The Importance of Mathematics for Information
Technology
(情報テクノロジーでの数学の役割と重要性)
Discrete Mathematics I
(情報数学
I)
1st lecture, September 20, 2019
https://www.sw.it.aoyama.ac.jp/2019/Math1/lecture1.html
Martin J. Dürst
(テュールスト
マーティン ヤコブ)
duerst@it.aoyama.ac.jp
Building O, Room 529
© 2005-19 Martin
J. Dürst 青山学院大学
Today's Schedule
- Self-introduction
- About this course
- The relationship between Mathematics and Information Technology
- The importance of English
- Registration with Moodle
- This week's homework
自己紹介
Teaching Assistant: Kosuke Kurihara (栗原 光祐)
授業の位置づけ
- 情報テクノロジー学科:
数学・共通科目、必修 (◉)
- 機械創造工学科:
第一科目群、選択必修 (△)
- 経営システム工学科:
第二科目群、選択必修 (▼)
- 物理・数理学科: 選択科目
- 情報テクノロジーの初めての本格的な授業
- 理工学国際プログラム E科目 (英語講義):
授業全体 (今日の一部を抜く) が英語で実施
授業の進め方
- 資料の配布とウェブ公開
- 配布資料への書込みが不可欠
(資料に載ってないことが色々ある)
- 参考書の購入、熟読を強く推奨
- 出席は前提 (文科省); 遅延や未出席は大損
- 宿題、復習、予習は授業時間の二倍程度 (文科省)
- 質問はいつでも大歓迎 (日本語でも)
- 約束事 1: 私語禁止、脱帽、飲食禁止
- 約束事 2: 書き込み、宿題を必ずやること
英語の大切さ
- 青山学院の歴史
- 国際競争力
- 米国の会社や研究者は情報テクノロジーを長年にリード
- 英語は情報テクノロジーの共通語
(国際会議、学術論文、プログラムなど)
- 最新情報は英語以外で入手不可能
The Importance of English
Example: Ruby Kaigi (my talk in
English)
- Ruby is a programming language
created in Japan and used world-wide
- Ruby Kaigi is a yearly conference in Japan
- Attendees are at least 2/3 Japanese
- Presentations are half in Japanese, half in English
- Simultaneous translation Japanese → English available
- Program only in English
- NO simultaneous translation English → Japanese
Glossary
- Each lecture handout comes with a glossary at the end
- The glossary contains:
- technical terms for this lecture (e.g. binary (number
representation)/二進法) ⇐ part of examination
- technical terms for computer science (e.g.
compiler/コンパイラ)
- technical terms from other fields (e.g. topology/位相幾何学)
- general terms/expressions (e.g. technical term/専門用語)
- Please report missing terms
Video Recording
- Each lecture is being recorded on video
- You will receive an email when the video is available for viewing
(as early as Friday evening)
- Each video will only be available for a fixed time
- Please use video recordings to review each lecture, especially the parts
that you did not understand
- Video recordings are NOT a substitute for attending
lectures
Method of Evaluation
- Minitest(s) during lecture: ~20%
- Homework: ~30%
- Final exam: ~50%
Schedule
Schedule of Discrete Mathematics I
Book list
About Communication by E-mail
Use e-mail if you want to communicate with me (not Moodle chat,...). Always
include:
- Your name
- Your student number
- The relevant course
- Your actual request
- Any past communications
(E-mail is different from LINE)
[電子メールによる連絡の場合、名前、学籍番号、授業名、具体的な要件と過去の経緯を明確に!]
情報数学の概要
- ｢物理数学」や｢生物数学」は存在しない
- 「情報数学」も同様
- 情報テクノロジーの様々な分野において様々な数学の分野が基礎
- 情報数学の内容:
- 情報テクノロジー全般で特に基礎となるもの
- 一般の数学の授業であまり教えられていないもの
Examples of Relationship between
Mathematics and Information Technology
| Field of Mathematics |
Field of Information Technology |
| probability theory |
information transmission, natural language processing |
| Fourier analysis |
image processing, sound processing |
| linear algebra, geometry, topology |
computer graphics, robotics |
| (formal) language theory, type theory |
programming languages, compilers |
| number theory |
cryptography |
Discrete Mathematics I and II
- Discrete Mathematics I:
- Representations of numbers, modular arithmetic
- Logic: Boolean formulæ, Boolean functions, propositional logic,
predicate logic
- Sets, relations, etc.
- Proof methods
- Discrete Mathematics II (Prof. Ohara, Fall 2020):
- Information theory
- Graph theory
数学の考え方
- 数学は道具 (tool)
- 数学は言語 (language)
- 数学は考え方 (way of thinking)
言語としての数学
- 自然言語 (日本語、英語、ドイツ語など)
- 言葉もあるが、記号が多い
- 他の言語に比べて、正確で簡潔
- 使う記号に一部方言が存在
- 他に情報テクノロジーに大事な言語?
