The IMO compendium: a collection of problems suggested for the International Mathematical Olympiads: 1959 - 2009
"The International Mathematical Olympiad (IMO) has within its almost 50-year-old history become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competi...
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2011
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Problem books in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Zusammenfassung: | "The International Mathematical Olympiad (IMO) has within its almost 50-year-old history become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for high school students to measure up with students from the rest of the world." "Until now it has been almost impossible to obtain a complete collection of the problems proposed at the IMO in book form. "The IMO Compendium" is the result of a two year long collaboration between four former IMO participants from Yugoslavia, now Serbia and Montenegro, to rescue these problems from old and scattered manuscripts, and produce the ultimate source of IMO practice problems. This book attempts to gather all the problems and solutions appearing on the IMO, as well as the so-called "short-lists", a total of 864 problems. In addition, the book contains 1036 problems from various "long-lists" over the years, for a grand total of 1900 problems." "In short, "The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems. It will be an invaluable resource, not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates math."--BOOK JACKET. |
| Beschreibung: | XIV, 809 S. Ill., graph. Darst. |
| ISBN: | 9781441998538 |
Internformat
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| 245 | 1 | 0 | |a The IMO compendium |b a collection of problems suggested for the International Mathematical Olympiads: 1959 - 2009 |c Dušan Djukić ... |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2011 | |
| 300 | |a XIV, 809 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Problem books in mathematics | |
| 520 | 1 | |a "The International Mathematical Olympiad (IMO) has within its almost 50-year-old history become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for high school students to measure up with students from the rest of the world." "Until now it has been almost impossible to obtain a complete collection of the problems proposed at the IMO in book form. "The IMO Compendium" is the result of a two year long collaboration between four former IMO participants from Yugoslavia, now Serbia and Montenegro, to rescue these problems from old and scattered manuscripts, and produce the ultimate source of IMO practice problems. This book attempts to gather all the problems and solutions appearing on the IMO, as well as the so-called "short-lists", a total of 864 problems. In addition, the book contains 1036 problems from various "long-lists" over the years, for a grand total of 1900 problems." "In short, "The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems. It will be an invaluable resource, not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates math."--BOOK JACKET. | |
| 610 | 2 | 4 | |a International Mathematical Olympiad |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics |v Problems, exercises, etc | |
| 650 | 4 | |a Mathematics |x Competitions | |
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| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411872&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024411872 | ||
Datensatz im Suchindex
| _version_ | 1804148384477478912 |
|---|---|
| adam_text | Contents
1
Introduction
................................................... 1
1.1
The International Mathematical Olympiad
...................... 1
1.2
The
IMO
Compendium
...................................... 2
2
Basic Concepts and Facts
....................................... 5
2.1
Algebra
................................................... 5
2.1.1
Polynomials
........................................ 5
2.1.2
Recurrence Relations
................................ 6
2.1.3
Inequalities
......................................... 7
2.1.4
Groups and Fields
.................................... 9
2.2
Analysis
.................................................. 10
2.3
Geometry
................................................. 12
2.3.1
Triangle Geometry
................................... 12
2.3.2
Vectors in Geometry
.................................. 13
2.3.3
Barycenters
......................................... 14
2.3.4
Quadrilaterals
....................................... 14
2.3.5
Circle Geometry
..................................... 15
2.3.6
Inversion
........................................... 16
2.3.7
Geometric Inequalities
................................ 17
2.3.8
Trigonometry
....................................... 17
2.3.9
Formulas in Geometry
................................ 18
2.4
Number Theory
............................................ 19
2.4.1
Divisibility and Congruences
.......................... 19
2.4.2
Exponential Congruences
............................. 20
2.4.3
Quadratic Diophantine Equations
....................... 21
2.4.4
Farey Sequences
..................................... 22
2.5
Combinatorics
............................................. 22
2.5.1
Counting of Objects
.................................. 22
2.5.2
Graph Theory
....................................... 23
Contents
Problems...................................................... 27
3.1
IMO
1959................................................. 27
3.1.1
Contest
Problems.................................... 27
3.2
IMO
1960................................................. 29
3.2.1
Contest
Problems.................................... 29
3.3
IMO
1961.................................................
