A primer for mathematics competitions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2009
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| Series: | Oxford Mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 344 S. Ill., graph. Darst. |
| ISBN: | 9780199539871 0199539871 9780199539888 |
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Record in the Search Index
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| adam_text | A PRIMER FOR MATHEMATICS COMPETITIONS ALEXANDER ZAWAIRA AND GAVIN
HITCHCOCK OXFORD UNIVERSITY PRESS CONTENTS PREFACE IX 1 2 GEOMETRY 1.1
1.2 1.3 1.4 1.5 BRIEF REMINDER OF BASIC GEOMETRY 1.1.1 GEOMETRY OF
STRAIGHT LINES 1.1.2 GEOMETRY OF POLYGONS 1.1.3 GEOMETRY OF THE
FUNDAMENTAL POLYGON - THE TRIANGLE 1.1.4 GEOMETRY OF CIRCLES AND
CIRCULAR ARCS ADVANCED GEOMETRY OF THE TRIANGLE ADVANCED CIRCLE GEOMETRY
PROBLEMS SOLUTIONS ALGEBRAIC INEQUALITIES AND MATHEMATICAL INDUCTION 1 3
4 6 8 13 23 45 54 65 89 2.1 THE METHOD OF INDUCTION 90 2.2 ELEMENTARY
INEQUALITIES 99 2.3 HARDER INEQUALITIES 101 2.4 THE DISCRIMINANT OF A
QUADRATIC EXPRESSION 110 2.5 THE MODULUS FUNCTION 112 2.6 PROBLEMS 118
2.7 SOLUTIONS 120 DIOPHANTINE EQUATIONS 125 3.1 INTRODUCTION 125 3.2
DIVISION ALGORITHM AND GREATEST COMMON DIVISOR 126 3.3 EUCLIDEAN
ALGORITHM 127 3.4 LINEAR DIOPHANTINE EQUATIONS 128 3.4.1 FINDING A
PARTICULAR SOLUTION OF AX + BY = C 128 3.4.2 FINDING THE GENERAL
SOLUTION OF AX + BY = C 130 3.5 EUCLIDEAN REDUCTION, OR DIVIDE AND
CONQUER 131 3.6 SOME SIMPLE NONLINEAR DIOPHANTINE EQUATIONS 135
CONTENTS 4 5 6 3.7 3.8 PROBLEMS SOLUTIONS NUMBER THEORY 4.1 4.2 4.3 4.4
4.5 4.6 4.7 4.8 4.9 4.10 DIVISIBILITY, PRIMES AND FACTORIZATION TESTS
FOR DIVISIBILITY THE CONGRUENCE NOTATION: FINDING REMAINDERS RESIDUE
CLASSES TWO USEFUL THEOREMS THE NUMBER OF ZEROS AT THE END OF N! THE
UNIQUE FACTORIZATION THEOREM THE CHINESE REMAINDER THEOREM PROBLEMS
SOLUTIONS TRIGONOMETRY 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 ANGLES AND THEIR
MEASUREMENT TRIGONOMETRIC FUNCTIONS OF ACUTE ANGLES TRIGONOMETRIC
FUNCTIONS OF GENERAL ANGLES GRAPHS OF SINE AND COSINE FUNCTIONS
TRIGONOMETRIC IDENTITIES 5.5.1 THE PYTHAGOREAN SET OF IDENTITIES 5.5.2
ADDITION FORMULAS 5.5.3 DOUBLE ANGLE FORMULAS 5.5.4 PRODUCT FORMULAS
5.5.5 SUM FORMULAS TRIGONOMETRIC EQUATIONS PROBLEMS SOLUTIONS SEQUENCES
AND SERIES 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 GENERAL SEQUENCES THE
SUMMATION NOTATION ARITHMETIC PROGRESSIONS GEOMETRIC PROGRESSIONS SUM TO
INFINITY OF A GEOMETRIC PROGRESSION FORMULAS FOR SUMS OF SQUARES AND
CUBES PROBLEMS SOLUTIONS 138 139 145 146 147 148 152 154 159 161 162 166
169 181 182 186 189 194 197 197 198 200 201 202 202 207 208 213 214 214
216 218 220 222 226 228 CONTENTS VII BINOMIAL THEOREM 235 7.1 PASCAL S
TRIANGLE 236 7.2 A FORMULA FOR THE COEFFICIENTS 239 7.3 SOME PROPERTIES
OF PASCAL S TRIANGLE 242 7.4 PROBLEMS 244 7.5 SOLUTIONS 246 8
COMBINATORICS (COUNTING TECHNIQUES) 251 8.1 THE FUNDAMENTAL PRINCIPLE OF
ENUMERATION 252 8.2 FACTORIAL ARITHMETIC 254 8.3 PARTITIONS AND
PERMUTATIONS OF A SET 256 8.3.1 DEFINITION OF TERMS 256 8.3.2 THE
