MATH 479
Convex and Non‑Linear Analysis
Fall 2026
Topics
- Convex sets, separation theorems and polar sets
- Ellipsoids and John’s theorem
- Convex functions, differentiability criteria and inequalities
- Conjugate functions
- Brunn–Minkowski theorems
- Polarity and duality
- Symmetrizations and rearrangements
- Loomis–Whitney inequalities, projections and sections
- Centers of mass
- Selected topics in advanced convexity
Readings
- Reference (not explicitly required): C. P. Niculescu and L.-E. Persson. Convex Functions and Their Applications: A Contemporary Approach. Springer, 2018.
- Reference (not explicitly required): Boyd and Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
- Reference (not explicitly required): D. Hug and W. Weil. Lectures in Convex Geometry. Springer, 2020.
- Reference (not explicitly required): Peter M. Gruber. Convex and Discrete Geometry. Springer, 2007.
Fall 2022 · MATH 479
Readings
- Convex functions and their applications: a contemporary approach by C. P. Niculescu and L.-E. Persson, Springer (2018).
- Boyd and Vanderberghe, Convex Optimization, Cambridge University Press, 2004 (author spelling as printed).
- Selected Topics in Convex Geometry by Maria Moszynska, Birkhauser (2006).
- Convex and discrete geometry by Peter M. Gruber, Springer (2007).
Sources
- Course catalogue ↗2026–2027
- Syllabus or course outline ↗Fall 2026
- Historical course outline ↗Fall 2022
- Fall 2026 outline. Course header explicitly lists MATH 479, MAST 661, MAST 837. These are optional sources students “may consult”; author/publisher spelling in the second entry has been lightly normalized.
- 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.