ЗО
3.3.1
Contest
Problems.................................... 30
3.4
IMO
1962................................................. 31
3.4.1
Contest Problems
.................................... 31
3.5
IMO
1963................................................. 32
3.5.1
Contest Problems
.................................... 32
3.6
IMO
1964................................................. 33
3.6.1
Contest Problems
.................................... 33
3.7
IMO
1965................................................. 34
3.7.1
Contest Problems
.................................... 34
3.8
IMO
1966................................................. 35
3.8.1
Contest Problems
.................................... 35
3.8.2
Some Longlisted Problems
1959-1966.................. 35
3.9
IMO
1967................................................. 41
3.9.1
Contest Problems
.................................... 41
3.9.2
Longlisted Problems
................................. 41
3.10
IMO
1968................................................. 49
3.10.1
Contest Problems
.................................... 49
3.10.2
Shortlisted Problems
................................. 49
3.11
IMO
1969................................................. 53
3.11.1
Contest Problems
.................................... 53
3.11.2
Longlisted Problems
................................. 53
3.12
IMO
1970................................................. 61
3.12.1
Contest Problems
.................................... 61
3.12.2
Longlisted Problems
................................. 62
3.12.3
Shortlisted Problems
................................. 68
3.13
IMO
1971................................................. 70
3.13.1
Contest Problems
.................................... 70
3.13.2
Longlisted Problems
................................. 71
3.13.3
Shortlisted Problems
................................. 76
3.14
IMO
1972................................................. 79
3.14.1
Contest Problems
.................................... 79
3.14.2
Longlisted Problems
................................. 79
3.14.3
Shortlisted Problems
................................. 83
3.15
IMO
1973................................................. 86
3.15.1
Contest Problems
.................................... 86
3.15.2
Shortlisted Problems
................................. 87
3.16
IMO
1974................................................. 89
3.16.1
Contest Problems
.................................... 89
3.16.2
Longlisted Problems
................................. 90
Contents
XI
3.16.3
Shortlisted
Problems................................. 95
3.17
IMO
1975................................................. 97
3.17.1
Contest Problems
.................................... 97
3.17.2
Shortlisted Problems
................................. 97
3.18
IMO
1976................................................. 100
3.18.1
Contest Problems
.................................... 100
3.18.2
Longlisted Problems
................................. 100
3.18.3
Shortlisted Problems
................................. 105
3.19
IMO
1977................................................. 107
3.19.1
Contest Problems
.................................... 107
3.19.2
Longlisted Problems
................................. 107
3.19.3
Shortlisted Problems
................................. 113
3.20
IMO
1978................................................. 116
3.20.1
Contest Problems
.................................... 116
3.20.2
Longlisted Problems
................................. 116
3.20.3
Shortlisted Problems
................................. 121
3.21
IMO
1979................................................. 124
3.21.1
Contest Problems
.................................... 124
3.21.2
Longlisted Problems
................................. 125
3.21.3
Shortlisted Problems
................................. 132
3.22
IMO
1981................................................. 135
3.22.1
Contest Problems
.................................... 135
3.22.2
Shortlisted Problems
................................. 135
3.23
IMO
1982................................................. 138
3.23.1
Contest Problems
.................................... 138
3.23.2
Longlisted Problems
................................. 139
3.23.3
Shortlisted Problems
................................. 144
3.24
IMO
1983................................................. 147
3.24.1
Contest Problems
.................................... 147
3.24.2
Longlisted Problems
................................. 147
3.24.3
Shortlisted Problems
................................. 154
3.25
IMO
1984................................................. 158
3.25.1
Contest Problems
.................................... 158
3.25.2
Longlisted Problems
................................. 158
3.25.3
Shortlisted Problems
................................. 165
3.26
IMO
1985................................................. 168
3.26.1
Contest Problems
.................................... 168
3.26.2
Longlisted Problems
................................. 168
3.26.3
Shortlisted Problems
................................. 177
3.27
IMO
1986................................................. 181
3.27.1
Contest Problems
.................................... 181
3.27.2
Longlisted Problems
................................. 182
