• Discrete Mathematics (2)
    • School of Electronic, Information and Electrical Engineering
    • Credit. 3
    • MA133
    • Enroll
    • Spring , 2015
    • 5126
    • Course Description:
    • ( Exchange Programme )
    • The course introduces to the students the fundamentals of Discrete Mathematics and its applications.
      It aims to enhance the logic and analytic abilities of the students to model and solve computational problems in a rigorous manner.
      This is one of the core courses for computer science major, offering them the mathematical sophistications necessary for further study.
      The course is composed of 3 main topics:
      Module 1 Set Theory
      Module 2 Algebra
      Module 3 Cutting-edge problems in computer science
    • Course Syllabus:
    • After completing the course, students should learn the following:

      I. Set theory.
      1. Naive set theory: basic notions and properties.
      2. Naive set theory: relations and functions.
      3. Axiomatic set theory.
      4. Natural numbers.
      5. Real numbers.
      6. Ordinal numbers.
      7. Cardinal numbers.
      II. Abstract Algebra
      1. Introduction
      2. Group and subgroup
      3. Cyclic group
      4. Homomorphism and isomorphism
      5. Coset and Lagrange’s Theorem
      6. Permutation groups
      7. More about groups
      8. Ring & Field: basic notions
      9. Applications: RSA etc..
    • Schedule:
    • Topics / Credit hours / Teaching methodology / Tasks / Intended learning outcomes / Assessment methods

      1. Set theory / 30 Credit hours / lecturing / 9 assignments / Null / Homework
      2. Algebra / 18 Credit hours / lecturing / 5 assignments / Null / Homework
      3. Cutting-edge problems in computer science / 3 Credit hours / Paper reading / Null / Homework
  • Reading list
  • Other Materials
  • Discussion
  • Homework download/submit
    • Huan Long
    • Lecturer
    • Read more
    • Female
    • E-mail:
    • longhuan@sjtu.edu.cn
    • Profile
  • Prerequisite Course:

    Discrete Mathematics

  • Textbooks:

    1. Herbert B. Enderton, Elements of Set Theory, ACADEMIC PRESS, 1977
    2. Michael Artin, Algebra, Prentice Hall, 1991
  • Grading:

    30% / homework
    70% / final examination
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