This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. ". . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics." Publicationes Mathematicae Debrecen
The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints andsolutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level. Praise for the German edition ... This book is a well-written introduction to discrete mathematics and is highly recommended to every student ofmathematics and computer science as well as to teachers of these topics. --Konrad Engel for MathSciNet Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of theMAA for expository writing, and his book Proofs from the BOOK with Gunter M. Ziegler has been an international success with translations into 12 languages.
This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questio ns so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011.
This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov’s theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov’s theorem. What makes the Markov theme so attractive is that it appears in an astounding variety of different fields, from number theory to combinatorics, from classical groups and geometry to the world of graphs and words. On the way, there are also introductory forays into some fascinating topics that do not belong to the standard curriculum, such as Farey fractions, modular and free groups, hyperbolic planes, and algebraic words. The book closes with a discussion of the current state of knowledge about the uniqueness conjecture, which remains an open challenge to this day. All the material should be accessible to upper-level undergraduates with some background in number theory, and anything beyond this level is fully explained in the text. This is not a monograph in the usual sense concentrating on a specific topic. Instead, it narrates in five parts – Numbers, Trees, Groups, Words, Finale – the story of a discovery in one field and its many manifestations in others, as a tribute to a great mathematical achievement and as an intellectual pleasure, contemplating the marvellous unity of all mathematics.
Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. There are 666 exercises, and every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.
The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" understandable and enjoyable.
In a society begging to be duped, Martin Gardner, the most devastating debunker of scientific fraud and chicanery of our time, ranges here from science and mathematics to literature, philosophy, religion, and mysticism. With keen skepticism, he skewers the fallacies of pseudoscience, from Dr. Bruno Bettelheim's erroneous theory of autism to the farce of Primal Scream therapy, and he examines the bizarre tangents produced by Freudians and deconstructionists in their critiques of "Little Red Riding Hood." Book jacket.
Perseverance is Remembrance" outlines the struggles, and strength, but also the endurance of heartbreak time and time again. This is a true and very personal story of my life. While it may seem long, it briefly skims the troubling experiences I have had in the past with single parenthood and dating to find someone to complete me. While today I am proud of my memories, this project has allowed me to reflect on my life and forced me to realize that people are seasonal and for good reasons. Even though Hakeem betrayed me, I share something with him that is more sacred than my own life. While Nate loved me, his love for something and someone else was much greater. And the pain I experienced as my face hit the ground, will always make me remember Tony. The tales told in this book didnt capture all but it did capture enough experiences in my life to make me realize that my life is what I make it and not what anyone else says it should be. These characters are real even though the names are fictitious. My story is my legacy and the legacy of so many other single parents today and by sharing my personal story, I am encouraged to show others that "Perseverance is Remembrance".
Syphilis, a sexually transmitted disease was first described in 15th century, is caused by Treponema pallidum subsp. pallidum and occurs worldwide. This book is a collection of chapters presenting the novel knowledge about the T. pallidum and some historical and up to date information about venereal disease and syphilis. The collection of articles includes: immunological aspects recognition of T. pallidum by the pattern recognition receptors of the innate immune; the whole genome analysis of treponemes and new targets for its molecular diagnosis; some historical aspects of venereal diseases treatment; natural history of syphilis including clinical manifestation and epidemiology; a clinical aspects dealing with psychiatric manifestations of neurosyphilis; spatial and temporal patterns of primary syphilis and secondary syphilis described by the spatial and space-time scan statistics; a commonly used methods for laboratorial diagnosis, the serological response to treatment of syphilis and safety in blood transfusion. I hope this book will be useful for students and research fellows as well for the wide audience.
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