In this class, students will learn mathematics which will be the basics of computer programs. This mathematical knowledge
can be used to consider various theoretical issues of programs including the complexity of algorithms.
Sets, relations, functions, algebra will be included in the class.
In FY2020, the class will be held via the internet, by using zoom. A pdf file of the PowerPoint and a video for each class will be opened by Scomb.
The mid-term exam will be held in the 8th class and the final exam will be held in the 14th class. Any materials for the class, books, etc. can be referred for these exams, but please solve them alone without exchange information with other students.
Questions will be made by using "chat" of the zoom or voice during classes, and by e-mails.
In several classes, you will have quizzes, and the grade will be calculated by weighted average of quizzes (30%), mid-term exam (30%), and the final exam (40%).
Sets, relations, functions, algebra will be included in the class.
In FY2020, the class will be held via the internet, by using zoom. A pdf file of the PowerPoint and a video for each class will be opened by Scomb.
The mid-term exam will be held in the 8th class and the final exam will be held in the 14th class. Any materials for the class, books, etc. can be referred for these exams, but please solve them alone without exchange information with other students.
Questions will be made by using "chat" of the zoom or voice during classes, and by e-mails.
In several classes, you will have quizzes, and the grade will be calculated by weighted average of quizzes (30%), mid-term exam (30%), and the final exam (40%).
Acquiring basic knowledge on discrete mathematics and understanding its importance for algorithms and programs.
- Students are expected to Understand basics of sets, relations, functions, algebra etc.
- Students are expected to think of programs and algorithms from mathematical point of view.
- Students are expected to learn further topics in the field of discrete mathematics.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Set 1 What is set. Representation of sets. Basic operation on sets. |
Reading Syllabus. | 10minutes |
| Reviewing contents of the class, finish quiz. | 30minutes | ||
| 2. | Set 2 Cardinality of sets Countable infinite set, non-countable infinite set and diagonal method |
Reviewing contents of the class, finish quiz. | 30minutes |
| 3. | Relation 1 What is relation. Representation of relations |
Reviewing contents of the class, finish quiz. | 30minutes |
| 4. | Relation 2 Equivalence relation |
Reviewing contents of the class, finish quiz. | 30minutes |
| 5. | Relation 3 Partial order |
Reviewing contents of the class, finish quiz. | 30minutes |
| 6. | Relation 4 Total order |
Reviewing contents of the class, finish quiz. | 30minutes |
| 7. | Function What is function Relation and function Composite function |
Reviewing contents of the class, finish quiz. | 30minutes |
| 8. | Mid-term exam | Reviewing mid-term exam | 45minutes |
| 9. | Inductive definition | Reviewing contents of the class, finish quiz. | 30minutes |
| 10. | Inductive proof Mathematical induction Structural inductio |
Reviewing contents of the class, finish quiz. | 30minutes |
| 11. | Algebra 1 Monoid, semi-group |
Reviewing contents of the class, finish quiz. | 30minutes |
| 12. | Algebra 2 Group, ring, field |
Reviewing contents of the class, finish quiz. | 30minutes |
| 13. | Boolean algebra | Reviewing contents of the class, finish quiz. | 30minutes |
| 14. | Final exam | Reviewing final-exam | 45minutes |
| Total. | - | - | 460minutes |
| Quiz | Mid-term examination | Final examination | Total. | |
|---|---|---|---|---|
| 1. | 20% | 20% | 30% | 70% |
| 2. | 10% | 5% | 5% | 20% |
| 3. | 0% | 5% | 5% | 10% |
| Total. | 30% | 30% | 40% | - |
Students will be evaluated by weighted average of quiz, mid-term exam, and final exam.
Students who can understand what is asked in exam will be graded as 70%.
Students who can understand what is asked in exam will be graded as 70%.
Not specified.
The followings are reference books written in Japanese:
Conprehensive:
(1) D.グリース、シュナイダー著、難波莞爾、土居範久監訳『コンピュータのための数学：論理的アプローチ』日本評論社、2001年
(2) Seymour Lipschutz著、 成嶋 弘訳『離散数学―コンピュータサイエンスの基礎数学 (マグロウヒル大学演習)』オーム社、1995年
(3)小倉 久和 『はじめての離散数学』近代科学社、2011年
Set Theory, Relations and Functions:
(1) 赤摂也『集合論入門』ちくま学芸文庫、筑摩書房、2014年
(2) 上江洲忠弘『集合論入門－無限への誘い－』遊星社、2004年
(3) 稲垣武『一般集合論』至文堂、1968年
Algebra:
(1) 横田一郎『初めて学ぶ人のための群論入門』現代数学社、2019
(2) 松坂和夫『代数系入門』岩波書店、2018
(3) 東京大学工学教程編纂委員会編『代数学』丸善出版、2018
Boolean Algebra:
(1) Raymond Smullyan（川辺治之訳）『スマリヤン先生のブール代数入門 : 嘘つきパズル・パラドックス・論理の花咲く庭園』共立出
版、2008
(2) 永田博義『初めて学ぶディジタル回路とブール代数』オーム社、1996
(3) 成島弘, 小高明夫『ブール代数とその応用』東海大学出版会、1983
The followings are reference books written in Japanese:
Conprehensive:
(1) D.グリース、シュナイダー著、難波莞爾、土居範久監訳『コンピュータのための数学：論理的アプローチ』日本評論社、2001年
(2) Seymour Lipschutz著、 成嶋 弘訳『離散数学―コンピュータサイエンスの基礎数学 (マグロウヒル大学演習)』オーム社、1995年
(3)小倉 久和 『はじめての離散数学』近代科学社、2011年
Set Theory, Relations and Functions:
(1) 赤摂也『集合論入門』ちくま学芸文庫、筑摩書房、2014年
(2) 上江洲忠弘『集合論入門－無限への誘い－』遊星社、2004年
(3) 稲垣武『一般集合論』至文堂、1968年
Algebra:
(1) 横田一郎『初めて学ぶ人のための群論入門』現代数学社、2019
(2) 松坂和夫『代数系入門』岩波書店、2018
(3) 東京大学工学教程編纂委員会編『代数学』丸善出版、2018
Boolean Algebra:
(1) Raymond Smullyan（川辺治之訳）『スマリヤン先生のブール代数入門 : 嘘つきパズル・パラドックス・論理の花咲く庭園』共立出
版、2008
(2) 永田博義『初めて学ぶディジタル回路とブール代数』オーム社、1996
(3) 成島弘, 小高明夫『ブール代数とその応用』東海大学出版会、1983
- Non-social and professional independence development course
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Sun Apr 04 04:08:13 JST 2021