🌌 Functional Analysis

"Functional analysis is the study of infinite-dimensional vector spaces and the mappings between them."

📈 Course Metadata

• Department: School of Mathematical Sciences
• Prerequisites: Mathematical Analysis, Higher Algebra, Real Analysis, Point Set Topology
• Course Nature: Core undergraduate course for Mathematics majors

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📚 References & Credits

The construction of these notes is primarily based on the following resources:

1. Course PPT: Special thanks to the instructor for providing detailed lecture slides. The logical structure and derivation paths of these MkDocs notes deeply reference the PPT's organization.
2. Wang Shengwang & Zheng Weixing, Outline of Real Analysis and Functional Analysis (Volume II)

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🗺️ Syllabus & Navigation

The following notes are continuously being updated:

Part I: Theory of Metric Spaces

• Chapter 1: Metric Spaces

• Chapter 2: Topology and Completeness

• Chapter 3: Compactness

• Chapter 4: Contraction Mapping Theorem

Part II: Normed Linear Spaces and Banach Spaces

• Chapter 5: Normed Linear Spaces

• Chapter 6: Banach Spaces

Part III: Inner Product Spaces and Hilbert Spaces

• Chapter 7: Inner Product Spaces

• Chapter 8: Hilbert Space Theory

• Chapter 9: Linear Operators

Part IV: Four Fundamental Theorems and Dual Spaces

• Chapter 10: Open Mapping and Closed Graph Theorems

• Chapter 11: Dual Spaces

• Chapter 12: Extension of Bounded Linear Functionals and the Uniform Boundedness Principle

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📝 Notes & Formatting Details

Construction Complete

This page is now substantially complete. Long theorems and exercise solutions in the notes feature a folded box design. If you spot any typos, please feel free to raise an Issue or contact me directly for corrections!

"The passage from finite to infinite dimensions is a fundamental shift in mathematical thinking."

💬 Comments