math 411: topics in advanced analysis
- Instructor: Kyle Ormsby
- Syllabus
- Course meetings: MWF 9-9:50 in Lib 389
- Drop-in hours: Tu 14-15, Th 11-12 in Lib 306
- Zulip workspace
- Gradescope
week 1
Monday 27 January: Welcome & warmup, intake survey, notes, demo 1, demo 2
Wednesday 29 January: Review of inner product spaces, notes
Friday 31 January: Review of $L^2$ and Hilbert spaces, notes
week 2
Monday 3 February: Fourier series notes, demo 1, demo 2
Wednesday 5 February: Dirac kernels and the inversion theorem, homework due, notes, demo
Friday 7 February: Examples
week 3
Monday 10 February: Weyl’s equidistribution theorem, notes, demo 1, demo 2
Wednesday 12 February: Riemann zeta values, homework due, notes
Friday 14 February: Snow day ❄️
week 4
Monday 17 February: Operators on Hilbert spaces, notes
Wednesday 19 February: Heat equation homework due, notes, 3b1b
Friday 21 February: Solving the heat equation, notes
week 5
Monday 24 February: Eigenbasis method and the wave equation, notes, demo
Wednesday 26 February: Fourier transform, homework due, notes
Friday 28 February: Schwartz space, notes
week 6
Monday 3 March: Inversion theorem for Fourier transforms, notes
Wednesday 5 March: Plancherel’s theorem and Poisson summation, homework due, notes
Friday 7 March: Exam review
week 7
Monday 10 March: Harmonic analysis preview, midterm exam distributed, notes
Wednesday 12 March: no class, midterm exam due
Friday 14 March: Discuss projects, project assignment, notes
week 8
Monday 17 March: Locally compact Abelian groups, notes
Wednesday 19 March: Pontryagin duals of LCA groups, homework due, notes
Friday 21 March: Pontryagin duality for LCA groups
spring break: 23-28 March
week 9
Monday 31 March: Haar integration, project proposal due, notes
Wednesday 2 April: Fubini’s theorem for Haar integrals, homework due, notes
Friday 4 April: Guest lecture: Josh Zahl, notes
week 10
Monday 7 April: Plancherel’s theorem for LCA groups, notes
Wednesday 9 April: Fourier analysis on Euclidean space, notes
Friday 11 April: Minkowski-Siegel’s geometry of numbers via Fourier analysis I, notes
week 11
Monday 14 April: Minkowski-Siegel’s geometry of numbers via Fourier analysis II, notes
Wednesday 16 April: Primes as sums of squares, homework due, notes, extremal body demo, $p=a^2+b^2$ demo
Friday 18 April: Poisson summation as a trace formula, notes
week 12
Monday 21 April: class optional (work time on drafts), paper draft due
Wednesday 23 April: no class (practice presentations)
Friday 25 April: student presentations: DD (distributions), SG (Heisenberg uncertainty)
week 13
Monday 28 April: student presentations: EW-S (discrete Fourier transform), NS (spectral bias and machine learning)
Wednesday 30 April: student presentations: GW (central limit theorem), NE (Levy’s continuity theorem)
Friday 2 May: student presentations: AK (Fourier transforms for non-Abelian groups)