabilizer Theorem; 11.1 The orbit-stabilizer theorem; 11.2 Fixed subsets; 11.3 Counting orbits; 11.4 Further exercises on Chapter 11; Chapter 12. Colouring Problems; 12.1 Colouring problems; 12.2 Groups of symmetries in three dimensions; 12.3 Three-dimensional colouring problems 12.4 Further exercises on Chapter 12Chapter 13. Conjugates, Centralizers and Centres; 13.1 Conjugates; 13.2 Conjugacy classes; 13.3 Conjugacy classes in Sn; 13.4 Centralizers; 13.5 Centres; 13.6 Conjugates and centralizers; 13.7 Further exercises on Chapter 13; Chapter 14. Towards Classification; 14.1 An action of S3 on three-dimensional space; 14.2 Cauchy's theorem; 14.3 Direct products; 14.4 Further exercises on Chapter 14; Chapter 15. Kernels and Normal Subgroups; 15.1 Kernels of homomorphisms; 15.2 Kernels of actions; 15.3 Conjugates of a subgroup; 15.4 Normal subgroups Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Théorie des groupes. MATHEMATICS Group Theory. bisacsh Group theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85057512 |
| title | Groups / |
| title_auth | Groups / |
| title_exact_search | Groups / |
| title_full | Groups / C.R. Jordan & D.A. Jordan. |
| title_fullStr | Groups / C.R. Jordan & D.A. Jordan. |
| title_full_unstemmed | Groups / C.R. Jordan & D.A. Jordan. |
| title_short | Groups / |
| title_sort | groups |
| topic | Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Théorie des groupes. MATHEMATICS Group Theory. bisacsh Group theory fast |
| topic_facet | Group theory. Théorie des groupes. MATHEMATICS Group Theory. Group theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=480358 |
| work_keys_str_mv | AT jordancr groups AT jordanda groups |