GENERAL PARTITIONING FORMULA 256 8.3.3 THE GENERAL PERMUTATION FORMULA
258 8.3.4 CIRCULAR PERMUTATIONS 259 8.4 COMBINATIONS 265 8.5
DERANGEMENTS 268 8.6 THE EXCLUSION-INCLUSION PRINCIPLE 272 8.7 THE
PIGEON-HOLE PRINCIPLE 280 8.8 PROBLEMS 283 8.9 SOLUTIONS 285 9
MISCELLANEOUS PROBLEMS AND SOLUTIONS 293 293 306 337 339 9.1 I 9.2
FURTHER INDEX PROBLEMS SOLUTIONS TRAINING RESOURCES
|
| any_adam_object | 1 |
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| author_role | aut aut |
| author_sort | Zawaira, Alexander 1978- |
| author_variant | a z az g h gh |
| building | Verbundindex |
| bvnumber | BV025568738 |
| classification_rvk | SM 940 |
| ctrlnum | (OCoLC)605156571 (DE-599)BVBBV025568738 |
| dewey-full | 510.76 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.76 |
| dewey-search | 510.76 |
| dewey-sort | 3510.76 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:36:39Z |
| institution | BVB |
| isbn | 9780199539871 0199539871 9780199539888 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020167329 |
| oclc_num | 605156571 |
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| physical | XVII, 344 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Oxford Univ. Press |
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| series2 | Oxford Mathematics |
| spelling | Zawaira, Alexander 1978- Verfasser (DE-588)137688881 aut A primer for mathematics competitions Alexander Zawaira and Gavin Hitchcock Oxford [u.a.] Oxford Univ. Press 2009 XVII, 344 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford Mathematics Mathematik (DE-588)4037944-9 gnd rswk-swf Schülerwettbewerb (DE-588)4053390-6 gnd rswk-swf (DE-588)4144384-6 Beispielsammlung gnd-content Mathematik (DE-588)4037944-9 s Schülerwettbewerb (DE-588)4053390-6 s DE-604 Hitchcock, Gavin 1946- Verfasser (DE-588)137688911 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020167329&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zawaira, Alexander 1978- Hitchcock, Gavin 1946- A primer for mathematics competitions Mathematik (DE-588)4037944-9 gnd Schülerwettbewerb (DE-588)4053390-6 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4053390-6 (DE-588)4144384-6 |
| title | A primer for mathematics competitions |
| title_auth | A primer for mathematics competitions |
| title_exact_search | A primer for mathematics competitions |
| title_full | A primer for mathematics competitions Alexander Zawaira and Gavin Hitchcock |
| title_fullStr | A primer for mathematics competitions Alexander Zawaira and Gavin Hitchcock |
| title_full_unstemmed | A primer for mathematics competitions Alexander Zawaira and Gavin Hitchcock |
| title_short | A primer for mathematics competitions |
| title_sort | a primer for mathematics competitions |
| topic | Mathematik (DE-588)4037944-9 gnd Schülerwettbewerb (DE-588)4053390-6 gnd |
| topic_facet | Mathematik Schülerwettbewerb Beispielsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020167329&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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