[PDF] A Path To Combinatorics For Undergraduates eBook

Author : Titu Andreescu
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 31,82 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 081768154X

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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.

Author : Titu Andreescu
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 39,15 MB
Release : 2003-11-11
Category : Mathematics
ISBN : 9780817642884

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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.

Author : Titu Andreescu
Publisher : Springer Science & Business Media
Page : 125 pages
File Size : 23,66 MB
Release : 2013-11-27
Category : Mathematics
ISBN : 0817682228

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"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.

Author : T. Kyle Petersen
Publisher : Springer
Page : 238 pages
File Size : 33,75 MB
Release : 2019-06-28
Category : Mathematics
ISBN : 3030183084

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This textbook offers the opportunity to create a uniquely engaging combinatorics classroom by embracing Inquiry-Based Learning (IBL) techniques. Readers are provided with a carefully chosen progression of theorems to prove and problems to actively solve. Students will feel a sense of accomplishment as their collective inquiry traces a path from the basics to important generating function techniques. Beginning with an exploration of permutations and combinations that culminates in the Binomial Theorem, the text goes on to guide the study of ordinary and exponential generating functions. These tools underpin the in-depth study of Eulerian, Catalan, and Narayana numbers that follows, and a selection of advanced topics that includes applications to probability and number theory. Throughout, the theory unfolds via over 150 carefully selected problems for students to solve, many of which connect to state-of-the-art research. Inquiry-Based Enumerative Combinatorics is ideal for lower-division undergraduate students majoring in math or computer science, as there are no formal mathematics prerequisites. Because it includes many connections to recent research, students of any level who are interested in combinatorics will also find this a valuable resource.

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
Page : 304 pages
File Size : 39,55 MB
Release : 2020-10-16
Category : Education
ISBN : 1470460327

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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.

Author : J. H. van Lint
Publisher : Cambridge University Press
Page : 620 pages
File Size : 36,93 MB
Release : 2001-11-22
Category : Mathematics
ISBN : 9780521006019

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This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.

Author : John Harris
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 36,78 MB
Release : 2009-04-03
Category : Mathematics
ISBN : 0387797114

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These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

Author : Pablo Soberón
Publisher : Springer Science & Business Media
Page : 178 pages
File Size : 24,95 MB
Release : 2013-03-20
Category : Mathematics
ISBN : 3034805977

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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.

Author : Titu Andreescu
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 16,1 MB
Release : 2000-04-26
Category : Mathematics
ISBN : 9780817641900

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A collection of problems put together by coaches of the U.S. International Mathematical Olympiad Team.