Combinatorial Problems in Mathematical C
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This book focuses on combinatorial problems in mathematical competitions. It provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces important solutions to combinatorial problems and some typical problems with often-used solutions. Some enlightening and novel examples and exercises are well chosen in this book.With this book, readers can explore, analyze and summarize the ideas and methods of solving combinatorial problems. Their mathematical culture and ability will be improved remarkably after reading this book.Contents:Fundamental Knowledge:Principles and Formulas of CountingPigeonhole Principle and Mean Value PrincipleThe Generating FunctionsRecurrence Sequence of NumbersBasic Method:Classification and Method of Fractional StepsCorrespondent MethodCounting in Two WaysRecurrence MethodColoring Method and Evaluation MethodReduction to Absurdity and the Extreme PrincipleLocal Adjustment MethodConstructive MethodTypical Problems:Combinatorial Counting ProblemsExistence Problems and the Proof of Inequalities in Combinatorial ProblemsCombinatorial Extremum ProblemsReadership: Students and teachers of high school, coaches of mathematical olympiads, undergraduates and graduates in mathematics, non-experts interested in mathematical competitions.