Discrete Mathematics

Jean Gallier is a Professor in the Computer and Information Science Department, School of Engineering and Applied Science at the University of Pennsylvania.

• Mathematical Reasoning, Proof Principles and Logic.- Relations, Functions, Partial Functions.- Graphs, Part I: Basic Notions.-  Some Counting Problems; Multinomial Coefficients.- Partial Orders, GCD's, RSA, Lattices.- Graphs, Part II: More Advanced Notions.- Answers to Selected Problems.

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)