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Have you ever experienced any fascinating mathematical problems in real life but you do not know how to solve them? Would you like to know how mathematics approaches these problems? This course will give you a taste about those most fundamental methods in mathematics. Many interesting examples will be provided. Topics includes: logics, methods of proofs, mathematical induction, recursion, graphs, graph matching, graph coloring, sets, counting, binomial coefficients, inclusion-exclusion principle, functions, counting by mapping, and if time permitted, number sequences, modular arithmetic, Chinese remainder theorem etc.
This book is a textbook of discrete mathematics which is aimed to lay the mathematical foundation for computer science courses. It presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. The book is unique in a spiral approach to concept development. Concepts introduced include logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics. This fourth edition features expansion on the number of exercises, discussion of historical background and recent results, and directions for writing proofs and discussion of common mistakes.
This book covers the key combinatorial ideas–including the pigeon-hole principle, counting techniques, permutations and combinations, Pólya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, combinatorial structures (matchings, designs, graphs), and flows in networks. The chapters go successively through permutations and combinations, pigeonhole principle, counting techniques and properties of some of the resulting counting sequences, systems of distinct representatives, aspects of the vast theory of combinatorial designs, graphs, digraphs and network flows, and Burnside’s theorem. This fifth edition incorporates feedback from users to the exposition throughout and adds a wealth of new exercises.
This book introduces the concept and techniques of discrete mathematics, and stresses mathematical reasoning and the different ways problems are solved. Important themes interwoven in the text include mathematical reasoning, which serves as the foundation for the subsequent discussions of methods of proof; combinatorial analysis, which begins with the basic techniques of counting; discrete structures, which includes sets, permutations, relations, graphs, trees, and finite-state machines; algorithmic thinking, for computer program problem solving; and applications and modeling, not only in the field of computer science and data networking, but also to areas of chemistry, biology, linguistics, geography, business, and the Internet.
This book explains how to use mathematical models and methods to analyze problems that arise in computer science and engineering. Examining mathematical concepts and data types, the book emphasizes mathematical definitions and proofs as well as applicable methods. Topics covered in this text include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
