A Path To Combinatorics For Undergraduates
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A Path to Combinatorics for Undergraduates
Author | : Titu Andreescu,Zuming Feng |
Publsiher | : Springer Science & Business Media |
Total Pages | : 235 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 9780817681548 |
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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.
A Path to Combinatorics for Undergraduates
Author | : Titu Andreescu,Zuming Feng |
Publsiher | : Unknown |
Total Pages | : 254 |
Release | : 2014-09-01 |
Genre | : Electronic Book |
ISBN | : 0817681558 |
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102 Combinatorial Problems
Author | : Titu Andreescu,Zuming Feng |
Publsiher | : Springer Science & Business Media |
Total Pages | : 125 |
Release | : 2013-11-27 |
Genre | : Mathematics |
ISBN | : 9780817682224 |
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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.
Inquiry Based Enumerative Combinatorics
Author | : T. Kyle Petersen |
Publsiher | : Springer |
Total Pages | : 238 |
Release | : 2019-06-28 |
Genre | : Mathematics |
ISBN | : 9783030183080 |
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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.
Combinatorics and Graph Theory
Author | : John Harris,Jeffry L. Hirst,Michael Mossinghoff |
Publsiher | : Springer Science & Business Media |
Total Pages | : 392 |
Release | : 2009-04-03 |
Genre | : Mathematics |
ISBN | : 9780387797113 |
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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.
Combinatorics The Art of Counting
Author | : Bruce E. Sagan |
Publsiher | : American Mathematical Soc. |
Total Pages | : 304 |
Release | : 2020-10-16 |
Genre | : Education |
ISBN | : 9781470460327 |
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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.
A Course in Combinatorics
Author | : J. H. van Lint,Richard Michael Wilson |
Publsiher | : Cambridge University Press |
Total Pages | : 620 |
Release | : 2001-11-22 |
Genre | : Mathematics |
ISBN | : 0521006015 |
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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.
Principles and Techniques in Combinatorics
Author | : Chuan-Chong Chen,Khee Meng Koh,Koh Khee-Meng |
Publsiher | : World Scientific |
Total Pages | : 314 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : 9810211392 |
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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.