MATH 464
Real Analysis
Fall 2026
Topics
- Sets, functions, relations and countability
- Construction and topology of the real numbers
- Metric spaces, normed linear spaces and point-set topology
- Compactness, Heine–Borel and Bolzano–Weierstrass properties
- Baire category theorem
- Continuous functions, connectedness and intermediate values
- Function spaces and uniform convergence
- Arzelà–Ascoli theorem
- Stone–Weierstrass approximation
- Fixed-point theorems and applications
Readings
- Reference (not explicitly required): H. L. Royden. Real Analysis, 2nd, 3rd or 4th edition. MacMillan.
- Reference (not explicitly required): W. Rudin. Principles of Mathematical Analysis.
Fall 2024 · MATH 464
Readings
- W. Rudin, Principles of Mathematical Analysis, 3rd edition.
- E. T. Copson, Metric Spaces.
Sources
- Course catalogue ↗2026–2027
- Syllabus or course outline ↗Fall 2026
- Historical course outline ↗Fall 2024
- Historical course outline ↗Fall 2023
- Historical course outline ↗Fall 2022
- Historical course outline ↗Fall 2021
- Fall 2026 outline. Course header explicitly lists MATH 464, MAST 661, MAST 837. Books are listed as reference textbooks; no required status is stated.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. The source states that purchasing the book is not required. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.