Bona M A Walk Through Combinatorics An Intr Enumeration Graph Theory 4ed 2016 | 8.54 MB
English | 625 Pages

Title: A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory
Author: Miklós Bóna
Year: 2022

English | 2022 | ISBN: 978-1470469306 | 187 pages | True PDF | 7.69 MB
This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.

Cornel Baetica, "Combinatorics of Determinantal Ideals"
English | 2006 | pages: 146 | ISBN: 1594549184 | PDF | 0,6 mb

Polya G Notes on Introductory Combinatorics 2010 | 14.78 MB
English | 201 Pages

Title: Notes on Introductory Combinatorics (Modern Birkhäuser Classics)
Author: George Pólya
Year: 2009

Nicholas A. Loehr, "Combinatorics, 2nd Edition (Discrete Mathematics and Its Applications)"
English | ISBN: 1498780253 | 2017 | EPUB | 618 pages | 9 MB
Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics.

A First Course in Graph Theory and Combinatorics: Second Edition
English | 2022 | ISBN: 9811913358 | 237 Pages | PDF EPUB (True) | 12 MB
This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick's theorem on areas of lattice polygons and Graham-Pollak's work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.

Combinatorics: A Problem-Based Approach by Pavle Mladenović
English | EPUB | 2019 | 372 Pages | ISBN : 3030008304 | 15.4 MB
This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary probability.

English | 2021 | ISBN: 3110751178 | 344 pages | True PDF EPUB | 30.17 MB
This textbook is devoted to Combinatorics and Graph Theory, which are cornerstones of Discrete Mathematics. Every section begins with simple model problems. Following their detailed analysis, the reader is led through the derivation of definitions, concepts and methods for solving typical problems. Theorems then are formulated, proved and illustrated by more problems of increasing difficulty. Topics covered include elementary combinatorial constructions, application to probability theory, introduction to graphs and trees with application to hierarchical clustering algorithms, more advanced counting techniques, and existence theorems in combinatorial analysis.

Computation and Combinatorics in Dynamics, Stochastics and Control: The Abel Symposium, Rosendal, Norway, August 2016 by Elena Celledoni
English | EPUB | 2018 | 734 Pages | ISBN : 3030015920 | 12.1 MB
The Abel Symposia volume at hand contains a collection of high-quality articles written by the world's leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory.

English | 2021 | ISBN: 168507152X , 978-1685071523 | 352 pages | True PDF | 13.63 MB
The main goal of our book is to provide easy access to the basic principles and methods that combinatorial calculations are based upon. The rule of product, the identity principle, recurrence relations and inclusion-exclusion principle are the most important of the above. Significant parts of the book are devoted to classical combinatorial structures, such as: ordering (permutations), tuples, and subsets (combinations). A great deal of attention is paid to the properties of binomial coefficients, and in particular, to model proofs of combinatorial identities. Problems concerning some exact combinatorial configurations such as paths in a square, polygonal chains constructed with chords of a circle, trees (undirected graphs with no cycles) etc. are included too. All chapters contain a considerable number of exercises of various complexity, from easy training tasks to complex problems which require decent persistence and skill from the one who dares to solve them. If one aims to passively familiarize oneself with the subject, methods and the most necessary facts of combinatorics, then it may suffice to limit one's study to the main text omitting the exercise part of the book. However, for those who want to immerse themselves in combinatorial problems and to gain skills of active research in that field, the exercise section is rather important. The authors hope that the book will be helpful for several categories of readers. University teachers and professors of mathematics may find somewhat unusual coverage of certain matters and exercises which can be readily applied in their professional work. We believe that certain series of problems may serve as a base for serious creative works and essays. This especially refers to students at pedagogical universities and colleges who need to prepare themselves to the teaching of the basics of combinatorics, mainly building on arithmetic and geometry. Most of the exercises of the book are of this very origin.