Combinatorial Mathematics

Name: Combinatorial Mathematics
ISBN: 9787301261057

冯荣权 / 宋春伟Peking University Press · ChinaAug 2025

3.8

Word count: 65 words
Chapters: 7
ISBN: 9787301261057

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Summary

Combinatorics introduces the main branches of the discipline—enumerative combinatorics, combinatorial design, set theory, graph theory, and probabilistic methods in combinatorics—while remaining concise and refreshingly contemporary.

Editor's review

Written by Feng Rongquan and Song Chunwei and published by Peking University Press in 2025, this is a textbook-style work covering the main branches of combinatorics. It introduces core areas such as enumerative combinatorics, combinatorial design, set theory, graph theory, and probabilistic methods in combinatorics, while emphasizing concise content and a contemporary feel; it is suitable as an introductory and advanced reader for systematic study. Its value lies in helping readers build an overall framework of combinatorial knowledge, understand the connections among branches, and appreciate how combinatorial thinking analyzes discrete problems. For readers who need to solidify their mathematical foundations, prepare for related courses, or whose research involves discrete structures and algorithm analysis, the book offers a fairly complete conceptual thread and theoretical tools. When reading, it is advisable to work through exercises and concrete examples, mastering counting techniques before moving on to design and graph theory.

Who it's for

A good fit for

Undergraduates in mathematics, computer science, and related majors who need systematic grounding in combinatorics
Students preparing for combinatorics course exams or graduate entrance examinations
Readers in algorithms and discrete optimization who want to complete their theoretical framework in combinatorics
Self-learners interested in graph theory and counting methods who have some mathematical maturity

Not a good fit for

Readers with no background in discrete mathematics or elementary mathematics who want a from-scratch introduction
Practical readers who only want to look up individual formulas quickly and prefer not to read theoretical derivations systematically
General readers seeking light popular-science reading who are unaccustomed to definition-and-theorem exposition

Reading tips

Read through enumerative combinatorics and set theory first to build basic concepts before moving on to graph theory and probabilistic methods
Work through end-of-chapter exercises in each chapter, attempting proofs independently before consulting solutions
Read graph theory alongside combinatorial design, noting how methods transfer and connect across branches
Keep a notebook of typical counting models and proof ideas for cross-comparison during review

About the publisher

Peking University Press China · Founded in 1979

Peking University Press is a comprehensive university press whose publishing areas cover classical literature, popular science, social culture, world history, Western philosophy, and culture. Its catalogue contains 6,031 titles, with representative books including A Dream of Red Mansions, Relativity: The Special and General Theory (15th Edition) (with Einstein's classic papers on unified field theory and other topics), Elements, Conics, The Aristocratic Families of the Eastern Jin, The Philosophy of Mythology (Volume I), The Philosophy of Mythology (Volume II), and The Origin of Continents and Oceans. Representative authors include Cao Xueqin, Zhou Ruchang, Albert Einstein, Euclid, Apollonius, Tian Yuqing, Schelling, and Xian Gang. The press has developed distinctive strengths in classical Chinese literature and in the translation of Western philosophical classics, while also covering scientific classics and social and cultural studies. As public information is limited, this description is based only on the books in the catalogue and offers no further extrapolation.

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FAQ

What mathematical background is needed to read this book?

A foundation in elementary mathematics and some discrete mathematics is recommended; familiarity with sets, mappings, and basic counting ideas will make reading smoother. Without such background, readers should first study introductory discrete mathematics, otherwise proofs and abstract concepts may be difficult.

What main content does the book cover?

According to the materials, the book covers major areas including enumerative combinatorics, combinatorial design, set theory, graph theory, and probabilistic methods in combinatorics. It introduces several main branches of the discipline and emphasizes concise content and a contemporary feel.

Is it suitable as a textbook for graduate entrance exams or courses?

This is a textbook-style work published by Peking University Press, covering the main branches of combinatorics and suitable for systematic study alongside a course. Whether it directly matches a particular school's exam syllabus depends on the specific requirements; readers should consult the syllabus to select key chapters.

How should self-learners pace their reading?

Proceed in the order of counting, set theory, graph theory, combinatorial design, and probabilistic methods. In each chapter, first understand definitions and typical examples, then complete an appropriate number of exercises. When stuck on a proof, review the relevant concepts first; there is no need to finish all content in one pass.

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About the author

冯荣权 Author

Feng Rongquan: public information is limited, and only one book by this author is held in the library, namely Combinatorics. The book is often classified under examinations, suggesting that its content is closely tied to course study and exam preparation, and that its main readers are students taking combinatorics courses or preparing for related examinations. Combinatorics itself covers basic methods such as counting, permutations and combinations, recurrence relations, and introductory graph theory, emphasizing logical reasoning and problem-solving practice; teaching materials or study guides of this kind therefore tend to be well organized and rich in worked examples, allowing readers to practice chapter by chapter. Because biographical details, education, and positions for Feng Rongquan are currently unavailable, no account of his academic background or writing career can be given; based only on the existing catalogue record, his signed work serves teaching and examination contexts and can be used as a reference in related course study.

宋春伟 Author

Song Chunwei: publicly available information about this author is currently limited, and details such as biography, nationality, and dates of birth and death cannot be confirmed. According to the library's holdings, only one work appears under this name, Combinatorics, commonly classified under exam preparation. It may therefore be intended for test takers or course learners, focusing on the basic methods and problem-solving practice of combinatorics. Combinatorics is an important branch of mathematics dealing with counting, permutations and combinations, and discrete structures, and it often appears in entrance examinations and competition preparation. The available materials do not provide the book's background, content features, or reader feedback, so its writing style and academic influence cannot be further assessed. Readers are advised to rely on bibliographic information and the actual pages of the book.