The IMO Compendium de Dusan Djukic

The IMO Compendium: Problem Books in Mathematics

Autor Dusan Djukic, Vladimir Janković, Ivan Matic, Nikola Petrovic

en Limba Engleză Hardback – 16 mai 2011

Până la apariția primei ediții a acestui volum, comunitatea matematică se confrunta cu o lacună majoră: absența unei colecții complete și sistematizate a problemelor propuse la Olimpiada Internațională de Matematică (IMO), acestea fiind adesea dispersate în manuscrise greu accesibile sau publicații locale. The IMO Compendium rezolvă această problemă, oferind cea mai vastă resursă de antrenament pentru competițiile de elită. Considerăm că forța acestui compendiu rezidă în munca de recuperare istorică realizată de autori, care au centralizat nu doar problemele oficiale, ci și pe cele propuse pentru selecție.

Din punct de vedere structural, volumul este organizat riguros pentru a facilita progresia învățării. Primele capitole introduc conceptele fundamentale și faptele matematice necesare, oferind baza teoretică înainte de a trece la secțiunea masivă de probleme. Extinde cadrul propus de MATH OLYMPIAD IN CHINA(2007-2008) cu date noi și o perspectivă globală, acoperind cinci decenii de competiție, spre deosebire de focusul regional și temporal limitat al lucrării lui Bin Xiong. În timp ce Winning Solutions de Edward Lozansky se concentrează pe strategii de rezolvare, acest compendiu pune accentul pe exhaustivitate, oferind soluții complete pentru fiecare problemă menționată.

Recomandăm acest titlu pentru rigoarea cu care sunt prezentate cele peste 800 de pagini de conținut tehnic. Tonul este precis, academic, iar cele 200 de ilustrații alb-negru sprijină demonstrațiile geometrice complexe. Este o resursă esențială care transformă pregătirea pentru olimpiadă dintr-o căutare haotică de materiale într-un proces structurat și documentat istoric.

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Specificații

ISBN-13: 9781441998538
ISBN-10: 1441998535
Pagini: 809
Ilustrații: 200 schwarz-weiße Abbildungen
Dimensiuni: 159 x 244 x 53 mm
Greutate: 1.4 kg
Ediția:2nd Edition
Editura: Springer Verlag GmbH
Seria Problem Books in Mathematics

Locul publicării:New York, NY, United States

Public țintă

Professional/practitioner

De ce să citești această carte

Recomandăm această lucrare elevilor de liceu cu aptitudini înalte și profesorilor coordonatori. Cititorul câștigă acces la arhiva completă a celei mai prestigioase competiții de matematică din lume (1959-2009). Este un instrument de antrenament indispensabil care oferă atât provocarea problemelor de nivel olimpic, cât și rigoarea soluțiilor demonstrate, fiind standardul de aur în seria Problem Books in Mathematics.

Despre autor

Echipa de autori formată din Dusan Djukic, Vladimir Janković, Ivan Matic și Nikola Petrovic reprezintă o colaborare de elită a unor foști participanți la Olimpiada Internațională de Matematică din spațiul ex-iugoslav (Serbia și Muntenegru). Această experiență directă în competițiile de vârf le-a permis să identifice și să salveze probleme matematice valoroase din manuscrise vechi. Expertiza lor academică transformă acest compendiu dintr-o simplă listă de exerciții într-o resursă pedagogică solidă, publicată sub egida editurii Springer Verlag GmbH, fiind recunoscuți la nivel internațional pentru contribuția lor la literatura de specialitate dedicată competițiilor de matematică.

Descriere scurtă

"The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems and is an invaluable resource not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates mathematics.
The International Mathematical Olympiad (IMO), nearing its 50th anniversary, has 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 the first edition of this book appearing in 2006, 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 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 through 2009. This second edition contains 143 new problems, picking up where the 1959-2004 edition has left off.

Cuprins

-Preface.-1. Introduction.-2. Basic Concepts and Facts.-3. Problems.-4. Solutions.-Appendix A. Notations and Abbreviations.-Appendix B. Codes of the Countries of Origin.-References.

Recenzii

"The International Mathematical Olympiad, or IMO is the premier international competition 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 faculty looking for hard elementary problems. No library will want to be without a copy, nor will anyone involved in mathematics competitions … ."
—(Fernando Q. Gouvêa, MathDL, March, 2006)

Notă biografică

The authors of this volume have published the first edition with Springer in 2006. The first edition has gone through 3 printings and 2510 print sales. Links to the first edition can be found on the IMO website.
Each of the authors are from Serbia and all were medalists in the mathematical olympiads. Dusan Djusic is an expert in number theory and took part in 3 IMOs. He won 2 silver medals and 1 gold. He has also participates in 2 Balkan IMOs and medaled in each.
Ivan Matic's area of research is partial differential equations and won a silver medal at the 1999 IMO along with a number of awards in other competitions.
Vladimir Jankovic's areas of study are extreme problems in optimal control. He was awarded 2 silver medals at the IMOs in 1969 and 1970 and has been the main gatekeeper for the shortlist problems from IMOs of years past.
Nikola Petrovic took part in 3 IMOs and 2 Balkan IMOs and has been awarded silver and bronze medals.

Textul de pe ultima copertă

The IMO Compendium is the ultimate collection of challenging high school level mathematics 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) competition, 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. The IMO host country appoints a special committee to which each country submits up to six problems. From this composite “longlist” of problems, a “shortlist” of 25-30 problems is created. The jury, consisting of one professor from each country, makes the final selection from the shortlist a few days before the IMO begins.
The IMO has sparked a burst of creativity among enthusiasts to create new and interesting mathematics problems. It can be safely said that the IMO and shortlisted problems are among the well-crafted problems created in a given year. This book attempts to gather all of these problems with their solutions. In addition, the book contains all the available longlist problems, for a total of more than 2000 problems.

From the reviews of the first edition:
"The International Mathematical Olympiad, or IMO is the premier international competition fortalented 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 faculty looking for hard elementary problems. No library will want to be without a copy, nor will anyone involved in mathematics competitions …"
— (Fernando Q. Gouvêa, MathDL, March, 2006)

Caracteristici

Only publication to gather all of the problems given at the IMO from 1959-2009 including both long and short list problems. Second edition includes 143 additional problems. First edition sold nearly 2900 copies. Best preparation at the high school level for the International Mathematical Olympiad (IMO) All authors are IMO medalists. Includes supplementary material: sn.pub/extras