A clear and self-contained introduction to discrete mathematics for undergraduates and early graduates. This second edition of Invitation to Discrete Mathematics is a clear and self-contained introduction to discrete mathematics. Aimed mainly at undergraduate and early graduate students of mathematics and computer science, it is written with the goal of stimulating interest in mathematics and an active, problem-solving approach to the presented material. The reader is led to an understanding of the basic principles and methods of actuallydoing mathematics (and having fun atthat). By focussing on a more selective range of topics than many discrete mathematics textbooks, allowing greater depth of treatment using a number of different approaches, the book reflects the conviction of the authors, active andinternationally renowned mathematicians, that the most important gain fromstudying mathematics is the cultivation of clear and logical thinking and habits useful for attacking new problems. More than 400 enclosed exercises with awide range of difficulty, many of them accompanied by hints for solution, support this approach to teaching. The readers will appreciate the lively and informal style of the text accompanied by more than 200 drawings and diagrams. Specialists in various parts of science with a basic mathematical education wishing to apply discretemathematics in their field can use the book as a useful source, and even experts in combinatorics may occasionally learn from pointers to research literature or from presentations of recent results. Invitation to Discrete Mathematicsshould make delightful reading both for beginners and for mathematicalprofessionals.The main topics include: elementary counting problems, asymptotic estimates, partially ordered sets, basic graph theory and graph algorithms, finite projective planes, elementary probability and the probabilistic method, generating functions, Ramsey's theorem, and combinatorial applications of linear algebra.General mathematical notions going beyond the high-school level are thoroughly explained in the introductory chapter. An appendix summarizes the undergraduate algebra needed in some ofthe more advanced sections of the book. INDICE: Preface to the second edition Preface to the first edition Introduction and basic concepts Orderings Combinatorial counting Graphs: an introduction Trees Drawing graphs in the plane Double-counting The number of spanning trees Finite projective planes Probability and probabilistic proofs Order from disorder: Ramsey's theorem Generating functions Applications of linear algebraAppendix Bibliography Hints to selected exercises Index
- ISBN: 978-0-19-857042-4
- Editorial: Oxford University
- Encuadernacion: Rústica
- Páginas: 464
- Fecha Publicación: 09/10/2008
- Nº Volúmenes: 1
- Idioma: Inglés