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This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers high school and college students an excellent mathematics workbook of rigorous problems that will assist in developing and cultivating their logic and probability skills.These 20 sets of intriguing problems test originality and insight rather than routine competence. They involve theorizing and verifying mathematical facts; examining the results of general statements; discovering that highly plausible conjectures can be incorrect; solving sequences of subproblems to reveal theory construction; and recognizing "red herrings," in which obvious relationships among the data prove irrelevant to solutions. Hints for each problem appear in a separate section, and a final section features solutions that outline the appropriate procedures.Ideal for teachers seeking challenging practice math problems for their gifted students, this book will also help students prepare for mathematics, science, and engineering programs. Mathematics buffs of all ages will also find it a source of captivating challenges.
About the Author
George Pólya (1887–1985) was a professor of mathematics at Stanford University who made lasting contributions to combinatorics, number theory, numerical analysis, and probability theory. He was also very well-known for his work in mathematics education. In his later days, Dr. Pólya spent considerable effort to document the methods that people use to solve problems, and to describe how problem-solving should be taught and learned. He wrote four books on the subject.