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‏206.00 ₪
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COMBINATORIAL PROBLEMS IN MATHEMATICAL COMPETITIONS

‏206.00 ₪
ISBN13
9789812839497
הוצאה לאור
World Scientific Publishing
עמודים / Pages
289
תאריך יציאה לאור
30 במרץ 2011

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 Counting
    • Pigeonhole Principle and Mean Value Principle
    • The Generating Functions
    • Recurrence Sequence of Numbers
  • Basic Method:
    • Classification and Method of Fractional Steps
    • Correspondent Method
    • Counting in Two Ways
    • Recurrence Method
    • Coloring Method and Evaluation Method
    • Reduction to Absurdity and the Extreme Principle
    • Local Adjustment Method
    • Constructive Method
  • Typical Problems:
    • Combinatorial Counting Problems
    • Existence Problems and the Proof of Inequalities in Combinatorial Problems
    • Combinatorial Extremum Problems

Readership: Students and teachers of high school, coaches of mathematical olympiads, undergraduates and graduates in mathematics, non-experts interested in mathematical competitions.
main product photo
מידע נוסף
עמודים / Pages 289
הוצאה לאור World Scientific Publishing
תאריך יציאה לאור 30 במרץ 2011
תוכן עניינים

FRONT MATTER Pages:i–xii

PART ONE Fundamental Knowledge

Principles and Formulas of Counting Pages:1–19

Pigeonhole principle and Mean Value principle Pages:20–32

The Generating Functions Pages:33–39

Recurrence Sequence of Numbers Pages:40–55


PART TWO Basic Method

Classification and Method of Fractional steps Pages:56–66

Correspondent Method Pages:67–86

Counting in Two Ways Pages:87–99

Recurrence Method Pages:100–111

Coloring Method and Evaluation Method Pages:112–122

Reduction to Absurdity and the Extreme principle Pages:123–131

Local Adjustment Method Pages:132–142

Construction Method Pages:143–152


PART THREE Typical Problems

Combinatorial Counting Problems Pages:153–166

Existence problems and the proofs of Inequalities in Combinatorial Problems Pages:167–181

Combinatorial Extremum Problems Pages:182–200

BACK MATTER Pages:201–289
Author Yao Zhang