This textbook presents fundamental topics in discrete mathematics introduced from the perspectives of a pure mathematician and an applied computer scientist. The synergy between the two complementary perspectives is seen throughout the book; key concepts are motivated and explained through real-world examples,and yet are still formalized with mathematical rigor. The book is an excellent introduction to discrete mathematics for computer science, software engineering, and mathematics students. The first author is a leading mathematician in the area of logic, computability, and theoretical computer science, with more than 25 years of teaching and research experience. The second author is a computer science PhD student at the University of Washington specializing in database systems. The father-and-daughter team merges two different views to createa unified book for students interested in learning discrete mathematics, the connections between discrete mathematics and computer science, and the mathematical foundations of computer science. Readers will learn how to formally define abstract concepts, reason about objects (such as programs, graphs and numbers), investigate properties of algorithms, and prove their correctness. The textbook studies several well-known algorithmic problems including the path problem for graphs and finding the greatest common divisor, inductive definitions,proofs of correctness of algorithms via loop invariants and induction, the basics of formal methods such as propositional logic, finite state machines, counting, probability, as well as the foundations of databases such as relationalcalculus. INDICE: Definitions, Theorems, and Proofs; Proof Methods; Integers and Divisibility; Euclidean Algorithm and Congruence Relations; Secret Message Passing; Basics of Directed Graphs; The Path Problem and Undirected Graphs; Circuit Problems in Graphs; Rooted Trees; Sets and Operations on Sets; Relations on Sets; Equivalence Relations and Partial Orders; Databases and Relational Structures; Relational Calculus; Program Correctness Through Loop Invariants; Induction and Recursion; Spanning Trees; Shortest Paths in Directed Weighted Graphs; Games Played on Finite Graphs; Functions; Types of Functions; Syntax of Propositional Logic; Semantics of Propositional Logic; Normal Forms and the SAT Problem; Deterministic Finite Automata; Designing Finite Automata; Nondeterministic Finite Automata; The Subset Construction; Regular Expressions and Finite Automata; Algorithms for Finite Automata; Counting Principles; Permutations and Combinations; Basics of Probability.
- ISBN: 978-981-4340-50-2
- Editorial: World Scientific
- Encuadernacion: Cartoné
- Páginas: 364
- Fecha Publicación: 21/05/2012
- Nº Volúmenes: 1
- Idioma: Inglés