情報テクノロジーに必要な言語
(合計四つ、順不同)
- 数学
- 英語
- 母国語 (日本語)
- プログラム言語 (複数)
Besides a mathematical inclination, an exceptionally good mastery of
one's native tongue is the most vital asset of a competent
programmer.
Edsger W. Dijkstra, EWD498,
Selected Writings on Computing: A Personal Perspective,
Springer-Verlag, 1982, pp. 129-131.
英語の勉強の仕方
- 英語と専門・趣味の連結
- ウェブ上に山ほどの材料
- 飛び込んで、足が付けない場所で泳ぐ
- 目・耳・口・手・体で勉強
- 英語で考える
- 慣れるのは大変; 慣れた後は楽しい
How to Study English
- Use English for your studies and your hobbies
- On the Web, there are many materials (texts, audio, video)
- Learn to swim where your feet can't reach the ground
- Use eyes, ears, mouth, hands, and your whole body
- Think in English
- Starting is tough, but it gets easier and more fun as you progress
Simple Arithmetic in English
Addition: Two plus two is four.
Subtraction: Twelve minus five equals seven.
Multiplication: Fifteen times two is thirty.
Division: Two hundred divided by five is forty.
(see https://en.wikipedia.org/wiki/English_numerals)
Registration with Moodle
Moodle is an open-source electronic learning support system.
We will use Moodle in this course.
Today, we will learn how to:
- Create a new account (not necessary for repeaters)
- Enroll for our course (everybody including repeaters)
- Using a browser, go to https://moo.sw.it.aoyama.ac.jp
- Select "Discrete Mathematics I" or "Login"
- Below "Is this your first time here?", select "New Account"
- Fill in the form for a new account (following all the rules on the next
slide!)
Account Creation Details
- Username: Your student number (8 digits, e.g.
15819178)
- Password: Something that you can easily remember, but than nobody else
can guess (never forget it!)
- Email address: Official aoyama.jp address only! (e.g.:
a5819178@aoyama.jp)
- Last name (姓, 苗字) / first name (名): Same as on your student
identification card (e.g.: 高崎 vs. 髙﨑)
- Do not confuse last name (姓, 苗字) and first name (名前)
Account Creation Process
- Select "Create my new account" when you filled in all items
- After some time, you will receive a confirmation email
- Click on the link in the confirmation email to confirm your account
creation
- If you do not get an email soon, then check your spam/junk folder
- If you still cannot find the confirmation email, then send me mail or
visit my office
Account Creation: Caution
- Students who have used https://moo.sw.it.aoyama.ac.jp
before only need to register for the course
- If you forgot the password, please select "Forgotten your username or
password?"
Then enter only your user name or your mail address, but not
both.
Course Enrollment (everybody!)
After logging in, select "Discrete Mathematics I (2019)"
Enter the enrollment key:
Attention: Both Moodle course enrollment and course registration are
necessary for successful course completion.
Attention: Repeaters also have to enroll in the course.
Attention: The deadline for course enrollment is September 26, 21:00. But
better enroll today.
This Week's Homework
- Create your account on https://moo.sw.it.aoyama.ac.jp
and enroll for Discrete
Mathematics I (deadline: September 26, 21:00)
- Solve the Quiz Simple
Arithmetic in English (repeat until you get it 100% correct;
deadline: September 26, 22:00)
- Review decimal number representation, binary number representation, and
n-ary number representation based on high-school notes and Web
resources
- Check out/buy/lend a textbook or reference book
次回までの宿題
Glossary
- technical term
- 専門用語
- probability theory
- 確率論
- information transmission
- 情報通信
- natural language processing
- 自然言語処理
- fourier analysis
- フーリエ解析
- image processing
- 画像処理
- sound processing
- 音声処理
- representations of numbers
- 数の表現
- modular arithmetic
- 合同算術
- logic
- 論理
- Boolean formulæ
- 論理式
- Boolean function
- 論理関数
- propositional logic
- 命題論理
- predicate logic
- 述語論理
- set
- 集合
- relation
- 関係
- proof methods
- 証明の仕方、証明方法
- information theory
- 情報理論
- linear algebra
- 線形代数
- geometry
- 幾何学
- topology
- 位相幾何学
- computer graphics
- コンピュータグラフィクス
- robotics
- ロボット工学
- (formal) language theory
- (形式) 言語理論
- programming language
- プログラム言語
- compiler
- コンパイラ
- number theory
- 整数論
- cryptography
- 暗号学
- graph theory
- グラフ理論
- simultaneous translation
- 同時通訳
- native tongue
- 母国語
- (course) registration
- (履修) 登録
- enrollment
- (履修) 登録
- electronic learning support system
- 電子学習支援システム
- repeater
- 再履修者
- digit
- 桁
- spam/junk
- 迷惑メール
- deadline
- 締切
- decimal (number representation)
- 十進法
- binary (number representation)
- 二進法
- n-ary (number representation)
- n進法
- textbook
- 教科書
- reference book
- 参考書