Markov's theorem and 100 years of the uniqueness conjecture: a mathematical journey from irrational numbers to perfect matchings
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham [u.a.]
Springer
2013
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| Subjects: | |
| Online Access: | BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9783319008875 9783319008882 |
| DOI: | 10.1007/978-3-319-00888-2 |
Staff View
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Record in the Search Index
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| adam_text | MARKOV S THEOREM AND 100 YEARS OF THE UNIQUENESS CONJECTURE
/ AIGNER, MARTIN
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
APPROXIMATION OF IRRATIONALNUMBERS
MARKOV S THEOREM AND THE UNIQUENESS CONJECTURE
THE MARKOV TREE
THE COHN TREE
THE MODULAR GROUP SL(2,Z)
THE FREE GROUP F2
CHRISTOFFEL WORDS
STURMIAN WORDS
PROOF OF MARKOV S THEOREM
THE UNIQUENESS CONJECTURE.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
MARKOV S THEOREM AND 100 YEARS OF THE UNIQUENESS CONJECTURE
/ AIGNER, MARTIN
: 2013
ABSTRACT / INHALTSTEXT
THIS BOOK TAKES THE READER ON A MATHEMATICAL JOURNEY, FROM A
NUMBER-THEORETIC POINT OF VIEW, TO THE REALM OF MARKOV’S THEOREM AND
THE UNIQUENESS CONJECTURE, GRADUALLY UNFOLDING MANY BEAUTIFUL
CONNECTIONS UNTIL EVERYTHING FALLS INTO PLACE IN THE PROOF OF MARKOV’S
THEOREM.WHAT MAKES THE MARKOV THEME SO ATTRACTIVE IS THAT IT APPEARS
IN AN ASTOUNDING VARIETY OF DIFFERENT FIELDS, FROM NUMBER THEORY TO
COMBINATORICS, FROM CLASSICAL GROUPS AND GEOMETRY TO THE WORLD OF GRAPHS
AND WORDS. ON THE WAY, THERE ARE ALSO INTRODUCTORY FORAYS INTO SOME
FASCINATING TOPICS THAT DO NOT BELONG TO THE STANDARD CURRICULUM, SUCH
AS FAREY FRACTIONS, MODULAR AND FREE GROUPS, HYPERBOLIC PLANES, AND
ALGEBRAIC WORDS. THE BOOK CLOSES WITH A DISCUSSION OF THE CURRENT STATE
OF KNOWLEDGE ABOUT THE UNIQUENESS CONJECTURE, WHICH REMAINS AN OPEN
CHALLENGE TO THIS DAY. ALL THE MATERIAL SHOULD BE ACCESSIBLE TO
UPPER-LEVEL UNDERGRADUATES WITH SOME BACKGROUND IN NUMBER THEORY, AND
ANYTHING BEYOND THIS LEVEL IS FULLY EXPLAINED IN THE TEXT. THIS IS NOT A
MONOGRAPH IN THE USUAL SENSE CONCENTRATING ON A SPECIFIC TOPIC. INSTEAD,
IT NARRATES IN FIVE PARTS – NUMBERS, TREES, GROUPS, WORDS, FINALE –
THE STORY OF A DISCOVERY IN ONE FIELD AND ITS MANY MANIFESTATIONS IN
OTHERS, AS A TRIBUTE TO A GREAT MATHEMATICAL ACHIEVEMENT AND AS AN
INTELLECTUAL PLEASURE, CONTEMPLATING THE MARVELLOUS UNITY OF ALL
MATHEMATICS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Aigner, Martin 1942-2023 |
| author_GND | (DE-588)13205387X |
| author_facet | Aigner, Martin 1942-2023 |
| author_role | aut |
| author_sort | Aigner, Martin 1942-2023 |
| author_variant | m a ma |
| building | Verbundindex |
| bvnumber | BV041272296 |
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| 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 | 10.1007/978-3-319-00888-2 |
| era | Geschichte 1913-2013 gnd |
| era_facet | Geschichte 1913-2013 |
| format | Electronic eBook |
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| spelling | Aigner, Martin 1942-2023 Verfasser (DE-588)13205387X aut Markov's theorem and 100 years of the uniqueness conjecture a mathematical journey from irrational numbers to perfect matchings Martin Aigner Cham [u.a.] Springer 2013 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Markov, Andrej A. 1856-1922 (DE-588)118578014 gnd rswk-swf Geschichte 1913-2013 gnd rswk-swf Diophantische Gleichung (DE-588)4012386-8 gnd rswk-swf Markov, Andrej A. 1856-1922 (DE-588)118578014 p Diophantische Gleichung (DE-588)4012386-8 s Geschichte 1913-2013 z 1\p DE-604 https://doi.org/10.1007/978-3-319-00888-2 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026245879&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=026245879&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Aigner, Martin 1942-2023 Markov's theorem and 100 years of the uniqueness conjecture a mathematical journey from irrational numbers to perfect matchings Markov, Andrej A. 1856-1922 (DE-588)118578014 gnd Diophantische Gleichung (DE-588)4012386-8 gnd |
| subject_GND | (DE-588)118578014 (DE-588)4012386-8 |
| title | Markov's theorem and 100 years of the uniqueness conjecture a mathematical journey from irrational numbers to perfect matchings |
| title_auth | Markov's theorem and 100 years of the uniqueness conjecture a mathematical journey from irrational numbers to perfect matchings |
| title_exact_search | Markov's theorem and 100 years of the uniqueness conjecture a mathematical journey from irrational numbers to perfect matchings |
| title_full | Markov's theorem and 100 years of the uniqueness conjecture a mathematical journey from irrational numbers to perfect matchings Martin Aigner |
| title_fullStr | Markov's theorem and 100 years of the uniqueness conjecture a mathematical journey from irrational numbers to perfect matchings Martin Aigner |
| title_full_unstemmed | Markov's theorem and 100 years of the uniqueness conjecture a mathematical journey from irrational numbers to perfect matchings Martin Aigner |
| title_short | Markov's theorem and 100 years of the uniqueness conjecture |
| title_sort | markov s theorem and 100 years of the uniqueness conjecture a mathematical journey from irrational numbers to perfect matchings |
| title_sub | a mathematical journey from irrational numbers to perfect matchings |
| topic | Markov, Andrej A. 1856-1922 (DE-588)118578014 gnd Diophantische Gleichung (DE-588)4012386-8 gnd |
| topic_facet | Markov, Andrej A. 1856-1922 Diophantische Gleichung |
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