Introduction to number theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific Europe Ltd.
[2018]
|
| Schriftenreihe: | Essential textbooks in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis: Seite 243-244 |
| Beschreibung: | xiv, 247 Seiten Diagramme |
| ISBN: | 9781786344892 9781786344717 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV044874597 | ||
| 003 | DE-604 | ||
| 005 | 20181203 | ||
| 007 | t | ||
| 008 | 180320s2018 |||| |||| 00||| eng d | ||
| 020 | |a 9781786344892 |c pbk |9 978-1-78634-489-2 | ||
| 020 | |a 9781786344717 |c hc |9 978-1-78634-471-7 | ||
| 035 | |a (OCoLC)1031424628 | ||
| 035 | |a (DE-599)OBVAC14538296 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 |a DE-91G |a DE-20 | ||
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a MAT 100f |2 stub | ||
| 100 | 1 | |a Hill, Richard Michael |e Verfasser |0 (DE-588)1155099125 |4 aut | |
| 245 | 1 | 0 | |a Introduction to number theory |c Richard Michael Hill |
| 264 | 1 | |a New Jersey |b World Scientific Europe Ltd. |c [2018] | |
| 300 | |a xiv, 247 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Essential textbooks in mathematics | |
| 500 | |a Literaturverzeichnis: Seite 243-244 | ||
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030268957&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-030268957 | ||
Datensatz im Suchindex
| _version_ | 1804178408099282944 |
|---|---|
| adam_text | Contents
About the Author v
Acknowledgments vii
Introduction xi
1 Euclid’s Algorithm 1
1.1 Some Examples of Rings................................ 1
1.2 Euclid’s Algorithm...................................... 5
1.3 Invertible Elements Modulo n............................ 9
1.4 Solving Linear Congruences............................. 13
1.5 The Chinese Remainder Theorem.......................... 16
1.6 Prime Numbers.......................................... 19
Hints for Some Exercises.................................... 26
2 Polynomial Rings 27
2.1 Long Division of Polynomials........................... 28
2.2 Highest Common Factors................................. 34
2.3 Uniqueness of Factorization ........................... 38
2.4 Irreducible Polynomials................................ 40
2.5 Unique Factorization Domains........................... 46
Hints for Some Exercises.................................... 50
3 Congruences Modulo Prime Numbers 53
3.1 Fermat’s Little Theorem................................ 55
3.2 The Euler Totient Function ............................ 57
3.3 Cyclotomic Polynomials and Primitive Roots............. 61
3.4 Public Key Cryptography................................ 68
3.5 Quadratic Reciprocity ................................. 73
3.6 Congruences in an Arbitrary Ring....................... 84
ix
X
Introduction to Number Theory
3.7 Proof of the Second Nebensatz........................... 91
3.8 Gauss Sums and the Proof of Quadratic Reciprocity .... 93
Hints for Some Exercises..................................... 99
4 p-Adic Methods in Number Theory 101
4.1 Hensel’s Lemma......................................... 101
4.2 Quadratic Congruences.................................. 112
4.3 p-Adic Convergence of Series........................... 116
4.4 p-Adic Logarithms and Exponential
Maps................................................... 124
4.5 Teichmiiller Lifts .................................... 130
4.6 The Ring of p-Adic Integers............................ 139
Hints for Some Exercises.................................... 148
5 Diophantine Equations and Quadratic Rings 149
5.1 Diophantine Equations and Unique
Factorization.......................................... 149
5.2 Quadratic Rings........................................ 152
5.3 Norm-Euclidean Quadratic Rings........................ 159
5.4 Decomposing Primes in Quadratic Rings.................. 167
5.5 Continued Fractions................................... 176
5.6 Pell’s Equation ....................................... 185
5.7 Real Quadratic Rings and Diophantine Equations......... 193
Hints for Some Exercises.................................... 199
Solution to Exercises 201
Bibliography 243
Index 245
|
| any_adam_object | 1 |
| author | Hill, Richard Michael |
| author_GND | (DE-588)1155099125 |
| author_facet | Hill, Richard Michael |
| author_role | aut |
| author_sort | Hill, Richard Michael |
| author_variant | r m h rm rmh |
| building | Verbundindex |
| bvnumber | BV044874597 |
| classification_rvk | SK 180 |
| classification_tum | MAT 100f |
| ctrlnum | (OCoLC)1031424628 (DE-599)OBVAC14538296 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01487nam a2200373 c 4500</leader><controlfield tag="001">BV044874597</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20181203 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">180320s2018 |||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781786344892</subfield><subfield code="c">pbk</subfield><subfield code="9">978-1-78634-489-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781786344717</subfield><subfield code="c">hc</subfield><subfield code="9">978-1-78634-471-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1031424628</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)OBVAC14538296</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-739</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 100f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hill, Richard Michael</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1155099125</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to number theory</subfield><subfield code="c">Richard Michael Hill</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New Jersey</subfield><subfield code="b">World Scientific Europe Ltd.</subfield><subfield code="c">[2018]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xiv, 247 Seiten</subfield><subfield code="b">Diagramme</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">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Essential textbooks in mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverzeichnis: Seite 243-244</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="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</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="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau - ADAM Catalogue Enrichment</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=030268957&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-030268957</subfield></datafield></record></collection> |
| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV044874597 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:03:29Z |
| institution | BVB |
| isbn | 9781786344892 9781786344717 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030268957 |
| oclc_num | 1031424628 |
| open_access_boolean | |
| owner | DE-739 DE-91G DE-BY-TUM DE-20 |
| owner_facet | DE-739 DE-91G DE-BY-TUM DE-20 |
| physical | xiv, 247 Seiten Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | World Scientific Europe Ltd. |
| record_format | marc |
| series2 | Essential textbooks in mathematics |
| spelling | Hill, Richard Michael Verfasser (DE-588)1155099125 aut Introduction to number theory Richard Michael Hill New Jersey World Scientific Europe Ltd. [2018] xiv, 247 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Essential textbooks in mathematics Literaturverzeichnis: Seite 243-244 Zahlentheorie (DE-588)4067277-3 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Zahlentheorie (DE-588)4067277-3 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030268957&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hill, Richard Michael Introduction to number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4151278-9 |
| title | Introduction to number theory |
| title_auth | Introduction to number theory |
| title_exact_search | Introduction to number theory |
| title_full | Introduction to number theory Richard Michael Hill |
| title_fullStr | Introduction to number theory Richard Michael Hill |
| title_full_unstemmed | Introduction to number theory Richard Michael Hill |
| title_short | Introduction to number theory |
| title_sort | introduction to number theory |
| topic | Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Zahlentheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030268957&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hillrichardmichael introductiontonumbertheory |