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National Taiwan Normal University Course Outline Fall , 2025 |
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| I.Course information |
| Serial No. | 2601 | Course Level | Master / PhD |
| Course Code | MAC8039 | Chinese Course Name | 調和分析 |
| Course Name | Harmonic Analysis | ||
| Department | Department of Mathematics | ||
| Two/one semester | 1 | Req. / Sel. | Sel. |
| Credits | 3.0 | Lecturing hours | Lecture hours: 3 |
| Prerequisite Course | ◎1. This is a cross-level course and is available for junior and senior undergraduate students, master's students and PhD students. 2. If the listed course is a doctroal level course, it is only available for master's students and PhD students. | ||
| Comment | |||
| Course Description | |||
| Day & Class Period/Location | Wed. 2-3 Gongguan M210, Thur. 8 Gongguan M210 | ||
| Curriculum Goals | Corresponding to the Departmental Core Goal | ||
| 1. Basic Proficiency in Harmonic Analysis |
Master: 1-1 Equipped with professional mathematics competences Doctor: 1-1 Equipped with professional mathematics competences |
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| 2. Ability to Solve Exercises in Harmonic Analysis |
Master: 1-3 Being able to think mathematically and critically Doctor: 1-3 Being able to think mathematically and critically |
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| 3. Collaborative Homework |
Master: 3-3 Being willing to work collaboratively Doctor: 3-3 Being willing to work collaboratively |
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| 4. Individual Exams with Exercises to Test Understanding of Theory |
Master: 3-2 Possessing the abilities to think independently, criticize, and reflect Doctor: 3-2 Possessing the abilities to think independently, criticize, and reflect |
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| II. General Syllabus |
| Instructor(s) | Daniel Spector/ 司靈得 | ||
| Schedule | |||
This course is a first year graduate level course in harmonic analysis. We assume familiarity with the construction of the Lebesgue integral and cover select topics from Grafakos’ Classical Fourier Analysis Book: Lp and Weak Lp Spaces; Interpolation; Convolution and Approximate Identities; Lorentz Spaces; Maximal Functions; Fourier Transform; Distributions; Fourier Series; Singular Integrals of Convolution Type; Littlewood-Paley Theory and Multipliers; Weighted Inequalities. Week 1: Weak Lp and the Distribution Function (p.1-10) Week 2: Convolution and Approximate Identities (p.16-28) Week 3-4: Real and Complex Interpolation (p.30-39) Week 5: Lorentz Spaces (p. 44-63) Week 6: Maximal Functions (p.77-89) Week 7-8: The Fourier Transform (p.94-106) Week 9: Tempered Distributions (p.109-122) Week 10: Laplacian and Riesz Potentials (p.124-133) Week 11: Fourier Multipliers (p. 135-143) Week 12-14: Singular Integrals (p. 249-297) Week 15-16: Littlewood-Paley Theory (p.341-371) |
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| Instructional Approach | |||
| Methods | Notes | ||
| Formal lecture | |||
| Grading assessment | |||
| Methods | Percentage | Notes | |
| Assignments | 20 % | ||
| Midterm Exam | 20 % | ||
| Final exam | 20 % | ||
| Class discussion involvement | 20 % | ||
| Attendances | 20 % | ||
| Required and Recommended Texts/Readings with References | Grafakos’Classical Fourier Analysis | ||