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Hungarian Problem Book IV
By: Robert Barrington Leigh (Editor, Translator), Andy Liu (Editor)
Paperback | 30 December 2011
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Hungarian Problem Book IV is intended for beginners, although the experienced student will find much here. Beginners are encouraged to work the problems in each section, and then to compare their results against the solutions presented in the book. They will find ample material in each section to help them improve their problem-solving techniques.
Industry Reviews
""World Federation of National Mathematics Competitions Every young (or not so young) mathematician enjoys a good problem to ponder, hence the popularity of mathematics competitions, ranging from local in-school contests to international meetings where (a bit of) national prestige is at stake. The oldest, and one of the most famous, of these is the Hungarian mathematics competition (Eotvos/Kurschak) held annually since 1894. This volume, published by the MAA, collects the problems from this competition from 1947 to 1963 along with solutions and commentary. Since the competition is for senior high school students the problems need less mathematical background knowledge than, for example, the Putnam competition problems and are concentrated mainly in combinatorics, geometry and elementary number theory. The MAA has also published collections of problems from earlier years (Volume 1, 1894 to 1905, Volume 2, 1906 to 1928, Volume 3, 1929 to 1943) and it is an interesting exercise to compare these to see how taste in the choice of problems has evolved. The current volume contains extensive commentary and alternative solutions for many of the problems as well as valuable advice for students and coaches preparing for similar competitions and concludes with an interesting discussion of possible extensions of some of the problems. This is a valuable resource which should be part of every college and high school library."" -Keith Johnson, CMS Notes
""Anticipated to widen the originality of elementary mathematics problems and deepen the creativity and diversity of their solutions, Hungarian Problem Book IV proves to be a valuable tool for students interested in preparing for mathematics competitions and for all those involved in organizing them. The book is a precious collection of problems from the Kurschak Mathematics Competition, which is the oldest high school mathematics competition in the world. Robert Barrington Leigh and Andy Liu have worked diligently in the translation of the original 48 problems from the Hungarian Kurschak Competition of 1947 to 1963, editing and organizing them by subject: combinatorics, graph theory, number theory, divisibility, sums and difference, algebra, geometry, tangent lines and circles, geometric inequalities, combinatorial geometry, trigonometry and solid geometry. The experienced reader will find some new and intriguing problems here. Hungarian Problem Book IV is of course a sequel to Hungarian Problem Book III. The latter discusses Polya's four-step method for problem-solving, focusing mostly on the first three steps (understanding the problem, making a plan, and carrying out the plan). The final chapter of Hungarian Problem Book IV, ""looking Back,"" illustrates the usage of the fourth step in Polya's problem-solving process, which is looking back and eliciting further insights into the problems. An example is the discussion of problems in number theory. The authors begin by proving that an integer can be expressed as the sum of two squares if and only if twice that number can be so expressed. then he deviates from this problem to another one, as he tries to determine all positive integers m such that (m-1)! is divisible by m. He draws the solution from Wilson's Theorem, and proves it using geometric intuition. Next, he digresses once again to consider the Fermat's Little Theorem (which is a result very close to Wilson's Theorem) and proceeds to prove it. Finally, he explores Waring's Problem and looks back at yet another related problem which involves the Fermat Numbers. Thus this discussion exhibits an astonishing interplay between results of the different problems. The problems and their solutions draw on numerous famous theorems and concepts; to name a few: Ramsey's Theorem, Hamiltonian cycles, Farey fractions, Chebyshev's Inequality, Vieta's Formulae, Cantor's Diagonalization Method, Hall's Theorem, Euler's formula, etc., all of which are introduced and explained. Hungarian Problem Book IV enriches its readers' problem-solving technique and challenges their creative thinking."" - MAA Reviews
ISBN: 9780883858318
ISBN-10: 0883858312
Series: Maa Problem Book
Published: 30th December 2011
Format: Paperback
Language: English
Number of Pages: 130
Audience: Primary, Secondary and High School
Publisher: CAMBRIDGE UNIV PR
Country of Publication: US
Dimensions (cm): 23.5 x 15.88 x 0.64
Weight (kg): 0.18
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