Discrete Mathematics with Applications 5th Edition Pdf Book Description:
Discrete mathematics describes processes that consist of a sequence of individual steps. This contrasts with calculus, which describes processes that change in a continuous fashion. Whereas the ideas of calculus were fundamental to the science and technology of the industrial revolution, the ideas of discrete mathematics underlie the science and technology of the computer age. The main themes of a first course in discrete mathematics are logic and proof, induction and recursion, discrete structures, combinatorics and discrete probability, algorithms and their analysis, and applications and modeling. Logic and Proof Probably the most important goal of a first course in discrete mathematics is to help students develop the ability to think abstractly. This means learning to use logically valid forms of argument and avoid common logical errors, appreciating what it means to reason from definitions, knowing how to use both direct and indirect arguments to derive new results from those already known to be true, and being able to work with symbolic representations as if they were concrete objects.combinatorics and discrete Probability Combinatorics is the mathematics of counting and arranging objects, and probability is the study of laws concerning the measurement of random or chance events. Discrete probability focuses on situations involving discrete sets of objects, such as finding the likelihood of obtaining a certain number of heads when an unbiased coin is tossed a certain number of times. Skill in using combinatorics and probability is needed in almost every discipline where mathematics is applied, from economics to biology, to computer science, to chemistry and physics, to business management.
DISCRETE MATHEMATICS WITH APPLICATIONS, 5th Edition, clarifies complicated, abstract concepts with clarity and accuracy and offers a solid foundation for computer science and also upper-level math classes of the computer era. Writer Susanna Epp gifts not just the significant topics of discrete mathematics, but also the rationale that underlies mathematical notion. Students develop the capacity to think abstractly because they examine the thoughts of logic and evidence. While learning about these theories as logic circuits and pc accession, algorithm evaluation, recursive thinking, computability, automata, cryptography and combinatorics, pupils discover the notions of discrete mathematics underlie and are crucial to the current science and engineering. algorithms and their analysis The word algorithm was largely unknown in the middle of the twentieth century, yet now it is one of the first words encountered in the study of computer science. To solve a problem on a computer, it is necessary to find an algorithm, or step-by-step sequence of instructions, for the computer to follow. Designing an algorithm requires an understanding of the mathematics underlying the problem to be solved. Determining whether or not an algorithm is correct requires a sophisticated use of mathematical induction. Calculating the amount of time or memory space the algorithm will need in order to compare it to other algorithms that produce the same output requires knowledge of combinatorics, recurrence relations, functions, and O-, V-, and Q-notations.