Mathematics of Discrete Structures for Computer Science

This well-balanced introduction to enterprise risk management integrates quantitative and qualitative approaches and motivates key mathematical and statistical methods with abundant real-world cases - both successes and failures. Worked examples and end-of-chapter exercises support readers in consolidating what they learn. The mathematical level, which is suitable for graduate and senior undergraduate students in quantitative programs, is pitched to give readers a solid understanding of the concepts and principles involved, without diving too deeply into more complex theory. To reveal the connections between different topics, and their relevance to the real world, the presentation has a coherent narrative flow, from risk governance, through risk identification, risk modelling, and risk mitigation, capped off with holistic topics - regulation, behavioural biases, and crisis management - that influence the whole structure of ERM. The result is a text and reference that is ideal for gradu

This book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions to aid readers in understanding the presented topics. "Safe" - that is, paradox-free - informal set theory is introduced following on the heels of Russell's Paradox as well as the topics of finite, countable, and uncountable sets with an exposition and use of Cantor's diagonalisation technique. Predicate logic "for the user" is introduced along with axioms and rules and extensive examples. Partial orders and the minimal condition are studied in detail with the latter shown to be equivalent to the induction principle. Mathematical induction is illustrated with several examples and is followed by a thorough exposition of inductive definitions of functions and sets. Techniques for solving recurrence relations i

Discrete Mathematics: Essentials and Applications offers a comprehensive survey of the area, particularly concentrating on the basic principles and applications of Discrete Mathematics. This up-to-date text provides proofs of significance, keeping the focus on numerous relevant examples and many pertinent applications. Written in a simple and clear tone, the title features insightful descriptions and intuitive explanations of all complex concepts and ensures a thorough understanding of the subject matter.