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1 University of Macau Faculty of Science and Technology Department of Computer and Information Science Department of Electrical and Computer Engineering CISB111/ECEB222 Discrete Structures Syllabus 2 nd Semester 2014/2015 Part A Course Outline Compulsory course in Computer Science Compulsory course in Electrical and Computer Engineering Catalog description: (2-2) 3 credits. Set Theory, Logic, Counting, Relations, Graph Theory, and other topics. Students will be trained in developing skills in mathematics, such as formulating problems, abstraction and proof methods. Course type: Theoretical Prerequisites: None Textbook(s) and other required material: Discrete Mathematical Structures, Kolman, Busby, Ross, 6th Edition, Pearson Prentice Hall, 2009, ISBN ; (Required) References: Discrete Mathematics and its applications, Rosen, Kenneth H. 7th Edition, McGraw-Hill Higher Education, 2012, ISBN Major prerequisites by topic: College algebra or pre-calculus Course objectives: Develop an understanding of mathematical statements (theorems) and how to read and construct valid mathematical arguments (proofs). [a, e, g] Introduce various problem-solving strategies, especially thinking algorithmically. [a, e, g] Introduce important discrete data structures such as sets, relations, discrete functions, graphs and trees. [a, e] Topics covered: Introduction to Discrete Mathematical Structures (1 hour): An introduction to the course. It starts with the meaning of discrete comparing with continuous, and the reason of taking the course in computer science. It then introduces the goals, objectives, and topics to be covered. Some warm-up questions are also raised. Sets and Sequences (2 hours): Concept of sets and subsets, operations on sets, algebraic properties of set operations, the addition principle; sequences, characteristic function, strings and regular expressions. Integers and Matrices (1 hours): Properties of integers, division in the integers, greatest common divisor, Euclidean algorithm, least common multiple, matrices, Boolean matrices, and Boolean matrix operations. Mathematical Structures (2 hours): Concept of mathematical structures, closure property, commutative, associative, distributive properties, De Morgan s laws, identity element and inverse. Propositions, Logical Operations, and Conditional Statements (3 hours): Definition of proposition, propositional variables, compound statements, negation, conjunction, disjunction, truth table, predicate, universal and existential quantification, conditional statements, converse, contrapositive, equivalence, tautology, absurdity, and contingency.

2 Methods of Proof and Mathematical Induction (4 hours): Introduce the rules of inference. Determine if an argument is valid or not. Introduce indirect method of proof, proof by contradiction, and disproof. Review the principle of mathematical induction, and introduce the strong form of mathematical induction. Study the use of mathematical induction to prove a loop invariant in programs. Counting, Pigeonhole Principle, and Recurrence Relations (1 hours): Pigeonhole principle and its use in existence proof, recurrence relations, Fibonacci sequence, finding explicit formula for linear homogenous relation of degree 2. Relations and Digraphs (8 hours): product sets, partitions, relations, the matrix of a relation, the digraph of a relation, paths in relations and digraphs, properties of relations, equivalence relations and partitions, operations on relations, closures and composition. Functions and Growth of Functions (2 hours): concept of functions, special types of functions, invertible functions, composition of functions, functions for computer science, growth of functions, Big-O notation, and rules for determining the growth of functions. Trees and Graphs (4 hours): Concept of trees, labeled trees, binary tree searching, searching general trees, undirected trees, spanning trees, minimal spanning trees, Prim s algorithm and Kruskal s algorithm, graphs. Class/laboratory schedule: Timetabled work in hours per week Lecture Tutorial Practice No of teaching weeks Total hours Total credits No/Duration of exam papers 2 2 Nil / 2 hours Student study effort required: Class contact: Lecture Tutorial Other study effort Self-study Homework Total student study effort 28 hours 28 hours 21 hours 15 hours 92 hours Student assessment: Final assessment will be determined on the basis of: Homework 20% Midterm Test 40% Final Exam 40% Course assessment: The assessment of course objectives will be determined on the basis of: Homework, test and exam Course evaluation Course outline: Weeks Topic Course work 1 Introduction to Discrete Mathematical Structures 2, 3 Sets and Sequences, Integers and Matrices Homework#1 4 Mathematical Structures 5 Propositions, Logical Operations, and Conditional Statements Homework#2 6, 7 Methods of Proof and Mathematical Induction Homework#3

3 8, 9 Counting, Pigeonhole Principle, and Recurrence Relations Midterm Test 10 Binary Relation, Geometric and Algebraic Representation Method 11 Properties, Equivalence Relations, Operations on Relations Homework#4 12 Functions and Growth of Functions Homework#5 13 Trees and Graphs 14 Conclusion & Review Contribution of course to meet the professional component: This course presents the foundations of many basic computer related concepts, such as set theory, logic, graph theory, and counting. Relationship to Computer Science program objectives and outcomes: This course primarily contributes to Computer Science program outcomes that develop student abilities to: (a) An ability to apply knowledge of computing and mathematics appropriate to the programme outcomes and to the discipline. (e) An ability to identify, formulate and solve engineering problems. (g) An ability to communicate effectively. Relationship to Computer Science program criteria: Criterion DS PF AL AR OS NC PL HC GV IS IM SP SE CN Scale: 1 (highest) to 4 (lowest) 1 Discrete Structures (DS), Programming Fundamentals (PF), Algorithms and Complexity (AL), Architecture and Organization (AR), Operating Systems (OS), Net-Centric Computing (NC), Programming Languages (PL), Human-Computer Interaction (HC), Graphics and Visual Computing (GV), Intelligent Systems (IS), Information Management (IM), Social and Professional Issues (SP), Software Engineering (SE), Computational Science (CN). Course content distribution: Percentage content for Mathematics Science and engineering subjects Complementary electives Total 100% 0% 0% 100% Persons who prepared this description: Dr. Yan Zhuang

4 Part B General Course Information and Policies 2 nd Semester 2014/2015 Instructor: Dr. Yan Zhuang Office: E Office Hour: By appointment Phone: Teaching Assistants: Ms. Ting Shu Time/Venue: Wed. 11:00 12:45, E (Lecture) Fri. 16:00 17:45, E (Tutorial) Grading Distribution: Percentage Grade Final Grade Percentage Grade Final Grade A A B B B C C C D D below 50 F Comment: The objectives of the lectures are to explain and to supplement the text material. Students are responsible for the assigned material whether or not it is covered in the lecture. Students who wish to succeed in this course should work all homework and exercises given in tutorial classes. You are encouraged to look at other sources (other texts, etc.) to complement the lectures and text. Homework Policy: Doing exercises is of vital importance to help the students to master the concepts covered, therefore: There will be approximately 5 homework assignments. Homework is due one week after assignment unless otherwise noted, no late homework is accepted. Test and Exam: One midterm test and one final exam will be held during the semester. Both are 2-hour and closed book. Note Attendance at both lectures and tutorial classes is strongly recommended. Check UMMoodle ( for announcement, homework and lectures. Report any mistake on your grades within one week after announcement. No make-up test is given except for clear medical proof. Cheating is absolutely prohibited by the university.

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