LEC # | TOPICS | KEY DATES |
---|---|---|

1 | Basic Banach Space Theory | |

2 | Bounded Linear Operators | Assignment 1 due |

3 | Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem | |

4 | The Open Mapping Theorem and the Closed Graph Theorem | Assignment 2 due |

5 | Zorn's Lemma and the Hahn-Banach Theorem | |

6 | The Double Dual and the Outer Measure of a Subset of Real Numbers | Assignment 3 due |

7 | Sigma Algebras | |

8 | Lebesgue Measurable Subsets and Measure | Assignment 4 due |

9 | Lebesgue Measurable Functions | |

10 | Simple Functions | Assignment 5 due |

11 | The Lebesgue Integral of a Nonnegative Function and Convergence Theorems | |

Midterm Exam | Midterm Exam due | |

12 | Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence Theorem | |

13 | L^{p} Space Theory | |

14 | Basic Hilbert Space Theory | Assignment 6 due |

15 | Orthonormal Bases and Fourier Series | |

16 | Fejer's Theorem and Convergence of Fourier Series | Assignment 7 due |

17 | Minimizers, Orthogonal Complements and the Riesz Representation Theorem | |

18 | The Adjoint of a Bounded Linear Operator on a Hilbert Space | Assignment 8 due |

19 | Compact Subsets of a Hilbert Space and Finite-Rank Operators | |

20 | Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert Space | Assignment 9 due |

21 | The Spectrum of Self-Adjoint Operators and the Eigenspaces of Compact Self-Adjoint Operators | |

22 | The Spectral Theorem for a Compact Self-Adjoint Operator | Assignment 10 due |

23 | The Dirichlet Problem on an Interval | |

Final Assignment | Final Assignment due |