The Art Of Problem Solving Volume 2

Author: Richard Rusczyk
Publisher: Aops Incorporated
ISBN: 9780977304592
Size: 24.59 MB
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"...offer[s] a challenging exploration of problem solving mathematics and preparation for programs such as MATHCOUNTS and the American Mathematics Competition."--Back cover

The Art Of Problem Solving Volume 1

Author: Sandor Lehoczky
Publisher: Aops Incorporated
ISBN: 9780977304578
Size: 44.62 MB
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"...offer[s] a challenging exploration of problem solving mathematics and preparation for programs such as MATHCOUNTS and the American Mathematics Competition."--Back cover

A Primer For Mathematics Competitions

Author: Alexander Zawaira
Publisher: OUP Oxford
ISBN: 0191561703
Size: 38.32 MB
Format: PDF, Mobi
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The importance of mathematics competitions has been widely recognised for three reasons: they help to develop imaginative capacity and thinking skills whose value far transcends mathematics; they constitute the most effective way of discovering and nurturing mathematical talent; and they provide a means to combat the prevalent false image of mathematics held by high school students, as either a fearsomely difficult or a dull and uncreative subject. This book provides a comprehensive training resource for competitions from local and provincial to national Olympiad level, containing hundreds of diagrams, and graced by many light-hearted cartoons. It features a large collection of what mathematicians call "beautiful" problems - non-routine, provocative, fascinating, and challenging problems, often with elegant solutions. It features careful, systematic exposition of a selection of the most important topics encountered in mathematics competitions, assuming little prior knowledge. Geometry, trigonometry, mathematical induction, inequalities, Diophantine equations, number theory, sequences and series, the binomial theorem, and combinatorics - are all developed in a gentle but lively manner, liberally illustrated with examples, and consistently motivated by attractive "appetiser" problems, whose solution appears after the relevant theory has been expounded. Each chapter is presented as a "toolchest" of instruments designed for cracking the problems collected at the end of the chapter. Other topics, such as algebra, co-ordinate geometry, functional equations and probability, are introduced and elucidated in the posing and solving of the large collection of miscellaneous problems in the final toolchest. An unusual feature of this book is the attention paid throughout to the history of mathematics - the origins of the ideas, the terminology and some of the problems, and the celebration of mathematics as a multicultural, cooperative human achievement. As a bonus the aspiring "mathlete" may encounter, in the most enjoyable way possible, many of the topics that form the core of the standard school curriculum.

Mathematical Circle Diaries Year 2 Complete Curriculum For Grades 6 To 8

Author: Anna Burago
Publisher: American Mathematical Soc.
ISBN: 147043718X
Size: 65.95 MB
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Mathematical circles, with their question-driven approach and emphasis on problem solving, expose students to the type of mathematics that stimulates the development of logical thinking, creativity, analytical abilities, and mathematical reasoning. These skills, while scarcely introduced at school, are in high demand in the modern world. This book, a sequel to Mathematical Circle Diaries, Year 1, teaches how to think and solve problems in mathematics. The material, distributed among twenty-nine weekly lessons, includes detailed lectures and discussions, sets of problems with solutions, and contests and games. In addition, the book shares some of the know-how of running a mathematical circle. The book covers a broad range of problem-solving strategies and proofing techniques, as well as some more advanced topics that go beyond the limits of a school curriculum. The topics include invariants, proofs by contradiction, the Pigeonhole principle, proofs by coloring, double counting, combinatorics, binary numbers, graph theory, divisibility and remainders, logic, and many others. When students take science and computing classes in high school and college, they will be better prepared for both the foundations and advanced material. The book contains everything that is needed to run a successful mathematical circle for a full year. This book, written by an author actively involved in teaching mathematical circles for fifteen years, is intended for teachers, math coaches, parents, and math enthusiasts who are interested in teaching math that promotes critical thinking. Motivated students can work through this book on their own. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Mathematical Discovery On Understanding Learning And Teaching Problem Solving Volumes I And Ii

Author: George Polya
Publisher: John Wiley & Sons Incorporated
ISBN:
Size: 16.25 MB
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A unique, heuristic approach to mathematical discovery and problem solving This combined edition of Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving is unique among mathematics texts. Espousing a heuristic approach to mathematical problem solving, the text may be followed sequentially or according to instructors' individualized curricula. Beginning with a discussion of patterns and practical approaches to problem solving, the book then presents examples from various branches of math and science to help students discover how to solve problems on their own – an invaluable skill for the classroom and beyond.

More Worlds To Negotiate

Author: Jennifer C. Berkshire
Publisher: Rowman & Littlefield
ISBN: 0761871136
Size: 64.92 MB
Format: PDF, Mobi
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This lively, accessible account of the problem-solving work of Harvard labor economist and former US Secretary of Labor John T. Dunlop illuminates its relevance to our present-day political and economic challenges.