Hardcover

ISBN 10: 9814340502 ISBN 13: 9789814340502

Publisher: World Scientific Publishing Company, 2012

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 create a 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 relational calculus.

Readership: Any reader who is interested in understanding the mathematical foundations of computer science, software design and reasoning. For example, students in statistics, physics and computational biology.

From the Inside Flap:

This textbook presents all the fundamental topics of discrete mathematics that are introduced from the perspectives of a pure mathematician and an applied computer scientist. The integration of the two perspectives is seen throughout the book; key concepts are motivated and explained through real-world examples, and yet are still formalized with mathematical rigor. Thus, it is an excellent introduction to computer science and software engineering.

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 bring together two different perspectives to create a unified book for students interested in learning discrete mathematics, 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 (e.g., programs, graphs and numbers), investigate properties of algorithms, and prove their correctness. The textbook concentrates on the study of several well-known algorithmic problems (e.g., 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 (e.g., propositional logic), finite state machines, counting, probability, and the foundations of databases (e.g., relational calculus).

Review:

"It is an excellent choice as a textbook for a first course in discrete mathematics for both computer science and mathematics students, or for self-study by undergraduates in these and related areas." --Prof Denis R Hirschfeldt, University of Chicago

"It is one of the best textbooks in the current market. The textbook is easy and a pleasure to read yet presents a good challenge for a typical undergraduate student. It is written with an ease and informality on the one hand, and sufficient mathematical rigour on the other. The style of the textbook represents both an experienced mathematician and a talented programmer. Pedagogically, the textbook suits any beginner who wants to learn basic modern discrete mathematics and turn into one who can grasp sophisticated concepts such as finite state machines and induction techniques. This textbook written by father and daughter Khoussainovs is highly recommended as a standard undergraduate teaching material in discrete mathematics." --Prof Olga Kharlampovich, Hunter College, CUNY