3.27.3
Shortlisted Problems
................................. 188
3.28
IMO
1987................................................. 192
3.28.1
Contest Problems
.................................... 192
ХП
Contents
3.28.2 Longlisted Problems ................................. 192
3.28.3
Shortlisted
Problems................................. 200
3.29
IMO
1988................................................. 203
3.29.1
Contest
Problems.................................... 203
3.29.2 Longlisted Problems ................................. 204
3.29.3
Shortlisted
Problems................................. 212
3.30
IMO
1989................................................. 217
3.30.1
Contest
Problems.................................... 217
3.30.2 Longlisted Problems ................................. 218
3.30.3
Shortlisted
Problems................................. 229
3.31
IMO
1990................................................. 234
3.31.1
Contest
Problems.................................... 234
3.31.2 Longlisted Problems ................................. 235
3.31.3
Shortlisted
Problems................................. 245
3.32
IMO
1991................................................. 249
3.32.1
Contest
Problems.................................... 249
3.32.2
Shortlisted
Problems................................. 249
3.33
IMO
1992................................................. 253
3.33.1
Contest
Problems.................................... 253
3.33.2 Longlisted Problems ................................. 253
3.33.3
Shortlisted
Problems................................. 262
3.34
IMO
1993................................................. 266
3.34.1
Contest
Problems.................................... 266
3.34.2
Shortlisted
Problems ................................. 267
3.35
IMO
1994................................................. 271
3.35.1
Contest
Problems.................................... 271
3.35.2
Shortlisted
Problems................................. 271
3.36
IMO
1995................................................. 275
3.36.1
Contest Problems
.................................... 275
3.36.2
Shortlisted Problems
................................. 275
3.37
EMO
19%................................................. 280
3.37.1
Contest Problems
.................................... 280
3.37.2
Shortlisted Problems
.................................281
3.38
EMO
1997................................................. 286
3.38.1
Contest Problems
.................................... 286
3.38.2
Shortlisted Problems
................................. 287
3.39
EMO
1998................................................. 291
3.39.1
Contest Problems
.................................... 291
3.39.2
Shortlisted Problems
................................. 291
3.40
EMO
1999................................................. 295
3.40.1
Contest Problems
.................................... 295
3.40.2
Shortlisted Problems
................................. 295
3.41
IMO
2000................................................. 300
3.41.1
Contest Problems
.................................... 300
3.41.2
Shortlisted Problems
................................. 300
Contents XIII
3.42
IMO
2001................................................. 304
3.42.1
Contest
Problems.................................... 304
3.42.2
Shortlisted Problems
................................. 304
3.43
IMO
2002................................................. 308
3.43.1
Contest Problems
.................................... 308
3.43.2
Shortlisted Problems
................................. 308
3.44
IMO
2003................................................. 312
3.44.1
Contest Problems
.................................... 312
3.44.2
Shortlisted Problems
................................. 312
3.45
IMO
2004................................................. 317
3.45.1
Contest Problems
.................................... 317
3.45.2
Shortlisted Problems
................................. 318
3.46
IMO
2005................................................. 322
3.46.1
Contest Problems
.................................... 322
3.46.2
Shortlisted Problems
................................. 322
3.47
IMO
2006................................................. 326
3.47.1
Contest Problems
.................................... 326
3.47.2
Shortlisted Problems
................................. 326
3.48
IMO
2007................................................. 331
3.48.1
Contest Problems
.................................... 331
3.48.2
Shortlisted Problems
................................. 332
3.49
IMO
2008................................................. 336
3.49.1
Contest Problems
.................................... 336
3.49.2
Shortlisted Problems
................................. 337
3.50
IMO
2009................................................. 341
3.50.1
Contest Problems
.................................... 341
3.50.2
Shortlisted Problems
................................. 341
Solutions
...................................................... 347
4.1
Contest Problems
1959...................................... 347
4.2
Contest Problems
1960...................................... 349
4.3
Contest Problems
1961...................................... 351
4.4
Contest Problems
1962...................................... 353
