Discrete Structure CS 203 Introduction

Lecture 1

Computer science Computer science or computing science (abbreviated CS or CompSci) is the scientific approach to computation and its applications. A computer scientist specializes in the theory of computation and the design of computers or computational systems.

CS Branches Its subfields can be divided into a variety of theoretical and practical disciplines. computational complexity theory (which explores the fundamental properties of computational problems), are highly abstract

CS Branches computer graphics emphasize real-world applications. programming language theory considers various approaches to the description of computation, whilst the study of computer programming itself investigates various aspects of the use of programming language and complex systems. Human-computer interaction considers the challenges in making computers and computations useful, usable, and universally accessible to humans.

CS Mobile Computing Computer Architecture Natural Language Processing Robotics Computer Networks Software Engineering Database Administration Data Warehousing and Data Mining Game Development

CS Concurrent, Parallel, and Distributed Systems Communications and Security  Web Science Artificial Intelligence User Interface Engineering Image Processing Computer Aided Engineering

CS Bioinformatics Medical Informatics Cryptography Algorithm Analysis Simulation and Modeling Operating Systems Performance Analysis

CS Career Designing and implementing software. Devising new ways to use computers(application of computer technology) Database developer & admininnstrator Game programmer Graphic design

CS Career System administrator Software tester Web design & developer & administrator

Lecture 1

Lecture 1

Lecture 1

CS Courses Programming (C & C+ & Java) Graphics AI Networks Database Data structure Operating system Lecture 1

CS Courses Theory of Computation Digital circuits Algorithms Etc معفى من مادة س 100

CS Staff د ياسر فؤاد د احمد يونس د اسلام ثروت د احمد شريف د خالد محمد د اشرف سعيد Lecture 1

CS Staff مروة عابدين نرمين محمود يسر حسين سعيد محمد احمد صالح شيماء المرسى Lecture 1

CS Staff نيللى سارة احمد عبد القادر اية هدير ايمان خالد Lecture 1

CS labs معملين مبنى أ الدور الاول معمل سى كاب معمل د Lecture 1

Class web page, e-mail E-mail y.fouad@sci.alexu.edu.eg http://www.alexu.edu.eg/index.php/ar/2011-09-26-07-06-34/25-staff-courses/computer-science/3791-discreet-cs203 Alexandria university site  مواقع المقررات الدراسية E-mail y.fouad@sci.alexu.edu.eg

Problems solved using Discrete Math How many secure passwords? Probability of winning Texas Hold’em? How can I encrypt a message? Shortest paths between two cities using public transportation? How many steps required to sort 10,000 numbers? Is this algorithm correct? How to design a circuit that multiply two integers?

Course content very approximately in temporal order Logic and Reasoning Sets, Functions, Sequences and Sums Number Theory, Algorithms, the Integers Induction and Recursion Counting, Relations Graph Theory

Overall course context First course in CS Major Students will have taken CS102, CS201 Broad range of mathematical background of entering students Goals of the course Formalism for later study Learn how to do a mathematical argument for CS

Course Overview Discrete Structure is essentially that branch of Computer science & Mathematics. As computers are discrete object operating one jumpy, discontinuous step at a time, Discrete Struct is the right framework for describing precisely Computer Science concepts.

Quick Overview Discrete Sturcture helps provide… …the machinery necessary for creating sophisticated algorithms …the tools for analyzing their efficiency …the means of proving their validity

Graph Theory Euler Paths and Circuits In order to minimize cost to the city, how should weekly garbage collection routes be designed for Detroit’s 350,000 households? 2. Paraphrase the text on the slide.

Quick Overview - Topics Logic and Sets Make notions you’re already used to from programming a little more rigorous (operators) Fundamental to all mathematical disciplines Useful for digital circuits, hardware design Elementary Number Theory Get to rediscover the old reliable number and find out some surprising facts Very useful in crypto-systems

Quick Overview - Topics Proofs (especially induction) If you want to debug a program beyond a doubt, prove that it’s bug-free Proof-theory has recently also been shown to be useful in discovering bugs in pre-production hardware Counting and Combinatorics Compute your odds of winning lottery Important for predicting how long certain computer program will take to finish Useful in designing algorithms

Counting & Arranging How secure are your passwords? If your password consists of 3 letters and 3 numerals, how likely is it that someone could successfully guess the configuration? 7. Here is a topic which we have already explored: Algorithms for solving this type of problem involve the application of the Counting Principle, permutations and combinations. Introducing Bruce Budzynski, Mathematics Education Consultant, Michigan Department of Education.

Coding Information Identification Numbers What mathematics is involved in the design of UPC codes? 8. The binary numeration system as well as “remainder arithmetic (mod 10)” are used in the Universal Product Code. Place a face with the voice of M3RP , introducing Sue Simons, Project Secretary.

Grading The overall grade will be based upon 30% for homework or assignment, quiz, and lab 70% final Extra credit questions will be always available.

Quick Test... Count the green squares… you will have three seconds…

How many were there?