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About this book :-
Combinatorial Problems in Mathematical Competitions written by
Yao Zhang .
This book covers six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations. It contains a selection of more than 500 problems and solutions based on the Ph.D. qualifying test papers of a decade of influential universities in North America. The mathematical problems under discussion are kept within the scope of the textbooks for graduate students.
Finding solutions to these problems, however, involves a deep understanding of mathematical principles as well as an acquisition of skills in analysis and computation. As a supplement to textbooks, this book may prove to be of some help to the students in taking relevant courses. It may also serve as a reference book for the teachers concerned.
It has to be pointed out that this book should not be regarded as an all purpose trouble shooter. Nor is it advisable to take the book as an exemplary text and commit to memory all the problems and solutions and make an indiscriminate use of them. Instead, the students are expected to make a selective survey of the problems, take a do-it-yourself approach and arrive at their own solutions which they may check against those listed in the book. It would be gratifying to see that the students can work out the problems on their own and come up with better solutions than those provided by the book. If the students fail to do so or their solutions may turn out to be incomplete, it may reveal the inadequacy of their knowledge or approach, thus spurring them to greater efforts to promote their skills. The very purpose of the authors in writing the book is just to help the students to discover the truth by trial and error.
Book Detail :-
Title: Combinatorial Problems in Mathematical Competitions
Edition:
Author(s): Yao Zhang
Publisher:
Series:
Year:
Pages:
Type: PDF
Language: English
ISBN:
Country:
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Book Contents :-
Combinatorial Problems in Mathematical Competitions written by
Yao Zhang
cover the following topics.
'
Part-1 Fundamental Knowledge
1 Principles and Formulas of Counting
2 Pigeonhole Principle and Mean Value Principle
3 The Generating Functions
4 Recurrence Sequence of Numbers
Part-2 Basic Method
5 Classification and Method of Fractional Steps
6 Correspondent Method
7 Counting in Two Ways
8 Recurrence Method
9 Coloring Method and Evaluation Method
10 Reduction to Absurdity and the Extreme Principle
11 Local Adjustment Method
12 Construction Method
Part-3 Typical Problems
13 Combinatorial Counting Problems
14 Existence Problems and the Proofs of Inequalities in Combinatorial Problems
15 Combinatorial Extremum Problems
Solutions to Exercises
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