كلية الهندسة - جامعة عين شمس, الرئيسية

الرئيسية  >  كلية الهندسة - جامعة عين شمس, الرئيسية

Discrete Mathematics

What Will Learn?

  • Course Aims
    By the end of this course, the student will be:  Familiar with propositional logic.  Aware of elementary number theory basic properties and definitions.  Able to use different methods of proof.  Familiar with sequences and their recurrence relations.  Explain and use the concepts of graphs and trees.
  • Course Goals
  • Quality Education

Requirements

Description

  • English Description

    Propositional logic: statements, logical connectives, quantifiers, truth tables, logical equivalence and arguments. Elementary number theory: even and odd, prime and composite, rational and irrational, divisibility, unique factorization theorem and floor and ceiling. Methods of proof: direct proof and counterexample, contradiction and contraposition and two classical theorems. Sequences, mathematical induction and recursion. Algorithms: big-O notation and complexity. Graphs and trees: definitions and basic properties, trails, paths, and circuits, planar graphs, matrix representations of graphs, function and relation definitions, equivalence relations (symmetric, reflexive and transitive properties), isomorphisms of graphs, rooted trees, spanning trees and shortest paths.
  • Arabic Description

    Propositional logic: statements, logical connectives, quantifiers, truth tables, logical equivalence and arguments. Elementary number theory: even and odd, prime and composite, rational and irrational, divisibility, unique factorization theorem and floor and ceiling. Methods of proof: direct proof and counterexample, contradiction and contraposition and two classical theorems. Sequences, mathematical induction and recursion. Algorithms: big-O notation and complexity. Graphs and trees: definitions and basic properties, trails, paths, and circuits, planar graphs, matrix representations of graphs, function and relation definitions, equivalence relations (symmetric, reflexive and transitive properties), isomorphisms of graphs, rooted trees, spanning trees and shortest paths.
  • قسم
    الفيزيقا والرياضيات الهندسية
  • الساعات المعتمدة
    3
  • الدرجات
    الإجمالي ( 100 ) = نصف العام (25) + tr.Student Activities (20 = tr.Industry 0% , tr.Project 5% , tr.Self_learning 0% , tr.Seminar 20% ) + tr.Oral/Practical (5) + درجة الامتحان (50)
  • الساعات
    ساعات المحاضرة: 3, ساعات التعليم: 1, ساعات المعمل: 0
  • Required SWL
    100
  • Equivalent ECTS
    4
  • - S. Epp., Discrete mathematics with applications. Nelson Education, 2010.
  • - O. Levin, Discrete mathematics: An open introduction. University of Northern Colorado; 2019.