Discrete structures lecture notes stanford university. Issues about data structures used to represent sets and the computational cost of set operations. Mathematics for computer science mit opencourseware. Instructors discrete mathematics lecture notes people. Lecture notes on discrete mathematics july 30, 2019. Slide set 0 c theodore norvell, memorial university discrete structures sets, functions, relations, trees, graphs are very useful for representing data in computers.
The text covers the mathematical concepts that students will encounter in many disciplines such as. This is an introductory course in discrete mathematics oriented toward computer science and engineering. Calculating probabilities for choosing the very best on a. But a sharp contrast between discrete and continuous mathematics is mainly a convenience. Mathematical logic, set theory, the real numbers, induction and recursion, summation notation, asymptotic notation, number theory, relations, graphs, counting, linear algebra, finite fields. This blog contains engineering notes, computer engineering notes,lecture slides, civil engineering lecture notes, mechanical engineering lectures ppt. Two computers in a network either are or are not directly. Malik teaches mathematics and computer science at creighton university. The course makes you familiar with basic concepts and notation, helps you to. He was solely responsible in ensuring that sets had a home in mathematics. Definitions, proofs, sets, functions, relations discrete structures. Free download engineering ppt pdf slides lecture notes seminars.
Discrete mathematics deals with the noncontinuous mathematics. An introduction to discrete mathematics and algorithms, 20, charles a. Lecture notes in discrete mathematics download book. 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. The discrete mathematics course tackles a selection of graph algorithms, which are studied from both the mathematical and computational point of view. In this unit, you will learn about sequences, series, probability, and statistics. Basic building block for types of objects in discrete mathematics. Discrete mathematics tutorial in pdf tutorialspoint.
I may keep working on this document as the course goes on, so these notes will not be completely. Notes on discrete mathematics 2 introduction these notes are intended to be a summary of the main ideas in course cs 310. Lecture notes and background materials for math 5467. Class notes for discrete mathematics note added 14 june 2008 these class notes were used for fifteen years in a discrete math class taught at. These lecture notes are based on the class material college discrete mathe matics for students in the. Lecture notes in discrete mathematics download link. Propositional equivalence, predicates and quantifiers, methods of proofs, proof strategy, sequences and summation, mathematical induction, recursive definitions and structural induction, program correctness.
Discrete mathematics and its applications, fifth edition, 2003, mcgrawhill. Notes on discrete mathematics northwestern university. This course will roughly cover the following topics and speci c applications in computer science. Lecture notes principles of discrete applied mathematics. Propositional equivalence, predicates and quantifiers, methods of proofs, proof strategy, sequences and summation, mathematical induction, recursive definitions and structural. We didnt finish doing this, but we introduced an idea corrected in these notes that prof. This is a course note on discrete mathematics as used in computer science. Lecture notes in discrete mathematics arkansas tech faculty web. The euclidean geometry furnishes an example of mathematical system. Discrete mathematics consists of many individual topics that, imprecisely, contrast with continuous mathematics, e. There are many examples in which it is natural and useful to limit our number.
Lecture and tutorial contents winter 2012 engineering. We often have the impression that graph algorithmic problems are either very basic. Number theory athe math behind the rsa crypto system. Discrete mathematics lecture notes linkedin slideshare.
The goal of this course is to introduce students to ideas and techniques from discrete mathematics that are widely used in science and engineering. The lecture schedule, course notes, and all assignments can be found in a single gigantic pdf file at. I may keep working on this document as the course goes on, so these notes will not be. This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. Many different systems of axioms have been proposed. Connecting a generator or load to a power grid is a discrete change. Richard kaye professor of mathematics university of birmingham chapter 11 sequences and. These are notes on discrete mathematics for computer scientists. We could then think of some more interesting in my opinion examples, such as the set n of all natural numbers.
Lecture notes for college discrete mathematics gabor horvath and szabolcs tengely 20. Discrete math for computer science students ken bogart dept. Edition 6 has been voted as the official edition for the course. Discrete mathematics uses a range of techniques, some of which is seldom found in its continuous counterpart. Discrete mathematics lecture notes, yale university, spring 1999 l. With few exceptions i will follow the notation in the book. To illustrate the idea, lets look at a small deck of cards. Preface this book is designed for a one semester course in discrete mathematics for sophomore or junior level students. Discrete mathematical structures nptel online videos. Discrete mathematics i cs127 lecture notes department of. Discrete mathematics discrete mathematics 574 unit 4 discrete mathematics discrete mathematics is the branch of mathematics that involves finite or discontinuous quantities. Tech cseit, discrete mathematical structures unit i logic.
Introduction to the mathematics of wavelets willard miller may 3, 2006. Contents 1 introduction from a signal processing point of view 7 2 vector spaces with inner product. P olyas enumeration theorem we started examining the number of essentially distinct colorings of an object with questions of the form \how many necklaces can be made with 3 black beads and white beads. Pdf discrete math lecture notes charles wells academia. This page intentionally left blank university of belgrade. Dec 07, 2016 preface this book is designed for a one semester course in discrete mathematics for sophomore or junior level students. A short course in discrete mathematics by edward a. Discrete mathematics lecture notes 2 december 8, 20 34. Mathematics for computer science electrical engineering. Rosen, discrete mathematics and its applications, sixth edition, mcgraw hill, 2007 or seventh edition, 2012. Discrete mathematics i cs127 lecture notes alexander tiskin university of warwick autumn term 200405 this course introduces some of the fundamental mathematical ideas that are used in the design and analysis of computer systems and software. Number theory for mathematical contests, 2007, david a.
The text covers the mathematical concepts that students will encounter in many disciplines such as computer science, engineering, business, and the sciences. Pdf discrete mathematics for computer science, some notes. These notes contain some questions and exercises intended to. Cantor developed the concept of the set during his study of the trigonometric series, which is now. Lecture notes glynn winskel c 2005, 2006, 2007 glynn winskel february 6, 2008. But a sharp contrast between discrete and continuous mathematics is. Besides reading the book, students are strongly encouraged to do all the. Discrete math chapter 1 notes mark dolan programming. Hutchinson these notes contain the material from discrete mathematics that you need to know in order to take the course in computability and complexity. Awedh spring 2008 course overview this is an introductory course in discrete mathematics.
Discrete structures lecture notes vladlen koltun1 winter 2008 1computer science department, 353 serra mall, gates 374, stanford university, stanford, ca 94305, usa. The numbers in parentheses give approximate pages and file sizes in the form pages ps, pdf. We now present three simple examples to illustrate this. Lecture notes for college discrete mathematics download book. Deviation of a sum on independent random variables. Lecture notes for college discrete mathematics, 20. He has published more than 45 papers and 15 books on abstract algebra, fuzzy automata theory and languages, fuzzy logic and its applications, information science, and programming. Two integers are congruent modulo 2 exactly if they have the same parity both are even or both are.
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