| 1 | Introduction | |
| 2 | Measures | Assignment 1 due (one day after Lecture 2) |
| 3 | Chebyshev's Inequality | |
| 4 | Law of Large Numbers | Assignment 2 due (one day after Lecture 4) |
| 5 | Measurable Functions | Assignment 3 due (one day after Lecture 5) |
| 6 | The Integral | |
| 7 | Linearity | Assignment 4 due (one day after Lecture 7) |
| 8 | Fatou's Lemma | |
| 9 | Integrable Functions | Assignment 5 due (one day after Lecture 9) |
| 10 | Bessel's Inequality | |
| 11 | Convergence of Fourier Series | Assignment 6 due (one day after Lecture 11) |
| 12 | Completeness | |
| 13 | First In-class Test | |
| 14 | Riesz Representation Theorem | |
| 15 | Schwartz Functions | Assignment 7 due (one day after Lecture 15) |
| 16 | Fourier Transform | |
| 17 | Approximation | Assignment 8 due (one day after Lecture 17) |
| 18 | Harmonic Oscillator | |
| 19 | Completeness of Eigenfunctions | Assignment 9 due (one day after Lecture 19) |
| 20 | Sobolev Spaces | Assignment 10 due (one day after Lecture 20) |
| 21 | Second In-class Test | |
| 22 | Wave Equation | |
| 23 | Bounded Operators | |
| 24 | Compact Operators | Assignment 11 due (one day after Lecture 24) |
| 25 | Spectral Theorem | |
| 26 | Hilbert-Schmidt Operators | |
| 27 | Final Exam | |
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