2026 (Current Year) Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis E
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Masato Hoshino
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- MTH.C501
- Number of credits
- 100
- Course offered
- 2026
- Offered quarter
- 3Q
- Syllabus updated
- Mar 30, 2026
- Language
- English
Syllabus
Course overview and goals
In this course, I will explain fundamental concepts and techniques from real analysis and probability theory that are used in the analysis of stochastic partial differential equations. In the first half, I will introduce real analytic notions such as Besov spaces and paraproducts. In the second half, I will discuss applications to stochastic partial differential equations. This course will be completed with "Advanced topics in Analysis F" in the next quarter.
Course description and aims
This course emphasizes the importance of rigorous treatment of various problems in stochastic partial differential equations by the use of concepts in real analysis and probability theory.
Keywords
Schwartz distributions, Besov spaces, Paraproduct, White noise, Stochastic partial differential equations
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
This is a standard lecture course. There will be some assignments.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | The following topics will be covered: -- Fourier transform of Schwartz distributions |
Details will be provided in class. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None required
Reference books, course materials, etc.
Details will be provided during each class.
Evaluation methods and criteria
Report (100%)
Related courses
- MTH.C305 ： Real Analysis I
- MTH.C306 ： Real Analysis II
- MTH.C351 ： Functional Analysis
- MTH.C211 ： Applied Analysis I
- MTH.C212 ： Applied Analysis II
Prerequisites
Basics of Lebesgue integral theory, Fourier analysis, and functional analysis are required.