This series of course lecture notes was prepared by the author with the assistance of OpenAI ChatGPT (GPT-5.6). All materials have been carefully reviewed, verified, and revised by the author, who takes full responsibility for their content. In particular, key proofs and important mathematical concepts have been refined and rewritten by the author based on his own mathematical expertise and teaching experience. Despite these efforts, errors or omissions may remain. Readers are warmly encouraged to inform the author of any errors they may find so that they can be corrected in future revisions.
Week 1 (2026.09.08, 2026.09.10):
Week 2 (2026.09.15, 2026.09.17):
Lecture Note [Link]
Exercises:
Section 1.1: 5, 6, 9
Section 1.2: 11-18, 31, 32, 43-48, 49, 54, 56, 60, 73, 74, 86, 87
Section 1.3: 5-22, 37, 38, 47-49, 54, 62, 91-92, 106-112, 115, 122
Section 1.4: 11-14, 19, 20, 29, 69-72
Week 3 (2026.09.22, 2026.09.24):
Lecture Note [Link]
Exercises:
Section 1.5: 30, 32, 39-56, 59, 60, 73-76, 77-80, 81, 84
Review exercises (Chapter 1): 1-5, 9-12, 21, 27, 36-38, 49, 53, 69, 70, 80, 82, 91, 95, 98
Week 4 (2026.09.29, 2026.10.01):
Lecture Note [Link]
Exercises:
Section 2.1: 9-14, 24, 25, 27, 28, 73, 99
Section 2.2: 31-38, 39-50, 85-90
Section 2.3: 5-10, 15, 16, 34, 39, 41-44, 53, 54, 139
Week 5 (2026.10.06, 2026.10.08):
Lecture Note, Part I [Link]
Lecture Note, Part II [Link]
Exercises:
Section 2.4:
Section 2.5:
Section 2.6:
Section 5.3: 5, 7, 11,
Week 6 (2026.10.13, 2026.10.15):
Lecture Note [Link]
Exercises:
Section 3.1:
Section 3.2:
Section 3.3:
Week 7 (2026.10.20, 2026.10.22):
Week 8 (2026.10.27, 2026.10.29):
Week 9 (2026.11.03, 2026.11.05): Mid-exam (Chapters 1, 2, Sections 3.1-3.6, Sections 5.3 & 5.6)