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Mathematical Olympiad Challenges de Titu Andreescu

Mathematical Olympiad Challenges

Autor Titu Andreescu, Razvan Gelca
en Limba Engleză Paperback – 9 dec 2008

Remarcăm în Mathematical Olympiad Challenges o lucrare fundamentală semnată de Titu Andreescu și Razvan Gelca, personalități cu o autoritate incontestabilă în pedagogia matematică de performanță. Titu Andreescu, fost director al competițiilor matematice americane și antrenor al echipei de elită a SUA pentru Olimpiada Internațională de Matematică, își bazează metodologia pe decenii de cercetare în analiza diofantică și pe experiența directă în pregătirea olimpicilor de top. Această a doua ediție, publicată de birkhäuser, este concepută pentru a simula procesul creativ al matematicii reale într-un format condensat. Descoperim aici o structură riguroasă, organizată simetric între enunțuri și rezolvări. Cartea trece prin patru piloni esențiali: Geometrie și Trigonometrie, Algebră și Analiză, Teoria Numerelor și Combinatorică. Spre deosebire de Mathematics as Problem Solving de Alexander Soifer, care oferă o introducere mai narativă și relaxată pentru liceeni, volumul de față impune un ritm mai intens, specific nivelului universitar (undergraduate). Lucrarea extinde cadrul propus anterior de autor în Mathematical Bridges cu date noi și o orientare mai pregnantă spre intuiția rapidă necesară în mediul competitiv. Suntem de părere că valoarea acestui manual rezidă în modul în care tratează „eșecul constructiv” și explorarea căilor multiple de rezolvare. În timp ce Problem-Solving Strategies de Arthur Engel se concentrează pe o colecție vastă de tehnici pentru competiții internaționale, Mathematical Olympiad Challenges reușește să creeze o punte teoretică între problemele de concurs și matematica de cercetare, păstrând în același timp un stil concis și extrem de aplicat.

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Specificații

ISBN-13: 9780817645281
ISBN-10: 0817645284
Pagini: 304
Ilustrații: XVII, 283 p. 108 illus.
Dimensiuni: 155 x 235 x 17 mm
Greutate: 0.46 kg
Ediția:2nd edition 2009
Editura: birkhäuser
Locul publicării:Boston, MA, United States

Public țintă

Lower undergraduate

De ce să citești această carte

Această carte este esențială pentru studenții și elevii de elită care doresc să își rafineze tehnicile de rezolvare a problemelor sub presiune. Dincolo de simpla pregătire pentru concursuri, cititorul câștigă o înțelegere profundă a legăturilor dintre algebră, geometrie și combinatorică. Este un instrument de antrenament mental condus de unul dintre cei mai respectați antrenori de matematică din lume, oferind soluții care dezvăluie eleganța din spatele calculelor complexe.

Despre autor

Titu Andreescu deține un doctorat de la Universitatea de Vest din Timișoara, cu o teză axată pe Analiza Diofantică. În prezent profesor la University of Texas at Dallas, cariera sa este strâns legată de excelența în competiții, servind ca lider și antrenor al echipei de matematică a SUA (IMO) între 1995 și 2002. Razvan Gelca, co-autorul său, completează această viziune academică prin expertiză în cercetare și educație universitară. Împreună, au publicat lucrări de referință precum Putnam and Beyond și Mathematical Bridges, consolidând o metodă de predare care pune accent pe gândirea critică și creativitate.

Descriere scurtă

Why Olympiads? Working mathematiciansoftentell us that results in the ?eld are achievedafter long experience and a deep familiarity with mathematical objects, that progress is made slowly and collectively, and that ?ashes of inspiration are mere punctuation in periods of sustained effort. TheOlympiadenvironment,incontrast,demandsarelativelybriefperiodofintense concentration,asksforquickinsightsonspeci?coccasions,andrequiresaconcentrated but isolated effort. Yet we have foundthat participantsin mathematicsOlympiadshave oftengoneontobecome?rst-classmathematiciansorscientistsandhaveattachedgreat signi?cance to their early Olympiad experiences. For many of these people, the Olympiad problem is an introduction, a glimpse into the world of mathematics not afforded by the usual classroom situation. A good Olympiad problem will capture in miniature the process of creating mathematics. It’s all there: the period of immersion in the situation, the quiet examination of possible approaches, the pursuit of various paths to solution. There is the fruitless dead end, as well as the path that ends abruptly but offers new perspectives, leading eventually to the discoveryof a better route. Perhapsmost obviously,grapplingwith a goodproblem provides practice in dealing with the frustration of working at material that refuses to yield. If the solver is lucky, there will be the moment of insight that heralds the start of a successful solution. Like a well-crafted work of ?ction, a good Olympiad problem tells a story of mathematical creativity that captures a good part of the real experience and leaves the participant wanting still more. And this book gives us more.

Cuprins

Problems.- Geometry and Trigonometry.- Algebra and Analysis.- Number Theory and Combinatorics.- Solutions.- Geometry and Trigonometry.- Algebra and Analysis.- Number Theory and Combinatorics.

