Discrete Mathematics for Computer Science

Slides:

Advertisements

Similar presentations

Properties of Regular Sets

Advertisements

College of Information Technology & Design

Introductory Lecture. What is Discrete Mathematics? Discrete mathematics is the part of mathematics devoted to the study of discrete (as opposed to continuous)

Courtesy Costas Busch - RPI1 A Universal Turing Machine.

Math 308 Discrete Mathematics Discrete Mathematics deals with “Separated” or discrete sets of objects (rather than continuous sets) Processes with a sequence.

CPSC 411, Fall 2008: Set 12 1 CPSC 411 Design and Analysis of Algorithms Set 12: Undecidability Prof. Jennifer Welch Fall 2008.

1 Linear Bounded Automata LBAs. 2 Linear Bounded Automata are like Turing Machines with a restriction: The working space of the tape is the space of the.

CSE115/ENGR160 Discrete Mathematics 03/03/11 Ming-Hsuan Yang UC Merced 1.

1 Lecture 2 Topics –Importance of this material Fundamental Limitations –Connecting Problems and Languages Problems –Search, function and decision problems.

Sequence A list of objects arranged in a particular order.

Chapter 1 Introduction to C Programming. 1.1 INTRODUCTION This book is about problem solving with the use of computers and the C programming language.

Fall 2004COMP 3351 A Universal Turing Machine. Fall 2004COMP 3352 Turing Machines are “hardwired” they execute only one program A limitation of Turing.

1 CS1001 Lecture Overview Midterm Midterm OOP Wrap-up OOP Wrap-up Functions, Hilbert’s Hotel Functions, Hilbert’s Hotel.

Copyright © Cengage Learning. All rights reserved.

Map Coloring to Graph Coloring Part of a unit on discrete mathematics.

Nama : Jehan binti Jamian No.matrik : UK Discrete Mathematics Area of mathematics that deals with the study of discrete objects. Discusses languages.

Functions Definition & purpose Notation Functions on binary / returning binary values Finite automaton model We haven’t completely left the world of counting.

Introduction to CS Theory Lecture 3 – Regular Languages Piotr Faliszewski

Korea Advanced Institute of Science and Technology, Dept. of EECS, Div. of CS, Information Systems Lab. 1/10 CS204 Course Overview Prof.

Relationships Between Structures “→” ≝ “Can be defined in terms of” Programs Groups Proofs Trees Complex numbers Operators Propositions Graphs Real.

Lecture 4 Sequences CSCI – 1900 Mathematics for Computer Science Fall 2014 Bill Pine.

Discrete Distributions The values generated for a random variable must be from a finite distinct set of individual values. For example, based on past observations,

DISCRETE COMPUTATIONAL STRUCTURES CS Fall 2005.

Major objective of this course is: Design and analysis of modern algorithms Different variants Accuracy Efficiency Comparing efficiencies Motivation thinking.

Week 10Complexity of Algorithms1 Hard Computational Problems Some computational problems are hard Despite a numerous attempts we do not know any efficient.

A Universal Turing Machine

Simulation is the process of studying the behavior of a real system by using a model that replicates the system under different scenarios. A simulation.

CS1Q Computer Systems Lecture 11 Simon Gay. Lecture 11CS1Q Computer Systems - Simon Gay 2 The D FlipFlop The RS flipflop stores one bit of information.

1 Principles of Information Technology Introduction to Software and Information Systems Copyright © Texas Education Agency, All rights reserved.

1 Linear Bounded Automata LBAs. 2 Linear Bounded Automata (LBAs) are the same as Turing Machines with one difference: The input string tape space is the.

1 Turing’s Thesis. 2 Turing’s thesis: Any computation carried out by mechanical means can be performed by a Turing Machine (1930)

CS1001 Lecture 7. Overview Computer Networks Computer Networks The Internet The Internet Internet Services Internet Services Markup Languages Markup Languages.

CompSci 102 Discrete Math for Computer Science February 7, 2012 Prof. Rodger Slides modified from Rosen.

Beginning Fortran Introduction 13 October 2009 *Black text on white background provided for easy printing.

Onlinedeeneislam.blogspot.com1 Design and Analysis of Algorithms Slide # 1 Download From

An Introduction to Quantum Computation Sandy Irani Department of Computer Science University of California, Irvine.

What is Discrete Math?. “Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.” mathematicalstructuresdiscrete.

Introductory Lecture. What is Discrete Mathematics? Discrete mathematics is the part of mathematics devoted to the study of discrete (as opposed to continuous)

1 A Universal Turing Machine. 2 Turing Machines are “hardwired” they execute only one program A limitation of Turing Machines: Real Computers are re-programmable.

Discrete Structures MT217 Lecture 01. Course Objectives Express statements with the precision of formal logic Analyze arguments to test their validity.

CS 2130 Computational Structures (Discrete Mathematics for Computing)

Data and Computer Communications Chapter 7 Circuit Switching and Packet Switching.

CSE15 Discrete Mathematics 03/06/17

Introduction to Discrete Probability

A Universal Turing Machine

CS 461 – Nov. 2 Sets Prepare for ATM finite vs. infinite Infinite sets

Computable Functions.

CSCI-235 Micro-Computer Applications

CIS Automata and Formal Languages – Pei Wang

MATH 224 – Discrete Mathematics

Principles of Information Technology

CS 21a: Intro to Computing I

Cardinality of Sets Section 2.5.

Functions Defined on General Sets

Discrete Mathematics and Its Applications

CSCE 411 Design and Analysis of Algorithms

Objective of This Course

CS 201 Fundamental Structures of Computer Science

Chapter 1 Introduction(1.1)

Discrete Math for CS CMPSC 360 LECTURE 43 Last time: Variance

Copyright © Cengage Learning. All rights reserved.

Unsigned Binary Encoding

Discrete Mathematics in the Real World

Cardinality Definition: The cardinality of a set A is equal to the cardinality of a set B, denoted |A| = |B|, if and only if there is a one-to-one correspondence.

Everything is an Integer Countable and Uncountable Sets

Circuit Switched Network

Discrete Mathematics and Its Applications

Microprocessor I 7/18/2019.

Turing Machines Everything is an Integer

Presentation transcript:

Discrete Mathematics for Computer Science Prof. Sandy Irani

What is Discrete Math?

What is Discrete Math? “Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.” [ wikipedia.com ]

What is Discrete Math? “Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous…. A distinct object takes on distinct, separate values.” [ wikipedia.com ]

Continuous/Discrete Set Example The set of real numbers is continuous. The set of integers is discrete.

A Continuous Function f(x) f(x) = x2-3x-4 x

A Discrete Function f(x) f(x) = x2-3x-4 x

Discrete math is typically concerned with sets of objects that are either: Finite One-to-one correspondence with the integers (countably infinite): For example the set of all binary strings: 0, 1, 00, 01, 10, 11, 000, 001, 010, 011, 110,… 1 2 3 4 5 6 7 8 9 10 11…….

1010111010101010101 1010101111110101000101001 101010101111101010101110110 111101010000000101001011001 101010000101000101010111010 100001010010101010101010 1010101101010101…

Discrete Structures in CS Circuits 0/1 0/1 0/1 0/1

Discrete Structures in CS: Networks

Discrete Structures in CS: Codes

Discrete Mathematics Mathematical language to specify discrete structures Tools to mathematically analyze discrete structures Proofs to formally establish facts about discrete structures

Discrete Math in CS Design a network connecting a set of devices that will minimize congestion. How likely is it that the network will become disconnected of communication links fail with a certain probability? What is the best assignment of tasks to computers in a distributed network that will even out the computational load on each computer?

Discrete Math in CS What is the most efficient way to encode a file so that if characters are lost in transmission the file can still be recovered? Given a desired input/output relationship for a circuit, what is the most efficient circuit (minimum number of gates) that will compute that function? How long does it take this program to run on an input file of a particular length?