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Graduate School
Discrete Mathematics and Exercise
Keiichirou KUSAKARI Associate Professor
Department: School of Engineering / Graduate School of Engineering
Class Time:  2013 Spring Thursday 
Recommended for:  Electrical and Electronic Engineering and Information Engineering freshman 
Course Overview
Course Aims
In this lecture, we will be learning about the basic concepts of set, function and relation. We will also focus on the elementary number theory and basic theories of algebra. In the exercise session you will be asked to establish proofs for exercise problems to get the basic understanding of the format.
Key Features
Lecture notes are uploaded for your convenience. Therefore, in this lecture, I would like you to focus on the lecture not just on taking notes. It is true that writing equations yourself by taking notes is important to get the fundamental understanding of the lecture. However, in this lecture students will be asked to solve lots of problems to get the fundamental techniques of writing logically wellconstructed proofs.
Mid term exam will be in the last lecture. Problems on the final exam will be the same one as in the mid term exam. It is because student will be forced to review all the problems on the mid term exam and this is good way for them to review and get them a chance to study.
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Syllabus
Contents
 Basic concepts about set, function and relation
 Elementary number theory
 Basic theories of algebra
Course Aims
Objectives of our course are as followed.
 Getting sufficient knowledge of basic mathematics in order to get through fouryear study in Nagoya University
 Getting sufficient knowledge of mathematical notational conventions in order to get through fouryear study in Nagoya University
 Obtaining logical thinking, or the ability to prove logically and clearly without any unclear reasoning. (Many example problems will be given in the exercise session) Logically wellconstructed proof has to follow following rules.
 No inconsistency in the proof
 No superfluous discussion
 Enough reasoning for the conclusion.
 Clear storyline
 Development of abstract thinking
Requirements and recommended courses
This lecture is designed for Electrical and Electronic Engineering and Information Engineering freshman. Therefore, one of our objectives is to get the basic skills and knowledge of basic mathematics. Furthermore, through intensive exercise I would like you to obtain logical thinking for writing thesis in senior year.
Assignments
Followings are the example problems given in the exercise session.
 Exercise problems (PDF, 52KB)
Course Schedule
Session  Contents 

1  Set, Proposition and Relation (1) 
2  Set, Proposition and Relation (2) 
3  Relation and Order (1) 
4  Relation and Order (2) 
5  Enumerative combinatorics 
6  Divisor, Multiple and Euclidean algorithm 
7  Prime Number (1) 
8  First Order Diophantine Equation 
9  Congruence expression and Chinese remainder theorem 
10  Prime Number (2) 
11  Group 
12  Ring, Integral Domain, and Field 
13  Polynomial Rings and Galois Field 
14  Mid term exam 
15  Summary / Final term exam 
Grading
Grading will be given based on your result of examination exercise problems and reports.
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Class Materials
Lecture Handouts
Note: All files are in Japanese.
 Session #1 and #2
 Set, Proposition and Relation (PDF, 236KB)
 Session #3 and #4
 Relation and Order (PDF, 201KB)
 Session #5
 Enumerative combinatorics (PDF, 250KB)
 Session #6
 Divisor, Multiple and Euclidean algorithm (PDF, 169KB)
 Session #7
 Prime Number (1) (PDF, 202KB)
 Session #8
 First Order Diophantine Equation (PDF, 188KB)
 Session #9
 Congruence expression and Chinese remainder theorem (PDF, 166KB)
 Session #10
 Prime Number (2) (PDF, 144KB)
 Session #11
 Group (PDF, 152KB)
 Session #12
 Ring, Integral Domain, and Field (PDF, 41KB)
 Session #13
 Polynomial Rings and Galois Field (PDF, 176KB)
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Page last updated June 25, 2010
The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.