A Beginner's Guide to Discrete Mathematics

This introduction to discrete mathematics is aimed primarily at undergraduates in mathematics and computer science at the freshmen and sophomore levels. The text has a distinctly applied orientation and begins with a survey of number systems and elementary set theory. Included are discussions of scientific notation and the representation of numbers in computers. An introduction to set theory includes mathematical induction, and leads into a discussion of Boolean algebras and circuits. Relations and functions are defined. An introduction to counting, including the Binomial Theorem, is used in studying the basics of probability theory. Graph study is discussed, including Euler and Hamilton cycles and trees. This is a vehicle for some easy proofs, as well as serving as another example of a data structure. Matrices and vectors are then defined. The book concludes with an introduction to cryptography, including the RSA cryptosystem, together with the necessary elementary number theory, such as the Euclidean algorithm. Good examples occur throughout, and most worked examples are followed by easy practice problems for which full solutions are provided. At the end of every section there is a problem set, with solutions to odd-numbered exercises. There is a full index. A math course at the college level is the required background for this text; college algebra would be the most helpful. However, students with greater mathematical preparation will benefit from some of the more challenging sections.