-PDF Download- 102 Combinatorial Problems EBOOK

102 Combinatorial Problems

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2013-11-27

Total Pages: 125

ISBN-13: 0817682228

"102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.

Problem-Solving Methods in Combinatorics

Author: Pablo Soberón

Publisher: Springer Science & Business Media

Published: 2013-03-20

Total Pages: 174

ISBN-13: 3034805977

DOWNLOAD EBOOK →

Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests. It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book. The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.

A Path to Combinatorics for Undergraduates

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 235

ISBN-13: 081768154X

DOWNLOAD EBOOK →

This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, "102 Combinatorial Problems," makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.

Combinatorics: The Art of Counting

Author: Bruce E. Sagan

Publisher: American Mathematical Soc.

Published: 2020-10-16

Total Pages: 304

ISBN-13: 1470460327

DOWNLOAD EBOOK →

This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Challenging Mathematical Problems with Elementary Solutions

Author: ?. ? ?????

Publisher: Courier Corporation

Published: 1987-01-01

Total Pages: 242

ISBN-13: 0486655377

DOWNLOAD EBOOK →

Volume II of a two-part series, this book features 74 problems from various branches of mathematics. Topics include points and lines, topology, convex polygons, theory of primes, and other subjects. Complete solutions.

103 Trigonometry Problems

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2006-03-06

Total Pages: 214

ISBN-13: 0817644326

DOWNLOAD EBOOK →

* Problem-solving tactics and practical test-taking techniques provide in-depth enrichment and preparation for various math competitions * Comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry * A cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training

104 Number Theory Problems

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2007-04-05

Total Pages: 204

ISBN-13: 0817645616

DOWNLOAD EBOOK →

This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

Principles and Techniques in Combinatorics

Author: Chuan-Chong Chen

Publisher: World Scientific

Published: 1992

Total Pages: 314

ISBN-13: 9789810211394

DOWNLOAD EBOOK →

A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.

Mathematical Olympiad Treasures

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2011-09-21

Total Pages: 256

ISBN-13: 0817682538

DOWNLOAD EBOOK →

Mathematical Olympiad Treasures aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of algebra, geometry, trigonometry, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus is on engaging a wider audience to apply techniques and strategies to real-world problems. Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools that will be useful beyond the classroom and in a number of disciplines.

Combinatorial Problems and Exercises

Author: L. Lovász

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 636

ISBN-13: 0080933092

DOWNLOAD EBOOK →

The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book. Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.