4.5
Contest Problems
1963...................................... 354
4.6
Contest Problems
1964...................................... 355
4.7
Contest Problems
1965...................................... 357
4.8
Contest Problems
1966...................................... 359
4.9
Longlisted Problems
1967................................... 361
4.10
Shortlisted Problems
1968................................... 374
4.11
Contest Problems
1969...................................... 380
4.12
Shortlisted Problems
1970................................... 383
4.13
Shortlisted Problems
1971................................... 389
4.14
Shortlisted Problems
1972................................... 396
4.15
Shortlisted Problems
1973................................... 401
4.16
Shortlisted Problems
1974................................... 407
XIV Contents
4.17
Shortlisted Problems
1975................................... 413
4.18
Shortlisted Problems
1976................................... 418
4.19
Longlisted Problems
1977................................... 422
4.20
Shortlisted Problems
1978................................... 437
4.21
Shortlisted Problems
1979................................... 445
4.22
Shortlisted Problems
1981................................... 453
4.23
Shortlisted Problems
1982................................... 461
4.24
Shortlisted Problems
1983................................... 467
4.25
Shortlisted Problems
1984................................... 476
4.26
Shortlisted Problems
1985................................... 483
4.27
Shortlisted Problems
1986................................... 491
4.28
Shortlisted Problems
1987................................... 498
4.29
Shortlisted Problems
1988................................... 508
4.30
Shortlisted Problems
1989................................... 523
4.31
Shortlisted Problems
1990................................... 537
4.32
Shortlisted Problems
1991................................... 550
4.33
Shortlisted Problems
1992................................... 563
4.34
Shortlisted Problems
1993................................... 573
4.35
Shortlisted Problems
1994................................... 585
4.36
Shortlisted Problems
1995................................... 593
4.37
Shortlisted Problems
1996................................... 606
4.38
Shortlisted Problems
1997................................... 622
4.39
Shortlisted Problems
1998................................... 636
4.40
Shortlisted Problems
1999................................... 650
4.41
Shortlisted Problems
2000................................... 664
4.42
Shortlisted Problems
2001................................... 677
4.43
Shortlisted Problems
2002................................... 691
4.44
Shortlisted Problems
2003................................... 702
4.45
Shortlisted Problems
2004................................... 715
4.46
Shortlisted Problems
2005................................... 730
4.47
Shortlisted Problems
2006................................... 742
4.48
Shortlisted Problems
2007................................... 754
4.49
Shortlisted Problems
2008................................... 765
4.50
Shortlisted Problems
2009................................... 777
A Notation and Abbreviations
..................................... 791
A.I Notation
.................................................. 791
A.2 Abbreviations
.............................................. 792
В
Codes of the Countries of Origin
................................. 795
С
Authors of Problems
............................................ 797
References
......................................................... 805
Problem
Books in Mathematics
Dušan Djukić
·
Vladimir
Janković
·
Ivan
Matic
·
Nikola
Petrović
The
IMO
Compendium
A Collection of Problems Suggested for The International
Mathematical Olympiads:
1959-2009,
Second Edition
The
IMO
Compendium is the ultimate collection of challenging high school level mathemat¬
ics problems. It is an invaluable resource, not only for students preparing for competitions,
but for anyone who loves and appreciates math. Training for mathematical olympiads is
enjoyed by talented students throughout the world. Olympiads have become one of the
primary ways to recognize and develop talented youth with a potential to excel in areas
that require abstract thinking. Although the problems appearing at
IMO do
not involve
advanced mathematics, they must be difficult and their solutions must arise from creative
and clever insights rather than tedious calculations.
In preparation for the distinguished International Mathematical Olympiad
(IMO)
competi¬
tion, each participating country selects the top six high school students every year through a
series of national olympiads. These students are invited to participate in the
IMO,
usually held
in July. The
IMO
is a two-day contest where each day competitors are given three problems
which they work on independently,
lhe
IMO
host country appoints a special committee
to which each country submits up to
sii
problems. From this composite
longlist
of prob¬
lems, a shortUst* of
25-30
problems is created. The jury, consisting of one professor from
each country,
maket
the final selection from the shortlist a few days before the
IMO
begins.
