Computer programs are engineering products created to solve various problems, but on the other hand, programs and their underlying
algorithms have a strong mathematical aspect. Knowledge of such aspects is necessary for the efficiency of execution of algorithms
and programs, and for the development of new algorithms. In other words, considering the mathematical aspects of programs
and algorithms is not only theoretically and mathematically interesting, but also has engineering implications. In this lecture,
students will learn the mathematical treatment of various concepts in the basic fields of mathematics, sets, relations, functions,
and Boolean algebra, which are necessary for thinking about algorithms and programs, by doing exercises as needed.
The mid-term and final examinations will be given during class time. The mid-term exam will be given in the 8th class and the final exam will be given in the 14th class.
The mid-term and final examinations will be given during class time. The mid-term exam will be given in the 8th class and the final exam will be given in the 14th class.
The objective of this course is to provide students with a basic knowledge of discrete mathematics and an understanding that
will be useful in the mathematical treatment of algorithms and programs in the future.
- Acquire a basic knowledge of sets, relations, functions, and Boolean algebra and be able to perform basic operations in these areas.
- Be able to view programs and algorithms from a discrete mathematical standpoint.
- Students will be able to further develop their studies based on what they have learned in this lecture.
| 演習課題 | 中間試験 | 期末試験 | Total. | |
|---|---|---|---|---|
| 1. | 20% | 20% | 30% | 70% |
| 2. | 10% | 5% | 5% | 20% |
| 3. | 0% | 5% | 5% | 10% |
| Total. | 30% | 30% | 40% | - |
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | What is a set, Inclusive and Extensive Representations, Basic Operations on Sets | Read the syllabus carefully | 30minutes |
| Review the class, familiarize yourself with the content, and review the exercises. | 200minutes | ||
| 2. | Continuation of basic operations on sets, Concentration of sets: countable infinite sets and non-countable infinite sets, Diagonal argument | Review the class, familiarize yourself with the content, and review the exercises. | 200minutes |
| 3. | About Relationships: What is a relationship, and how to express a relationship | Review the class, familiarize yourself with the content, and review the exercises. | 200minutes |
| 4. | Relation (1): equivalence relation and its properties | Review the class, familiarize yourself with the content, and review the exercises. | 200minutes |
| 5. | Relation (2): Semi-ordered relations and their properties | Review the class, familiarize yourself with the content, and review the exercises. | 200minutes |
| 6. | Relation (3): All-order relations and their properties | Review the class, familiarize yourself with the content, and review the exercises. | 200minutes |
| 7. | About functions: relations and functions, composition of functions, how to represent functions | Review the class, familiarize yourself with the content, and review the exercises. | 200minutes |
| 8. | Mid-term exam and its explanation | Review the mid-term exam | 200minutes |
| 9. | Algebraic structures (1): monoids, semigroups, groups | Review the class, familiarize yourself with the content, and review the exercises. | 200minutes |
| 10. | Algebraic structures (2): ring, field, bundles | Review the class, familiarize yourself with the content, and review the exercises. | 200minutes |
| 11. | Boolean algebra | Review the class, familiarize yourself with the content, and review the exercises. | 200minutes |
| 12. | Symbolic Logic (1) | Review the class, familiarize yourself with the content, and review the exercises. | 200minutes |
| 13. | Symbolic Logic (2) | Review the class, familiarize yourself with the content, and review the exercises. | 200minutes |
| 14. | Final exam and its explanation | Review final exam questions | 90minutes |
| Total. | - | - | 2720minutes |
The evaluation will be based on a weighted average of the exercises, mid-term exam and final exam.
The weighted average will be 30% for the exercises, 30% for the mid-term exam, and 40% for the final exam.
70% will be given when the student has a general understanding of the course content and is able to answer the questions in a reasonable manner.
The weighted average will be 30% for the exercises, 30% for the mid-term exam, and 40% for the final exam.
70% will be given when the student has a general understanding of the course content and is able to answer the questions in a reasonable manner.
Textbook
Kazuo Ushijima, "Discrete mathematics", Coronasha, 2006.
General reference books
(1) "Mathematics for Computers: A Logical Approach," by D. Griese and S. Schneider, translated by K. Namba and N. Doi, Nippon Hyoronsha, 2001.
(2) Seymour Lipschutz, "Discrete Mathematics: Fundamental Mathematics for Computer Science (McGraw-Hill University Seminar)", Ohmsha, 1995
(3) Hisakazu Ogura, Discrete Mathematics for Beginners, Kindai Kagaku-sha, 2011
Above (2) and (3) are available in our university library.
Reference books on set theory and relations and functions
(1) Aka Setsuya, Introduction to Set Theory, Chikuma Gakugei Bunko, Chikuma Shobo, 2014
(2) Tadahiro Uezu, "Introduction to Set Theory: An Invitation to Infinity," Yuseisha, 2004
(3) Takeshi Inagaki, General Set Theory, Shibundo, 1968
Reference books on algebra
(1) Ichiro Yokota, "Introduction to Group Theory for First-Time Learners," Modern Mathematics, 2019
(2) Kazuo Matsuzaka, "Introduction to Algebraic Systems," Iwanami Shoten, 2018
(3) The University of Tokyo, Engineering Teaching Editing Committee, Algebra, Maruzen Publishing, 2018
Reference books on Boolean algebra
(1) Raymond Smullyan (translated by Haruyuki Kawabe), "Mr. Smullyan's Introduction to Boolean Algebra : Lying Puzzles, Paradoxes, and the Flowering Garden of Logic," Kyoritsu Publishing, 2008
(2) Hiroyoshi Nagata, Digital Circuits and Boolean Algebra for Beginners, Ohmsha, 1996
(3) Hiroshi Narushima and Akio Odaka, Boolean Algebra and its Applications, Tokai University Press, 1983
Kazuo Ushijima, "Discrete mathematics", Coronasha, 2006.
General reference books
(1) "Mathematics for Computers: A Logical Approach," by D. Griese and S. Schneider, translated by K. Namba and N. Doi, Nippon Hyoronsha, 2001.
(2) Seymour Lipschutz, "Discrete Mathematics: Fundamental Mathematics for Computer Science (McGraw-Hill University Seminar)", Ohmsha, 1995
(3) Hisakazu Ogura, Discrete Mathematics for Beginners, Kindai Kagaku-sha, 2011
Above (2) and (3) are available in our university library.
Reference books on set theory and relations and functions
(1) Aka Setsuya, Introduction to Set Theory, Chikuma Gakugei Bunko, Chikuma Shobo, 2014
(2) Tadahiro Uezu, "Introduction to Set Theory: An Invitation to Infinity," Yuseisha, 2004
(3) Takeshi Inagaki, General Set Theory, Shibundo, 1968
Reference books on algebra
(1) Ichiro Yokota, "Introduction to Group Theory for First-Time Learners," Modern Mathematics, 2019
(2) Kazuo Matsuzaka, "Introduction to Algebraic Systems," Iwanami Shoten, 2018
(3) The University of Tokyo, Engineering Teaching Editing Committee, Algebra, Maruzen Publishing, 2018
Reference books on Boolean algebra
(1) Raymond Smullyan (translated by Haruyuki Kawabe), "Mr. Smullyan's Introduction to Boolean Algebra : Lying Puzzles, Paradoxes, and the Flowering Garden of Logic," Kyoritsu Publishing, 2008
(2) Hiroyoshi Nagata, Digital Circuits and Boolean Algebra for Beginners, Ohmsha, 1996
(3) Hiroshi Narushima and Akio Odaka, Boolean Algebra and its Applications, Tokai University Press, 1983
- Non-social and professional independence development course
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | not applicable |
Last modified : Tue Sep 17 18:19:32 JST 2024