| Academic Year |
2025Year |
School/Graduate School |
School of Science |
| Lecture Code |
HB282000 |
Subject Classification |
Specialized Education |
| Subject Name |
数理解析学Ｂ |
Subject Name
（Katakana） |
スウリカイセキガクB |
Subject Name in
English |
Mathematical Analysis B |
| Instructor |
HIRATA KENTARO |
Instructor
(Katakana) |
ヒラタ ケンタロウ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
4th-Year, Second Semester, 3Term |
| Days, Periods, and Classrooms |
(3T) Tues3-4,Weds5-6：SCI E211 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face |
| Lectures on blackboard |
| Credits |
2.0 |
Class Hours/Week |
4 |
Language of Instruction |
J
:
Japanese |
| Course Level |
4
:
Undergraduate Advanced
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
|
| Keywords |
|
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) | Mathematics
（Knowledge and Understanding）
・Acquiring knowledge and vision on advanced theories as an extension of core theory of modern mathematics. |
|---|
Class Objectives
/Class Outline |
Several properties of Hausdorff outer measure, the Hausdorff dimensions of self-similar sets, the box dimensions of the graphs of functions and some developments in the area of real analysis will be explained. |
| Class Schedule |
lesson1 Outer measure and measurability
lesson2 Hausdorff outer measure
lesson3 Vitali covering lemma
lesson4 Hausdorff and Lebesgue outer measures
lesson5 Cantor set
lesson6 Hausdorff dimension
lesson7 Iterated function system and self-similar set
lesson8 Dimensions of self-similar sets
lesson9 Examples of self-similar sets
lesson10 Box dimension
lesson11 Box dimensions of the graphs of functions
lesson12 Weierstrass function
lesson13 Kakeya problem
lesson14 Kakeya maximal function
lesson15 Davies theorem |
Text/Reference
Books,etc. |
Not specified |
PC or AV used in
Class,etc. |
Handouts, Microsoft Stream |
| (More Details) |
Blackboard, distributed materials and projector if necessary |
| Learning techniques to be incorporated |
Quizzes/ Quiz format, Post-class Report |
Suggestions on
Preparation and
Review |
Make a summary of what you have learned and do excercises. |
| Requirements |
|
| Grading Method |
Based on reports (70%) and class participation (30%) |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |