Manual Discrete Mathematics and Its Applications (Higher Math)

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I still highly recommend it for those not familiar with the topics covered in the book. The Foundations: Logic and Proofs. Number Theory and Cryptography. Induction and Recursion. Discret e Probability.

Advanced Counting Techniques. Boolean Algebra. Modeling Computation. This chapter introduces propositional sentential logic, predicate logic, and proof theory at a very introductory level. It starts by introducing the propositions of propositional logic! It then goes on to introduce the idea of logical equivalence between sentences of propositional logic, before introducing quantifiers and predicate logic and its rules of inference.

It then ends by talking about the different kinds of proofs one is likely to encounter — direct proofs via repeated modus ponens , proofs by contradiction, proof by cases, and constructive and non-constructive existence proofs. This chapter illustrates exactly why this book is excellent as an introductory text. Additionally, it also explains the common pitfalls for the different proof methods that it introduces. This chapter introduces the different objects one is likely to encounter in discrete mathematics.

This chapter presents … surprise, surprise… algorithms! It starts by introducing the notion of algorithms, and gives a few examples of simple algorithms. It then spends a page introducing the halting problem and showing its undecidability. Afterwards, it introduces big-o, big-omega, and big-theta notation and then gives a very informal treatment of a portion of computation complexity theory. It's quite unusual to see algorithms being dealt with so early into a discrete math course, but it's quite important because the author starts providing examples of algorithms in almost every chapter after this one.

This section goes from simple modular arithmetic 3 divides 12! It then gives several applications of number theory: hash functions, pseudorandom numbers, check digits, and cryptography. The last of these gets its own section, and the book spends a large amount of it introducing RSA and its applications.

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This chapter introduces mathematical induction and recursion, two extremely important concepts in computer science. With these two results, we can conclude that the property is true of all natural numbers positive integers. The book then goes on to introduce strong induction and recursively defined functions and sets. From this, the book then goes on to introduce the concept of structural induction, which is a generalization of induction to work on recursively-defined sets.

Then, the book introduces recursive algorithms, most notably the merge sort, before giving a high level overview of program verification techniques.


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The book now changes subjects to talk about basic counting techniques, such as the product rule and the sum rule, before interestingly moving on to the pigeonhole principle. It then moves on to permutations and combinations, while introducing the notion of combinatorial proof , which is when we show that two sides of the identity count the same things but in different ways, or that there exists a bijection between the sets being counted on either side.

Finally, it gives algorithms that generate all the permutations and combinations of a set of n objects. Compared to other sections, I feel that a higher proportion of readers would be familiar with the results of this chapter and the one on discrete probability that follows it.

Other than the last section, which I found quite interesting but not particularly useful, I felt like I barely got anything from the chapter. In this section the book covers probability, a topic that most of LessWrong should be quite familiar with. Like most introductory textbooks, it begins by introducing the notion of sample spaces and events as sets, before defining probability of an event E as the ratio of the cardinality of E to the cardinality of S. We are then introduced to other key concepts in probability theory: conditional probabilities, independence, and random variables, for example.

The textbook takes care to flesh out this section with a discussion about the Birthday Problem and Monte Carlo algorithms. Again, aside from the applications, most of this stuff is quite basic. As you can tell by the length of this section, I found this chapter quite helpful nevertheless. Finally, after a long trip through various recurrence-solving methods, the textbook introduces the principle of inclusion-exclusion, which lets us figure out how many elements are in the union of a finite number of finite sets.

Finally, 7 chapters after the textbook talks about functions, it finally gets to relations. Relations are defined as sets of n-tuples, but the book also gives alternative ways of representing relations, such as matrices and directed graphs for binary relations.

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MATH Introduction to Discrete Mathematics

We conclude with two special types of relations: equivalence relations, which are reflexive, symmetric, and transitive; and partial orderings, which are reflexive, anti-symmetric, and transitive. You can also find solutions immediately by searching the millions of fully answered study questions in our archive.

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Introduction to Discrete Mathematics for Computer Science Specialization

Get Started. Select your edition Below by. Author: Kenneth H. Rosen, Kenneth Rosen. Discrete Mathematics and Its Applications 6th Edition. ISBN Author: Kenneth H Rosen. How is Chegg Study better than a printed Discrete Mathematics and Its Applications student solution manual from the bookstore? Can I get help with questions outside of textbook solution manuals? How do I view solution manuals on my smartphone?