Mathematical Logic
Teachers WATANABE, Ryuji Year 1　2nd semest [Department of Information Science Correspondence Course, Faculty of Science and Engineering] Basic Major Subjects スクーリング授業 Requisites　2credit 4B103

#### Course Description

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.

#### Course 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.

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.

#### Textbook and Reference

KindTitleAuthorPublisher
Textbook“Guidance Book on Mathematical Logic”　R.Watanabe　(given on the LMS)
ReferencesReferences are introduced in the above guidance book.

#### 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.

#### Note

Students are asked to download the guidance book from the LMS, to print it and to bring it to the 2 days classes.

#### Schedule

1Set(LMS) : Definition and expression of set, Operation of set
2Set(LMS) : Law of operation of set, Direct product
3Mapping (LMS) : Definition of mapping, Epimorphism and injection, Inverse mapping, Composite mapping
4Relation (LMS) : Definition and expression of relation, Composition and Inverse relation, Union and intersection of relation
5Relation (LMS) : Law of relation, Equivalence relation and equivalence class, Order relation
6Set, Mapping(first half) : Practice
7Mapping(last half), Relation : Practice
8Propositional logic : Definition of proposition, Truth value and propositional variables, Logical operation
9Propositional logic : Propositional logic expression, Law of logical operation
10Propositional logic : Inference, Proof and technique of proof
11Propositional logic : Practice
12Predicate logic : Predicate logic, Predicate, Function
13Predicate logic : Quantifier, Predicate logic expression, Law of predicate logic operation
14Predicate logic : Practice
15Review, Term-end examination