Discrete optimization problems discrete optimization or combinatorial optimization means searching for an optimal solution in a finite or countably infinite set of potential solutions. About applied discrete stuctures applied discrete stuctures by al doerr and ken levasseur is a free open content textbook. We schedule the midterm at the beginning of the quarter so. Subscribe to the applied discrete structures blog to keep up to date on the progress of this project. Today we introduce set theory, elements, and how to build sets. Applied discrete structures al doerr university of massachusetts lowell ken levasseur university of massachusetts lowell may 12, 2019. Discrete mathematics deals with objects that come in discrete bundles, e. Discrete mathematics and its applications seventh edition. This course is an introduction to discrete mathematics for computer science. Chapter combinatorics discrete structures 4 example 2. It appears that enough readers are interested in the. Each element from the set 1, 2, ncan map the set 0, 1 in 2 ways. In reality, discrete mathematics is just that, math dealing with discrete values.
We talk about what statements are and how we can determine truth values. The objects in a set are called the elements, or members, of the set. In contrast, continuous mathematics deals with objects that vary continuously, e. Manohar, discrete mathematical structure with applications to computer science, mcgraw hill. Y denotes the set of all total functions from x to y, and yn denotes y y y n times. The material is o ered as the secondyear course comp 2804 discrete structures ii. In particular, this class is meant to introduce logic, proofs, sets, relations, functions, counting, and probability, with an emphasis on applications in computer science. We discuss several definitions and give examples of their applications. This study guide is written to accompany discrete structures, logic, and computability, third edition, by james l. A course in discrete structures cornell university. Discrete mathematics and its applications seventh edition kenneth rosen. Discrete mathematics is math that makes use of discrete structures.
How many elements of a given type must there be so that we can guarantee that some property. For example, if we have a finite set of objects, the function can be defined as a list of ordered pairs having these objects, and can be presented as a complete list of those pairs. I am away have a conflict at the scheduled midterm time. How many functions are there from the set 1, 2, n, where n is a positive integer, to the set 0, 1. For example, the set 2,4,17,23 is the same as the set 17,4,23,2. In other words, the first term of the sequence is 0, the next is 1, and each one afterwards is the sum of the two preceding terms. This concept is the starting pointonwhichwewillbuildmorecomplexideas,muchasingeometrywhere the concepts of point and line are left undefined. To expose you to some of the variation, we use two main resources, as well as include supplementary resources and our own original content. We have begun to embed some related material into webpages with sage cells. Will it be possible to take the midterm at another time. Aslam rajmohan rajaraman eric ropiak chris burrows ravi sundaram college of computer and information science. Discrete mathematics tutorial in pdf tutorialspoint.
It deals with continuous functions, differential and integral calculus. These topics vary depending on the institution or school, course, instructor, and text. The sage cell server is an opensource, scalable, and easytouse web interface to sage, a comprehensive opensource math software system. Discrete structures study guide chapter 2 number 1. Discrete structures study guide chapter 10 number 1. Discrete mathematical structures by tremblay and manohar pdf. You can essentially share it with anyone as long as you leave the creative commons license in place. Cs381 discrete structuresdiscrete mathematics web course. 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. In computer science, we frequently use the following additional notation these notation can be viewed as short hands. Discrete structures lecture notes vladlen koltun1 winter 2008 1computer science department, 353 serra mall, gates 374, stanford university, stanford, ca 94305, usa.
The purpose of this course is to understand and use abstract discrete structures that are backbones of computer science. Sets, relations and functions, sequences, sums, cardinality of sets richard mayr university of edinburgh, uk richard mayr university of edinburgh, uk discrete mathematics. Think of digital watches versus analog watches ones where the second hand loops around continuously without stopping. Hopefully this short introduction will shed some light on what the subject is about and what you can expect as you move forward in your studies. We conclude with several exercises from our text that are similar to those that are assigned. Discrete vs continuous examples of discrete data number of boys in the class. Most of the learning objectives are statements of the form, be able to. Jul 17, 2017 today we introduce propositional logic. Discrete structures introduces readers to the mathematical structures and methods that form the foundation of computer science and features multiple techniques that readers will turn to regularly throughout their careers in computer and information sciences. Cs381 discrete structures discrete mathematics web course material last update august 2, 2009 note. Welcome to csc 3, a course in discrete structures with an emphasis on applications to computer science. To introduce the student to the mathematical tools of logic and induction, and to the basic definitions and theorems concerning relations, functions, and sets. Discrete structures lecture notes stanford university.
The term set is intuitively understood by most people to mean a collection of objects that are called elements of the set. Venn diagrams of sets s, t, and v under universe u. Discrete structures are somewhat like constructs for discrete mathematics, but also deals with the topic matter. View discrete structures study guide chapter 2 number 1. View discrete structures study guide chapter 10 number 1. This video is an updated version of the original video released over two years ago. Discrete mathematics introduction to propositional logic. Discrete structures cs 335 mohsin raza university institute of information technology pmas arid agriculture university rawalpindi 2.
Given a set sand a natural number n2n, snis the set of length n\strings equivalently ntuples with alphabet. Logic is an extensive field of study and selected topics are included in discrete structures. We schedule the midterm at the beginning of the quarter so that you have plenty of time to plan. Reasonable efforts have been made to test interactive exercises and tools that have been developed here. Discrete structures are structures that are used in describing discrete mathematics. Discrete structures logic and computability solutions. Optimality is defined with respect to some criterion function, which is to be minimized or maximized. Propositional logic richard mayr university of edinburgh, uk richard mayr university of edinburgh, uk discrete mathematics.
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