MAST 661
Topics in Analysis
Fall 2026 · Convex and Non‑Linear Analysis
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 2026 · Real Analysis
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.
Winter 2026 · MATH 494
Readings
- Ingrid Daubechies, Ten Lectures on Wavelets.
- H. Dym and H. P. McKean, Fourier Series and Integrals.
- G. B. Folland, Fourier Analysis and Its Applications.
- G. B. Folland, Real Analysis: Modern Techniques and Their Applications.
- T. W. Korner, Fourier Analysis.
- W. Rudin, Real and Complex Analysis.
- W. Rudin, Functional Analysis.
- E. M. Stein and R. Shakarchi, Functional Analysis: Introduction to Further Topics in Analysis.
- Yves Meyer, Wavelets and Operators.
Winter 2024 · MATH 494
Readings
- Ingrid Daubechies, Ten Lectures on Wavelets.
- H. Dym and H. P. McKean, Fourier Series and Integrals.
- G. B. Folland, Fourier Analysis and Its Applications.
- G. B. Folland, Real Analysis: Modern Techniques and Their Applications.
- T. W. Korner, Fourier Analysis.
- W. Rudin, Real and Complex Analysis.
- W. Rudin, Functional Analysis.
- E. M. Stein and R. Shakarchi, Functional Analysis: Introduction to Further Topics in Analysis.
- Yves Meyer, Wavelets and Operators.
Fall 2023 · Non‑Linear Programming
Topics
- Multivariable calculus review
- Convex sets and convex functions
- Convex optimization and duality
- Selected topics in convex analysis
Readings
- Listed textbook (requirement not stated): Boyd and Vandenberghe. Convex Optimization. http://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf
- Accompanying lecture slides: http://www.stanford.edu/~boyd/cvxbook/bv_cvxslides.pdf
- Accompanying errata: https://web.stanford.edu/~boyd/cvxbook/cvxbook_errata.html
Fall 2023 · MATH 494
Readings
- M. S. Birman, M. Z. Solomjak, Spectral Theory of Self-Adjoint Operators in Hilbert Space.
Winter 2023 · Discrete Dynamical Systems, Chaos and Fractals
Topics
- Iteration of functions
- Periodic points, fixed points and bifurcations
- Sharkovsky theory
- Hénon map
- Complex dynamics
- Julia and Mandelbrot sets
- Iterated-function systems and fractals
Readings
- Saber Elaydi. Discrete Chaos, 2nd edition.
- Michael F. Barnsley. Fractals Everywhere.
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).
Fall 2021 · MATH 478
Readings
- Convex Optimization by Boyd and Vandenberghe.
Fall 2021 · MATH 494
Readings
- H. Dym and H. P. McKean, Fourier Series and Integrals.
- G. B. Folland, Fourier Analysis and Its Applications.
- G. B. Folland, Real Analysis: Modern Techniques and Their Applications.
- T. W. Korner, Fourier Analysis.
- W. Rudin, Real and Complex Analysis.
- W. Rudin, Functional Analysis.
- E. M. Stein and R. Shakarchi, Functional Analysis: Introduction to Further Topics in Analysis.
- P. Koosis, An Introduction to Hp Spaces.
- E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces.
- E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals.
- E. M. Stein, Singular Integrals and Differentiability Properties of Functions.
- C. Pereyra and L. Ward, Harmonic Analysis from Fourier to Wavelets.
- A. Zygmund, Trigonometric Series.
Sources
- Course catalogue ↗2026–2027
- Syllabus or course outline ↗Fall 2026
- Syllabus or course outline ↗Fall 2026
- Historical course outline ↗Winter 2026
- Historical course outline ↗Fall 2024
- Historical course outline ↗Winter 2024
- Syllabus or course outline ↗Fall 2023
- Historical course outline ↗Fall 2023
- Syllabus or course outline ↗Winter 2023
- Historical course outline ↗Fall 2022
- Historical course outline ↗Fall 2021
- Historical course outline ↗Fall 2021
- 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.
- 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. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Fall 2023 outline. Course header explicitly lists MATH 478, MAST 661. Additional materials are to be posted on Moodle but are not named in the public outline.
- 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.
- Winter 2023 outline. Course header explicitly lists MATH 475, MAST 661, MAST 865. Both books are explicitly recommended but not obligatory.
- 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. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.