About this book
This book gives an introduction to discrete mathematics for beginning undergraduates and starts with a chapter on the rules of mathematical reasoning.
This book begins with a presentation of the rules of logic as used in mathematics where many examples of formal and informal proofs are given. With this logical framework firmly in place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book deals with functions and relations, directed and undirected graphs and an introduction to combinatorics, partial orders and complete induction. There is a section on public key cryptography and RSA, with complete proofs of Fermat's little theorem and the correctness of the RSA scheme, as well as explicit algorithms to perform modular arithmetic. The last chapter provides more graph theory where Eulerian and Hamiltonian cycles are discussed. This book also includes network flows, matchings, covering, bipartite graphs, planar graphs and state the graph minor theorem of Seymour and Robertson.
The book is highly illustrated and each chapter ends with a list of problems of varying difficulty. Undergraduates in mathematics and computer science will find this book useful.
- Book Title Discrete Mathematics
- Series Title Universitext
- DOI https://doi.org/10.1007/978-1-4419-8047-2
- Copyright Information Springer Science+Business Media, LLC 2011
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Softcover ISBN 978-1-4419-8046-5
- eBook ISBN 978-1-4419-8047-2
- Edition Number 1
- Number of Pages XIV, 466
- Number of Illustrations 200 b/w illustrations, 20 illustrations in colour
Computer Imaging, Vision, Pattern Recognition and Graphics
Applications of Mathematics
- Buy this book on publisher's site
From the reviews:
“This well-written, highly illustrated book will be very useful and interesting to students in both mathematics and computer science. … Attractive features of this book include clear presentations, end-of-chapter summaries and references, a useful set of problems of varying difficulty, and a symbol as well as a subject index. Summing Up: Highly recommended. Upper-division undergraduates, graduate students, and professionals/practitioners.” (D. V. Chopra, Choice, Vol. 48 (11), July, 2011)
“This book is intended to be a textbook for students in Computer Science, covering basic areas of Discrete Mathematics. … lots of references to supplementary or more advanced literature are provided, and less basic and more sophisticated problems as well as connections to other areas of science are given. Each chapter closes with a rich collection of exercises, which often include hints to their solution and further explanations.” (Martina Kubitzke, Zentralblatt MATH, Vol. 1227, 2012)
“This book provides a rigorous introduction to standard topics in the field: logical reasoning, sets, functions, graphs and counting techniques. Its intended audience is computer science undergraduate students, but could also be used in a course for mathematics majors. … Each chapter has a summary and a generous number of exercises … . The exposition is structured as a series of propositions and theorems that are proved clearly and in detail. Historical remarks and an abundance of photographs of mathematicians enliven the text.” (Gabriella Pinter, The Mathematical Association of America, February, 2012)