Recenzii

From the reviews:
"The authors are experienced problem solvers and coaches of mathematics teams. This expertise shows through and the result is a volume that would be a welcome addition to any mathematician's bookshelf."—MAA Online
"This [book] is…much more than just another collection of interesting, challenging problems, but is instead organized specifically for learning. The book expertly weaves together related problems, so that insights gradually become techniques, tricks slowly become methods, and methods eventually evolve into mastery…. The book is aimed at motivated high school and beginning college students and instructors. It can be used as a text for advanced problem-solving courses, for self-study, or as a resource for teachers and students training for mathematical competitions, and for teacher professional development, seminars, and workshops.
I strongly recommend this book for anyone interested in creative problem-solving in mathematics…. It has already taken up a prized position in my personal library, and is bound to provide me with many hours of intellectual pleasure."—The Mathematical Gazette
"The Olympiad book is easier to describe since the format of the Olympiad competition and the books it has spawned will be well known to most Gazette readers. … The authors have organised the material to reduce the pain … and to make the material a genuine learning experience for Olympian hopefuls and their teachers. … a valuable addition to the problem literature, and their organisational features are generally helpful rather than merely attempts to look different." (John Baylis, The Mathematical Gazette, July, 2004)

Textul de pe ultima copertă

This signficantly revised and expanded second edition of Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory from numerous mathematical competitions and journals have been selected and updated. The problems are clustered by topic into self-contained sections with solutions provided separately. Historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on creative solutions to open-ended problems.
New to the second edition:
* Completely rewritten discussions precede each of the 30 units, adopting a more user-friendly style with more accessible and inviting examples
* Many new or expanded examples, problems, and solutions
* Additional references and reader suggestions have been incorporated
Featuring enhanced motivation for advanced high school and beginning college students, as well as instructors and Olympiad coaches, this text can be used for creative problem-solving courses, professional teacher development seminars and workshops, self-study, or as a training resource for mathematical competitions.
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This [book] is…much more than just another collection of interesting, challenging problems, but is instead organized specifically for learning. The book expertly weaves together related problems, so that insights gradually become techniques, tricks slowly become methods, and methods eventually evolve into mastery…. The book is aimed at motivated high school and beginning college students and instructors...I strongly recommend this book for anyone interested in creative problem-solving in mathematics…. It has alreadytaken up a prized position in my personal library, and is bound to provide me with many hours of intellectual pleasure.
—The Mathematical Gazette (Review of the First Edition)

Caracteristici

404 beautiful, challenging, and instructive problems, all including solutions and discussion. Organized by subject and difficulty to motivate students. Covers topics in algebra, geometry, trigonometry, combinatorics, and number theory. Provides historical insights and asides to stimulate further inquiry Emphasizes creative solutions to open-ended problems

Notă biografică

Titu Andreescu received his Ph.D. from the West University of Timisoara, Romania. The topic of his dissertation was "Research on Diophantine Analysis and Applications." Professor Andreescu currently teaches at The University of Texas at Dallas. He is past chairman of the USA Mathematical Olympiad, served as director of the MAA American Mathematics Competitions (1998-2003), coach of the USA International Mathematical Olympiad Team (IMO) for 10 years (1993-2002), director of the Mathematical Olympiad Summer Program (1995-2002), and leader of the USA IMO Team (1995-2002). In 2002 Titu was elected member of the IMO Advisory Board, the governing body of the world's most prestigious mathematics competition. Titu co-founded in 2006 and continues as director of the AwesomeMath Summer Program (AMSP). He received the Edyth May Sliffe Award for Distinguished High School Mathematics Teaching from the MAA in 1994 and a "Certificate of Appreciation" from the president of the MAA in 1995 for his outstanding service as coach of the Mathematical Olympiad Summer Program in preparing the US team for its perfect performance in Hong Kong at the 1994 IMO. Titu's contributions to numerous textbooks and problem books are recognized worldwide. Dorin Andrica received his Ph.D in 1992 from "Babes¿-Bolyai" University in Cluj-Napoca, Romania; his thesis treated critical points and applications to the geometry of differentiable submanifolds. Professor Andrica has been chairman of the Department of Geometry at "Babes¿-Bolyai" since 1995. He has written and contributed to numerous mathematics textbooks, problem books, articles and scientific papers at various levels. He is an invited lecturer at university conferences around the world: Austria, Bulgaria, Czech Republic, Egypt, France, Germany, Greece, Italy, the Netherlands, Portugal, Serbia, Turkey, and the USA. Dorin is a member of the Romanian Committee for the Mathematics Olympiad and is a member onthe editorial boards of several international journals. Also, he is well known for his conjecture about consecutive primes called "Andrica's Conjecture." He has been a regular faculty member at the Canada-USA Mathcamps between 2001-2005 and at the AwesomeMath Summer Program (AMSP) since 2006.