The queen of mathematics: an introduction to number theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer Acad. Publ.
1995
|
| Schriftenreihe: | Kluwer texts in the mathematical sciences
8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 389 S. |
| ISBN: | 0792332873 |
Internformat
MARC
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| 100 | 1 | |a Anglin, William S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The queen of mathematics |b an introduction to number theory |c W. S. Anglin |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1995 | |
| 300 | |a X, 389 S. | ||
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Datensatz im Suchindex
| _version_ | 1804124829479075840 |
|---|---|
| adam_text | Contents
Preface ix
1 Propaedeutics 1
1.1 Mathematical Induction 1
1.2 Bernoulli Numbers * 7
1.3 Primes 11
1.4 Perfect Numbers 14
1.5 Greatest Integer Function 19
1.6 Pythagorean Triangles 21
1.7 Diophantine Equations 25
1.8 Four Square Theorem * 32
1.9 Fermat s Last Theorem 36
1.10 Congruent Numbers * 43
1.11 Mobius Function * 49
2 Simple Continued Fractions 55
2.1 Convergents and Convergence 56
2.2 Uniqueness of SCF Expansions 66
2.3 SCF Expansions of Rationals 69
2.4 Farey Series * 74
2.5 Ax + By = C 78
2.6 SCF Approximations 80
2.7 SCF Expansions of Quadratic Surds 83
2.8 Periodic SCF Expansions 87
2.9 Pell Equation 92
2.10 Prefaced Palindromes * 96
v
vi CONTENTS
3 Congruence 103
3.1 Basic Properties 103
3.2 Euler s ^Function 106
3.3 Primitive Roots 110
3.4 Decimal Expansions * 113
3.5 x2 = R (mod C) 115
3.6 Palindromic SCF s * 123
3.7 Sums of Two Squares * 124
3.8 Quadratic Residues 130
3.9 Theorema Aureum 133
3.10 Jacobi Symbol 136
3.11 More on x2 = R (mod C) * 139
3.12 Ax2 + By = C * 146
4 x2 Ry2 = C 151
4.1 SCF Solution 151
4.2 Recursive Formulas for Solutions 157
4.3 Ax2 + Bxy + Cy2 + Dx + Ey = F * 160
4.4 Square Pyramid Problem 163
4.5 Lucas s Test for Perfect Numbers * 168
4.6 Simultaneous Fermat Equations * 173
5 Classical Construction Problems 187
5.1 Euclidean Constructions 187
5.2 Fields and Vector Spaces 191
5.3 Limits of Ruler and Compass Construction 200
5.4 Gauss s Constructions 206
5.5 Fermat Primes 212
5.6 The Transcendence of is * 213
6 The Polygonal Number Theorem 227
6.1 Gaussian Forms 228
6.2 Ternary Quadratic Form Matrices 235
6.3 Omega Kernel or Square Forms 250
6.4 Ambiguous or Self Inverse Forms 253
6.5 Sums of Triangular Numbers 264
6.6 Cauchy s Proof 270
CONTENTS vii
7 Analytic Number Theory 277
7.1 Characters 278
7.2 Dirichlet Series 282
7.3 Mangoldt Function 286
7.4 L(1,X)^O 288
7.5 Dirichlet s Theorem on Primes in AP 295
7.6 How Many Pythagorean Triangles? 296
7.7 Prime Preliminaries 302
7.8 Prime Number Theorem Proof 316
7.9 Partitions 326
7.10 Euler s Power Series 327
7.11 A Fractal Path of Ford Circles . . . 331
7.12 Mobius Transformations 335
7.13 Dedekind Sums 336
7.14 Eta Function 340
7.15 Bessel Functions Avoided 349
7.16 Rademacher s Proof 354
7.17 Numerical Calculations 359
Bibliography 363
A Appendix: Answers to Selected Exercises 365
Index 387
The stars indicate sections which can be skipped on a first reading.
Nothing in an unstarred section depends on anything in a starred sec¬
tion (with the exception of some material in Chapter 7). Since Chapter
6 does not depend on Chapter 5, a first reading might consist of the
unstarred sections in Chapters 1 to 4, followed by Chapter 6.
|
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| indexdate | 2024-07-09T17:51:53Z |
| institution | BVB |
| isbn | 0792332873 |
| language | English |
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| physical | X, 389 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| series | Kluwer texts in the mathematical sciences |
| series2 | Kluwer texts in the mathematical sciences |
| spelling | Anglin, William S. Verfasser aut The queen of mathematics an introduction to number theory W. S. Anglin Dordrecht u.a. Kluwer Acad. Publ. 1995 X, 389 S. txt rdacontent n rdamedia nc rdacarrier Kluwer texts in the mathematical sciences 8 Getaltheorie gtt Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Kluwer texts in the mathematical sciences 8 (DE-604)BV005450041 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006926817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Anglin, William S. The queen of mathematics an introduction to number theory Kluwer texts in the mathematical sciences Getaltheorie gtt Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | The queen of mathematics an introduction to number theory |
| title_auth | The queen of mathematics an introduction to number theory |
| title_exact_search | The queen of mathematics an introduction to number theory |
| title_full | The queen of mathematics an introduction to number theory W. S. Anglin |
| title_fullStr | The queen of mathematics an introduction to number theory W. S. Anglin |
| title_full_unstemmed | The queen of mathematics an introduction to number theory W. S. Anglin |
| title_short | The queen of mathematics |
| title_sort | the queen of mathematics an introduction to number theory |
| title_sub | an introduction to number theory |
| topic | Getaltheorie gtt Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Getaltheorie Number theory Zahlentheorie |
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