The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. The text covers the mathematical concepts that students will encounter in many disciplines such as computer science, engineering, business, and the sciences. We wrap up the section on counting by doing a few practice problems and showing the intuitions behind solving each problem. Cs 70 discrete mathematics and probability theory fall 2009 satish rao,david tse note 9 counting in the next major topic of the course, we will be looking at probability. For solving these problems, mathematical theory of counting are used. A set is an unordered collection of different elements. Besides reading the book, students are strongly encouraged to do all the. Mathematical logic, set theory, the real numbers, induction and recursion, summation notation, asymptotic notation, number theory, relations, graphs, counting, linear algebra, finite fields.
Suppose that i love discrete math tshirts come in five different. Share copy and redistribute the material in any medium or format adapt remix, transform, and build upon the material under the following terms. Basic counting department of computer science university of. Chapter 11 counting methods and probability theory 468 copyright 2015 pearson education, inc. Counting 101 pdf first law of countingmultiplying the possibilities.
This tutorial includes the fundamental concepts of sets, relations and functions, mathematical logic, group theory, counting theory, probability, mathematical induction, and recurrence relations, graph theory, trees and. Bookmark file pdf grimaldi discrete and combinatorial mathematics solutions grimaldi discrete and combinatorial mathematics solutions combinatoricsdiscrete math ii entire course discrete mathematics book i used for self study this is a book that i used for self study when i was learning discrete mathematics. For one thing, discrete probability theory illustrates how a lot of fairly dry material from chapter 4 is used. It is essential to understand the number of all possible outcomes for a series of events. This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. This course will roughly cover the following topics and speci c applications in computer science. Hopefully this short introduction will shed some light on what the subject is about and what you can expect as you move. The different ways in which 10 lettered pan numbers can be generated in such a way that the first five letters are capital alphabets and the next four are digits and the last is again a capital letter. Discrete mathematics introduction to graph theory duration. Next come chapters on logic, counting, and probability. However, the rigorous treatment of sets happened only in the 19th century due to the german math ematician georg cantor. Hauskrecht counting assume we have a set of objects with certain properties counting is used to determine the number of these objects examples. Instead, we will use what is callednaive set theory.
This is a course note on discrete mathematics as used in computer science. The first topic is infinity, where the notions of sets and functions will be introduced. Discrete mathematics counting theory tutorialspoint. Discrete structures lecture notes vladlen koltun1 winter 2008 1computer science department, 353 serra mall, gates 374, stanford university, stanford, ca 94305, usa. Discrete mathematics counting theory in daily lives, many a times one needs to find out the number of all possible outcomes for a series of events. How many bitstrings of length 8 start either with a bit 1 or end with 00. The number of choices decreases by 1 each time a sentence is. Often, we are interested in the cardinality of some nite set. This is a free textbook for an undergraduate course on discrete structures for computer science students, which i have been teaching at carleton university since the fall term of 20. It is always fascinating to see how geometricallyinspired concepts like orbits and stabilizers and transformations can be exploited to attack tricky counting problems. Dec 21, 2018 we introduce the rule of sum addition rule and rule of product product rule in counting. A set can be written explicitly by listing its elements using set bracket. For these students the current text hopefully is still of interest, but the intent is not to provide a solid mathematical foundation for computer science, unlike the majority of textbooks on the subject.
Infinity, graph theory, and cryptography this course will serve as an introduction to three topics, highlighting different ways of thinking and doing mathematics. The material is o ered as the secondyear course comp 2804 discrete structures ii. Ramsey theory studies problems of the following form. Discrete mathematics introduction to number theory instructor. Set theory forms the basis of several other fields of study like counting theory, relations, graph theory and finite state machines. The mathematical theory of counting is known as combinatorial analysis. This course serves both as an introduction to topics in discrete math and as the introduction to proofs course for math majors. Along the way, we recall some notions from discrete mathematics that. Counting colin stirling informatics slides originally by kousha etessami colin stirling informatics discrete mathematics chapter 6 today 1 39. This page intentionally left blank university of belgrade. The mathematics in these applications is collectively called discrete mathematics. Dec 21, 2014 discrete mathematics counting practice. Discrete mathematicsdiscrete mathematics and itsand its applicationsapplications seventh editionseventh edition chapter 4chapter 4 number theorynumber theory lecture slides by adil aslamlecture slides by adil aslam mailto.
Discrete mathematics counting saad mneimneh 1 n choose k consider the problem of seating n people on n chairs. Counting 101 pdf first law of counting multiplying the possibilities. Lets come up with an algorithm that generates a seating. Counting mainly encompasses fundamental counting rule, the permutation rule, and the.
Welcome to discrete mathematics 1, a course introducing set theory, logic, functions, relations, counting, and proofs. Two words that we shall often use are set and list. Lecture notes for college discrete mathematics download book. Product rule a count decomposes into a sequence of dependent counts. If there are m ways for one activity to occur, and n ways for a second activity to occur, then there are mn ways for both to occur. Discrete mathematics introduction to number theory 119 introduction to number theory i number theory is the branch of mathematics that deals with integers and their properties i number theory has a number of applications in computer. Grimaldi discrete and combinatorial mathematics solutions.
Discrete mathematics counting theory in discrete mathematics. Richard mayr university of edinburgh, uk discrete mathematics. 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. The aim of this book is not to cover discrete mathematics in depth it should be clear. He was solely responsible in ensuring that sets had a home in mathematics. Number theory athe math behind the rsa crypto system. In this chapter, we will cover the different aspects of set theory. Discrete mathematics rule of sum and rule of product. Hauskrecht basic counting rules counting problems may be hard, and easy solutions are not obvious approach. Cs 70 discrete mathematics and probability theory counting. Dieter van melkebeek updates by beck hasti and gautam prakriya in this reading we discuss counting. Below, you will find the videos of each topic presented. Discrete here is used as the opposite of continuous. Tricks to make counting harder for students discrete mathematics.
Basic counting introduction before beginning, we must confront some matters of notation. Discrete mathematics is the branch of mathematics dealing with objects that can consider only distinct, separated values. If you search this site for group theory, coloring and combinatorics you will get lots of interesting questions and answers related to the applications of group theory to counting. For example in discrete probability theory, which we wont get to in this course, we want to. Discrete mathematics uses a range of techniques, some of which is seldom found in its continuous counterpart. Some of those in use are apple banana pear peach a list of four items. Discrete mathematics old rule of sum and rule of product duration. Also, there no question that probability theory plays a crucial role in computing, for example, in the design of randomized algorithms and in the probabilistic analysis of algorithms. Nov 25, 2016 number theory in discrete mathematics 1. If we are dealing with the occurrence of more than one event or activity, sometimes it is important to be able to determine how many possible outcomes exist.
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