Course Name: Discrete Mathematics
| Course Code: S2293113
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Semester: 1
| Credit: 3
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Program: Computer Science
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Course Module: Specialized Compulsory
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Responsible:Bo Wang
| E-mail: 2944440@qq.com
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Department:School of Computer Science & Technology, Tianjin University
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Time Allocation(1 credit hour = 45 minutes)
Exercise
| Lecture
| Lab-study
| Project
| Internship
(days)
| Personal
Work
| 24
| 24
|
|
|
| 20
|
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Course Description
The course is a required course designed for Engineering Master of Computer Science in International Engineering Institute. This course introduces the basic concept, basic theory and basic methods of each branch of Discrete Mathematics. The concept, theory and methods are widely used in Digit Circuit, Compilers Principle, Data Structure, Operating System, Database system, analysis and design of the Algorithm, Artificial Intelligence, Computer Networks and other professional courses. At the same time, the training provided by this course is very beneficial to enhancing students' abilities to generalize abstraction, logical thinking and inductive structure, and also is beneficial to cultivating rigorous, complete and standardized scientific attitude.
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Prerequisite
Having understood the basic concept of set
Having grasped the concept and operation of matrix in linear algebra
Having mastered algebra and related knowledge
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Course Objectives
This course discusses basic concepts of Discrete Mathematics to help students understand the Discrete Mathematics better and enhance their professional skills. After this course, students should be able to:
Cultivate and develop the students' mathematical thinking ability and make them master the analytical reasoning skills,
Lay a solid foundation for the subjects such as computer science and electronic information,
Help students master systematically related mathematical model, the basic theory and application technology,and to
Strengthen the abstract thinking ability, logical reasoning ability and careful generalizing ability, and then improve the ability of analyzing and solving problems.
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Course Syllabus
Set theory part: Set and its operation, Binary relation and Function, Natural numbers and Natural numbers set, Cardinal number of set,
Graph theory part: The basic concept of the Graph, Euler diagram and Hamiltonian Graph, Tree, the matrix representation of Graph, Planar Graph, Graph Colouring, Dominating Set, Covering Set, Independent Set and Matching, Weighted Graph and its applications,
Algebraic structure part: the basic concept of Algebra system, Semi-group and Single point, Group, Rings and Fields, Lattices and Boolean algebra,
Combinatorial mathematics part: Combination existence theorem, basic counting formula, combinatorial counting method and combinatorial counting theorem, and to
Mathematical logic part: Propositional logic, the first-order predicate calculus, Resolution principle.
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Textbooks & References
Kenneth H. Rosen.Discrete Mathematics and its Applications(7th ed). Mechanical industry Press, 2012.
D. S. Malik.Discrete Mathematical Structures – Theory and Applications. Higher education Press, 2005.
Seymour Lipschutz.2000 Solved Problems in Discrete Mathematics. 1991.
Gerald J.Bierman.Factorization Methods for Discrete Sequential Estimation. 2015.
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Capability Tasks
CT1: To have a more comprehensive understanding of the basic concept of mathematical logic and set theory.
CT2: To grasp the classical content of the propositional calculus, predicate calculus and Naive set theory systematically.
CT3: To learn the basic ways of formal deductive reasoning and theorem proving.
CS1: To grasp the proving method and problem solving skills of constructing mathematics (such as counting: inclusion-exclusion principle, recurrence relation), and learn to apply mathematical modelling to solve practical problems.
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Achievements
To grasp the concept of proposition and the presentation of propositional formula. - Level: M
To understand the meaning of the Truth table, Tautology, Implication and the Equivalent formula and can perform simple proving. - Level: A
To master inference rules of the predicate calculus and can do reasoning proving. - Level: M
To grasp the meaning of inverse function and compound function and its related basic theorem and the basic meaning of characteristic function. - Level: M
To understand the concepts of tree and to grasp the traversal and search of tree. - Level: A
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Students: Computer science,Year 1
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