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Mathematical Logic

 WATANABE, Ryuji
  Requisites  2 credits
【Information Science Correspondence Course･Spring(1st term)】
19-1-1638-2015

１．
Outline
　This course covers basic mathematics necessary in the following study of computer science. The items are as follows: Set, mapping, relation, propositional logic, and predicate logic.
　The lessons from the first to the 5th are based on self-learning given by LMS, and the lessons from the 6th to the 15th will be given in the classroom for 2 days.
　This subject is related to the clause 1 of the diploma policy of the Department of Information Science Correspondence Course.
２．
Objectives
　This course aims to improve the basic knowledge of mathematics for computer scientists and engineers and to enhance students' logical thinking power by working on the practice exercises.
３．
Grading Policy
　The final examination (40%), presentations on homework assignments in the classes (40%) and quizzes prepared on the LMS (20%) will be evaluated. The acceptance line is the rate of 60% in the above final examination, presentations on homework assignments and quizzes given on the LMS.
４．
Textbook and Reference
Textbook:
“Guidance book on Mathematical Logic”, R.Watanabe ; given on the LMS
Reference: Introduced in the above guidance book.
５．
Requirements (Assignments)
　Answering the quizzes prepared on the LMS for the first five lessons is required before the 2 days classes. Also, answering the practice exercises prepared in the guidance book as the homework assignments is required. Attendance at the classes is strictly required.
　Preparation of the sets and proposition on a high school level is highly recommended.
６．
Note
　Students are asked to download the guidance book from the LMS, to print it and to bring it to the 2 days classes.　
　It is allowed for students to refer the textbook and notebook in the final exam.
７．
Schedule
１. Set(LMS) : Definition and expression of set, Operation of set
２. Set(LMS) : Law of operation of set, Direct product
３. Mapping (LMS) : Definition of mapping, Epimorphism and injection, Inverse mapping, Composite mapping
４. Relation (LMS) : Definition and expression of relation, Composition and Inverse relation, Union and intersection of relation
５. Relation (LMS) : Law of relation, Equivalence relation and equivalence class, Order relation
６. Set, Mapping(first half) : Practice
７. Mapping(last half), Relation : Practice
８. Propositional logic : Definition of proposition, Truth value and propositional variables, Logical operation
９. Propositional logic : Propositional logic expression, Law of logical operation
10. Propositional logic : Inference, Proof and technique of proof
11. Propositional logic : Practice
12. Predicate logic : Predicate logic, Predicate, Function
13. Predicate logic : Quantifier, Predicate logic expression, Law of predicate logic operation
14. Predicate logic : Practice
15. Review, Term-end examination
１．
Outline
　This course covers basic mathematics necessary in the following study of computer science. The items are as follows: Set, mapping, relation, propositional logic, and predicate logic.
　The lessons from the first to the 5th are based on self-learning given by LMS, and the lessons from the 6th to the 15th will be given in the classroom for 2 days.
　This subject is related to the clause 1 of the diploma policy of the Department of Information Science Correspondence Course.
２．
Objectives
　This course aims to improve the basic knowledge of mathematics for computer scientists and engineers and to enhance students' logical thinking power by working on the practice exercises.
３．
Grading Policy
　The final examination (40%), presentations on homework assignments in the classes (40%) and quizzes prepared on the LMS (20%) will be evaluated. The acceptance line is the rate of 60% in the above final examination, presentations on homework assignments and quizzes given on the LMS.
４．
Textbook and Reference
Textbook:
“Guidance book on Mathematical Logic”, R.Watanabe ; given on the LMS
Reference: Introduced in the above guidance book.
５．
Requirements (Assignments)
　Answering the quizzes prepared on the LMS for the first five lessons is required before the 2 days classes. Also, answering the practice exercises prepared in the guidance book as the homework assignments is required. Attendance at the classes is strictly required.
　Preparation of the sets and proposition on a high school level is highly recommended.
６．
Note
　Students are asked to download the guidance book from the LMS, to print it and to bring it to the 2 days classes.　
　It is allowed for students to refer the textbook and notebook in the final exam.
７．
Schedule
１. Set(LMS) : Definition and expression of set, Operation of set
２. Set(LMS) : Law of operation of set, Direct product
３. Mapping (LMS) : Definition of mapping, Epimorphism and injection, Inverse mapping, Composite mapping
４. Relation (LMS) : Definition and expression of relation, Composition and Inverse relation, Union and intersection of relation
５. Relation (LMS) : Law of relation, Equivalence relation and equivalence class, Order relation
６. Set, Mapping(first half) : Practice
７. Mapping(last half), Relation : Practice
８. Propositional logic : Definition of proposition, Truth value and propositional variables, Logical operation
９. Propositional logic : Propositional logic expression, Law of logical operation
10. Propositional logic : Inference, Proof and technique of proof
11. Propositional logic : Practice
12. Predicate logic : Predicate logic, Predicate, Function
13. Predicate logic : Quantifier, Predicate logic expression, Law of predicate logic operation
14. Predicate logic : Practice
15. Review, Term-end examination