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The Art Of Problem Solving Volume 2

Author: Richard Rusczyk
Publisher: Aops Incorporated
ISBN: 9780977304592
Size: 69.66 MB
Format: PDF
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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: 29.84 MB
Format: PDF
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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

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

Author: Anna Burago
Publisher: American Mathematical Soc.
ISBN: 147043718X
Size: 48.48 MB
Format: PDF
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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

Author: George Pólya
ISBN: 9784871878326
Size: 34.99 MB
Format: PDF, Mobi
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"Solving problems," writes Polya, "is a practical art, like swimming, or skiing, or playing the piano: You can learn it only by imitation and practice. This book cannot offer you a magic key that opens all the doors and solves all the problems, but it offers you good examples for imitation and many opportunities for practice: If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems." "In enough cases to allay . . . discouragement over not immediately discovering a solution, Professor Polya masterfully leads the reader down several unproductive paths. At the end of each chapter he provides examples for the render to solve. By means of these carefully selected and arranged problems, many of them directly related to others that precede, and guided by just the right suggestions at just the proper time, the reader's own ability is developed and extended. Solutions to the examples and, in many cases, outlines of procedures for discovering solutions. arc given at the back of the book. With striking promise for effectiveness, the entire book as a unit is one great experience in learning processes for problem solving through participation. The author has captured with great success the implication of his basic premise stated in the preface ..." The Mathematics Teacher

Problems Of Empiricism Volume 2

Author: Paul Feyerabend
Publisher: Cambridge University Press
ISBN: 9780521316415
Size: 50.75 MB
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Volume 1 presents papers on the interpretation of scientific theories, together with papers applying the views developed to particular problems in philosophy and physics. The essays in volume 2 examine the origin and history of an abstract rationalism, as well as its consequences for the philosophy of science and methods of scientific research.

Art Of Computer Programming Volume 2

Author: Donald E. Knuth
Publisher: Addison-Wesley Professional
ISBN: 0321635760
Size: 45.75 MB
Format: PDF, Docs
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The bible of all fundamental algorithms and the work that taught many of today's software developers most of what they know about computer programming. —Byte, September 1995 I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up. —Charles Long If you think you're a really good programmer... read [Knuth's] Art of Computer Programming... You should definitely send me a resume if you can read the whole thing. —Bill Gates It's always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers. —Jonathan Laventhol The second volume offers a complete introduction to the field of seminumerical algorithms, with separate chapters on random numbers and arithmetic. The book summarizes the major paradigms and basic theory of such algorithms, thereby providing a comprehensive interface between computer programming and numerical analysis. Particularly noteworthy in this third edition is Knuth's new treatment of random number generators, and his discussion of calculations with formal power series.