PMATH 753
Functional Analysis
Fall 2024
Topics
- Banach and Hilbert spaces
- Bounded linear maps
- Hahn–Banach theorem
- Open mapping and closed graph theorems
- Topologies, nets and Hausdorff spaces
- Tietze extension theorem
- Dual spaces and weak topologies
- Tychonoff and Banach–Alaoglu theorems
- Reflexive spaces
Fall 2019
Topics
- required.
Undated
Topics
- Preliminaries
- Hilbert Spaces
- Banach Spaces
- Topology
Readings
- Chapter 1. Preliminaries — https://www.math.uwaterloo.ca/~snew/PMATH453/Chap1Preliminaries.pdf
- Chapter 2. Hilbert Spaces — https://www.math.uwaterloo.ca/~snew/PMATH453/Chap2HilbertSpaces.pdf
- Chapter 3. Banach Spaces — https://www.math.uwaterloo.ca/~snew/PMATH453/Chap3BanachSpaces.pdf
- Chapter 4. Topology — https://www.math.uwaterloo.ca/~snew/PMATH453/Chap4Topology.pdf
- Appendix 1. Lecture Notes for PMATH 351 — https://www.math.uwaterloo.ca/~snew/PMATH453/PMATH351Notes.pdf
- Appendix 2. Lecture Notes for PMATH 450 — https://www.math.uwaterloo.ca/~snew/PMATH453/PMATH450Notes.pdf
Sources
- Course catalogue ↗2026–2027
- course_outline ↗Fall 2024
- course_outline ↗Fall 2019
- course_website ↗Undated
- Official public PDF outline or course description. Materials and topic extracts may be partial; consult the linked source for the full list.
- Official public PDF outline or course description. Materials and topic extracts may be partial; consult the linked source for the full list.
- Public lecture-note archive by Stephen New. Topics are the chapter headings in the posted notes; this is not a current-term syllabus. Source term/year not established.