ТЬе ШО
has sparked a bunt of creativity among enthusiasts to create new and interest-
ing mathematics problem*. It can be safely said that
tibe
IMO
and shortlisted problems are
dmagfv^
these problems with their solutions. In
addition,
tibe
book contains
»П
the «vailable
longlist
problems, for a total of more than aooo problems.
From me reviews of the first edition:
IhelnterrutåonalMatnematk^
Olympiad,
m
tion
for talented high school mathematics students.
...
This book collects statements and
solutions of all of the problems ever set in the
IMO,
together with many problems proposed
for the contest
...
serves as a vast repository of problems at the Olympiad level, useful both
to students
...
and to acuity looking for hard elementary problems. No library will want to
be without a copy, nor will anyone involved in mathematics competitions
...
—
(Fernando Q.
Gouvéa,
MathDL, March,
200«)
|
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| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| genre | (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV039560182 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:06:17Z |
| institution | BVB |
| isbn | 9781441998538 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024411872 |
| oclc_num | 751019942 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-20 DE-11 DE-83 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-20 DE-11 DE-83 DE-188 |
| physical | XIV, 809 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series2 | Problem books in mathematics |
| spelling | The IMO compendium a collection of problems suggested for the International Mathematical Olympiads: 1959 - 2009 Dušan Djukić ... 2. ed. New York, NY [u.a.] Springer 2011 XIV, 809 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Problem books in mathematics "The International Mathematical Olympiad (IMO) has within its almost 50-year-old history become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for high school students to measure up with students from the rest of the world." "Until now it has been almost impossible to obtain a complete collection of the problems proposed at the IMO in book form. "The IMO Compendium" is the result of a two year long collaboration between four former IMO participants from Yugoslavia, now Serbia and Montenegro, to rescue these problems from old and scattered manuscripts, and produce the ultimate source of IMO practice problems. This book attempts to gather all the problems and solutions appearing on the IMO, as well as the so-called "short-lists", a total of 864 problems. In addition, the book contains 1036 problems from various "long-lists" over the years, for a grand total of 1900 problems." "In short, "The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems. It will be an invaluable resource, not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates math."--BOOK JACKET. International Mathematical Olympiad Mathematik Mathematics Problems, exercises, etc Mathematics Competitions Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Mathematik (DE-588)4037944-9 s Mathematikunterricht (DE-588)4037949-8 s DE-604 Djukić, Dušan 1924- Sonstige (DE-588)131697935 oth Erscheint auch als Online-Ausgabe 978-1-4419-9854-5 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411872&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411872&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | The IMO compendium a collection of problems suggested for the International Mathematical Olympiads: 1959 - 2009 International Mathematical Olympiad Mathematik Mathematics Problems, exercises, etc Mathematics Competitions Mathematikunterricht (DE-588)4037949-8 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4037949-8 (DE-588)4037944-9 (DE-588)4143389-0 |
| title | The IMO compendium a collection of problems suggested for the International Mathematical Olympiads: 1959 - 2009 |
| title_auth | The IMO compendium a collection of problems suggested for the International Mathematical Olympiads: 1959 - 2009 |
| title_exact_search | The IMO compendium a collection of problems suggested for the International Mathematical Olympiads: 1959 - 2009 |
| title_full | The IMO compendium a collection of problems suggested for the International Mathematical Olympiads: 1959 - 2009 Dušan Djukić ... |
| title_fullStr | The IMO compendium a collection of problems suggested for the International Mathematical Olympiads: 1959 - 2009 Dušan Djukić ... |
| title_full_unstemmed | The IMO compendium a collection of problems suggested for the International Mathematical Olympiads: 1959 - 2009 Dušan Djukić ... |
| title_short | The IMO compendium |
| title_sort | the imo compendium a collection of problems suggested for the international mathematical olympiads 1959 2009 |
| title_sub | a collection of problems suggested for the International Mathematical Olympiads: 1959 - 2009 |
| topic | International Mathematical Olympiad Mathematik Mathematics Problems, exercises, etc Mathematics Competitions Mathematikunterricht (DE-588)4037949-8 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | International Mathematical Olympiad Mathematik Mathematics Problems, exercises, etc Mathematics Competitions Mathematikunterricht Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411872&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024411872&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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