3. 강의목표
This course is the second part of the graduate real analysis sequence. It builds upon the foundational topics covered in the first part, including abstract measure theory, Littlewood's three principles, convergence theorems, Lebesgue differentiation theorem, L^p spaces, interpolation theorems, and inequalities. In this course, we will focus on more advanced topics in real analysis, including functional analysis, its applications to PDEs, Distribution Theory, (and a hint of harmonic analysis via following Grafakos' "Classical Fourier Analysis" if time allows). By the end of this course, students should have a solid understanding of advanced real analysis techniques and be able to apply them to various mathematical problems.
4. 강의선수/수강필수사항
Real analysis I (Math 514)
5. 성적평가
Midterm Exam: 50%
Final Exam: 50%
6. 강의교재
| 도서명 |
저자명 |
출판사 |
출판년도 |
ISBN |
|
Functional Analysis, Sobolev Spaces and Partial Differential Equations.
|
Brezis, H.
|
Springer.
|
2010
|
|
|
Real Analysis: Modern Techniques and Their Applications
|
Folland, G. B.
|
Wiley-Interscience.
|
1999
|
|
7. 참고문헌 및 자료
Grafakos, L. (2014). Classical Fourier Analysis. Springer.
8. 강의진도계획
We will cover the following topics.
1. The Hahn–Banach Theorems. Introduction to the Theory of Conjugate Convex Functions
2. The Uniform Boundedness Principle and the Closed Graph Theorem
3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity
4. Distribution Theory
5. Sobolev Spaces
6. Compact Operators.
7. A Hint of Harmonic Analysis via following Grafakos' Classical Fourier Analysis if time allows.
10. 학습법 소개 및 기타사항
TA: Jungmin Lee (Room 411)
11. 장애학생에 대한 학습지원 사항
- 수강 관련: 문자 통역(청각), 교과목 보조(발달), 노트필기(전 유형) 등
- 시험 관련: 시험시간 연장(필요시 전 유형), 시험지 확대 복사(시각) 등
- 기타 추가 요청사항 발생 시 장애학생지원센터(279-2434)로 요청