Two sets are equal exactly if they contain the exact same elements. Function terminology examples i what is the range of this function. Integers aka whole numbers, rational numbers ones that can be expressed as the quotient of two integers, automobiles, houses, people etc. Many different systems of axioms have been proposed. Discrete mathematics is mathematics that deals with discrete objects. Instead of enumeration techniques and graph theory, the author discusses data structures, sets of.
But discrete mathematics deals with much more than just integers. Applied discrete structures al doerr university of massachusetts lowell ken levasseur university of massachusetts lowell may 12, 2019. What are some good books to learn discrete mathematics. The set is a welldefined collection of definite objects of perception or thought and the georg cantor is the father of set theory. We only give an informal description of sets and then proceed to establish their properties. Basic building block for types of objects in discrete mathematics.
Discrete mathematics uses a range of techniques, some of which is seldom found in its continuous counterpart. Discrete mathematical structures classic version 6th edition pearson modern classics for advanced mathematics series by bernard kolman, robert busby, et al. Sets, functions, sequences, sums, and matrices algorithms number theory and cryptography induction and recursion counting discrete probability advanced counting techniques. Rather, its a description of a set of branches of math that all have in common the feature that they are discrete rather than continuous. This is a text that covers the standard topics in a sophomorelevel course in discrete mathematics. Choose from 500 different sets of quiz 1 discrete math structures flashcards on quizlet. I supposed you could split that hair and say see, its just discrete mathematics warmed over. In this chapter, we will cover the different aspects of set theory.
Cantor developed the concept of the set during his study of the trigonometric series, which is now known as the limit point or the derived set operator. From this simple beginning, an increasingly complex and useful. What is the difference between discrete mathematics and symbolic logic. I bought this text because i am taking a college course in discrete structures this fall, 2011, for my major in computer science. The problem, originating from group theory, graph theory, and set theory can be worked out by the student with a network model involving computers to generate and analyze different scenarios. Learn discrete structures with free interactive flashcards. This course will roughly cover the following topics and speci c applications in computer science. A very important subject for a software engineer in his career. Set theory examples of set representation of a set famous sets in math equal sets equivalent sets empty set. Discrete structures are somewhat like constructs for discrete mathematics, but also deals with the topic matter. Discrete structures lecture notes vladlen koltun1 winter 2008 1computer science department, 353 serra mall, gates 374, stanford university, stanford, ca 94305, usa. Discrete structures are structures that are used in describing discrete mathematics. In reality, discrete mathematics is just that, math dealing with discrete values. Every piece of writing, whether it is a cover letter for a job application, a news article, or a fictional short story, has its own structure.
Issues about data structures used to represent sets and the computational cost of set operations. Cultivate a sense of familiarity and ease in working with mathematical notation and common concepts in discrete mathematics. Mathematics of discrete structures for computer science. Discrete implies noncontinuous and therefore discrete sets include finite and countable sets but not uncountable sets such as the real numbers. To expose you to some of the variation, we use two main resources, as well as include supplementary resources and our own original content.
Learn quiz 1 discrete math structures with free interactive flashcards. He developed two types of trans nite numbers, namely, trans nite ordinals and trans nite cardinals. Always, since our interest is in digital computation, our structures will be discrete. Empty set or null set, singleton set, finite set, infinite set, cardinal number of a set, equal sets. As such, the book is suitable for students who understand algebra and can program. In contrast to real numbers that have the property of varying smoothly, the objects studied in discrete mathematics such as integers, graphs, and statements in logic do not vary smoothly in this way, but have distinct, separated values. Free discrete mathematics books download ebooks online. Set theory and types of set in discrete mathematics. Discrete math is not the name of a branch of mathematics, like number theory, algebra, calculus, etc. Youcanthinkof ifandonlyifstatementsashavingtwoparts. How is discrete structures different from discrete math. While it might be true, i think its only a matter of focus. A set is an unordered collection of different elements.
Set theory forms the basis of several other fields of study like counting theory, relations, graph theory and finite state machines. Examples of discrete structures built with the help of sets. During a 12week term with three hours of classes per week, i cover most of the material in this book, except for chapter2, which has been included. The book is intended for sophomore or junior level, corresponding to the course b3, introduction to discrete structures, in the acm curriculum 68, as. A set may also be thought of as grouping together of single objects into a whole. What is the best book for studying discrete mathematics. These topics vary depending on the institution or school, course, instructor, and text. Teach the basic results in number theory, logic, combinatorics, and graph theory. A \wellde ned collection of distinct objects can be considered to be a set. Download discrete mathematical structures 6th edition. So i just started my discrete structures class, and im reading about sets only thing thats puzzling me, and the book doesnt explain really. Qand abackwardsdirection p q, whichisreallyjustsloppynotationfor q. Some of which are finite, infinite, subset, universal, proper, singleton set, etc.
Setset theory forms the basis of several other theory forms the basis of several other fields. Discrete structures lecture notes stanford university. Wealsosometimessaythat ifandonly if statements have two directions. My friend lent me his old discrete math book and it seemed to cover a great deal of the stuff symbolic logic covers. So im not sure if its that discrete math covers more details for if the focus is entirely different. A set can be written explicitly by listing its elements using set bracket. Therefore, discrete mathematics does not include calculus and analysis. Aslam rajmohan rajaraman eric ropiak chris burrows ravi sundaram college of computer and information science northeastern university boston, massachusetts. Discrete mathematicsset theory wikibooks, open books for an. His new and pathbreaking ideas were not well received by his contemporaries.
Hauskrecht basic discrete structures discrete math study of the discrete structures used to represent discrete objects many discrete structures are built using sets sets collection of objects examples of discrete structures built with the help of sets. Boolean functions and computer arithmetic, logic, number theory and cryptography, sets and functions, equivalence and order, induction, sequences and series. This book has ten chapters, and the first seven of them cover topics that are also covered at the beginning of all the wellknown discrete mathematics textbooks, such as formal logic, sets, and relations. For two sets a and b, the operations of union, intersection, and di. This video is an updated version of the original video released over two years ago. The standard topicsincluding propositional logic, predicate calculus, sets, relations, discrete structures, defining new structured types, numbers, and reasoning about programsare covered. A means that a is an element of a a is the set sets are equal if and only if they have the same elements. Sets and set operations cs 441 discrete mathematics for cs m. Number theory athe math behind the rsa crypto system. Two sets and are said to be equal if and only if they have exactly the same elements. Discrete objects are those which are separated from not connected todistinct from each other.
In addition, hein includes material relating important software concepts to abstract algebra, and he does this without slighting other common topics of discrete mathematics, such as sets, relations, functions, counting, automata, and computability. Two sets a and b are considered equal if and only if they have the same elements. Examples of objectswith discrete values are integers, graphs, or statements in logic. Discrete mathematics discrete mathematics study of mathematical structures and objects that are fundamentally discrete rather than continuous. Discrete structures for computer science george voutsadakis1 1mathematics and computer science. Discrete mathematics and its applications miri course list discrete mathematics and its applications contents. Today we introduce set theory, elements, and how to build sets. The different types of sets are explained below with examples. Elements of discrete mathematics virginia commonwealth university. Although discrete mathematics is a wide and varied field, there are certain rules that carry over into many topics. B from what ive gathered, x is in a or x is in b, because of the union. Choose from 443 different sets of discrete structures flashcards on quizlet.
In this video you will learn about types of sets in set theory where you different types of sets will be covered like equivalent sets, equal sets. With the growth of digital devices, especially computers, discrete mathematics has become more and more important. If youre looking for a free download links of discrete mathematical structures 6th edition pdf, epub, docx and torrent then this site is not for you. Hopefully this short introduction will shed some light on what the subject is about and what you can expect as you move. Discrete math knowledge is needed to become adept in proving the correctness and deriving the complexity of algorithms and data structures. Spiral workbook for discrete mathematics open textbook. Our use of standard terminology and notation makes applied discrete structures a valuable reference book for future courses. Unlike the many other ones mentioned above, discrete mathematics is not a branch, but a description of the study of mathematical structures that are discrete rather than continuous. We might say one is the if part, and theotheristhe onlyifpart. In this article, we will learn about the introduction of sets and the different types of set which is used in discrete mathematics. Discrete mathematics is math that makes use of discrete structures. Sets, discrete structures mathematics stack exchange.
You will be taught those in algods books, but you can only get the mathematical proficiency by practicing just discrete math. Discrete mathematicsset theory wikibooks, open books. Well now look at various ways in which sets may be related to one another. Discrete structures can be counted, arranged, placed into sets, and put into ratios with one another. Logic is an extensive field of study and selected topics are included in discrete structures. Discrete objects, in simple languages, are the countable objects such as integers. A function from ato b is an association to each element in aof. Discrete mathematicsdiscrete mathematics and itsand its. In this book, we will consider the intuitive or naive view point of sets. Hence, the need for a comprehensive text to scare the bejeebers out of me, and get a good, solid grasp of what the topic encompasses. Although calculus is not necessary to understand the ideas in this book.