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FACULTY OF INFORMATION TECHNOLOGY Course Specifications: (MATH 251) Month, Year: Fall 2008 University: Misr University for Science and Technology Faculty : Faculty of Information Technology Course Specifications for Discrete Mathematics Program(s) on which the course is given: Undergraduate Computer Science & Information Systems Department offering the program: Computer Science Department offering the course: Computer Science Academic year / Level: CS Level seven/ IS Elective Course Date of specification approval A- Basic Information Title: Discrete Mathematics Credit Hours: 3 Tutorial: 2 Code: math 251 Lecture : 2 Practical: Total: 4 B- Professional Information 1. Course Description: The course provides an introduction to mathematical structures fundamental to computer science. Topics discussed include logic of compound and quantified statements, number theory and methods of proof, mathematical induction, counting methods, finite state automata, functions and relations. 2. Course Objectives (Overall Aims of Course): Upon completion of this course, students should be able to: 1. Use logic to determine the validity of an argument. 2. Construct the proof of a theorem. 3. Understand the terminology, operations, and symbols of set theory. 4. Use combinatorial techniques when needed in solving problems. 5. Identify a function; specifically, 6. Identify relation, reflexive, symmetric, and transitive relations. Included too equivalence relations. 7. Understand the terminology, operations, and symbols of finite state automata and minimum language accepted. 3. Learning Outcomes : Upon completion of this course the student will be able to understand logic of compound and quantified statements, number theory and methods of proof, mathematical induction, counting methods, finite state automata, functions and relations 1. Knowledge and understanding : - Fundamental knowledge needed for mathematical structures. - Use logic to determine the validity of an argument. - Identify functions, and relation. - Finite state automata. 2. Intellectual skills: - Learning of mathematical structures - Design of finite state automata . - Use of functions, and relation. - Construct proof of a theorem. - Recognize and use various types of reasoning and methods of proof -How to use abstract algebraic structures in solving problems expressed by symbols 3. Professional and practical skills: - Use combinatorial techniques when needed in solving problems. - Use of logic to determine the validity of an argument. - Construct a proof of a theorem using mathematical induction - Learn the deductive nature of mathematics, the roles of definitions, axioms, and theorems to - construct viable arguments - How to develop conjectures and draw appropriate conclusions 4. General and transferable skills. - Learning of quantified statements, number theory and methods of proof, and mathematical induction, counting methods, permutation. - Emphasis operation on finite state automata. - Formulate mathematical ideas using the appropriate mathematical notation - Judge the validity of mathematical arguments 4. Course Contents Week 1 2 3 Topics Digital Logic of statement. -Logical forms . -logical equivalence, -conditional statement, -Valid and invalid arguments Logic of quantified statement -predicate and quantified statement 4 5 6 7 8 9 10 11 12 13 14 15 Elementary Number theory and method of proof. -Direct proof and counter example, rational numbers. -Mathematical Induction Counting, Permutation, permutation of selected elements Revision Mid-Term Exam Mid-Term Exam -Functions. -One to one, Onto Functions -Inverse functions, -Composition of functions Basic Relations. -Relations on sets, -Reflexivity, symmetry, and transitivity. -Equivalence relations. Finite-State automata Machines :Transition diagram, annotated next state table, minimum language accepted by the automaton. Revision Total/ hours 4 Lecture/ hr 2 Tutorial/hr 4 2 2 4 2 2 4 2 2 4 4 2 2 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 4 2 2 2 2 4 2 2 2 5– Teaching and Learning Methods 5.1-Lectures 5.2-Exercises 6- Student Assessment Methods 6.1 Written Exams: to assess Concepts related to Discrete Mathematics 6.2 Exercises to assess understanding of Discrete Mathematics topics. 6.3 Presentation: to assess workgroup collaboration and communication skills. Weighting of Assessments Mid-Term Examination 20% Final-term Examination 60% Semester Work and Project 20% __________________________________ Total 100% 6- List of References 6.1- Course Notes -given on board by instructor. 6.2- Essential Books (Text Books) Required Book: Sussana Epp, Discrete Mathematics with Applications, 3rd Edition , Thomson Learning, 2004. 6.3- Recommended Books: Judith L. Gersting, Mathematical Structures for Computer Science, 6th ed., W. H. Freeman Press, 2006. 7- Facilities Required for Teaching and Learning Data show, computer Lab Course coordinator: Prof. Assem Deif Date : 20 /4 /2008