Course Information

The first section (Thursday, September 26) will meet but will be introductory.

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**Office Hours**:

Babson: 10 Monday

Schenthal: 11 Thursday

**Course Outline:** The course will cover chapters 1 through 6.

The prerequisites for this course are (from the course catalog): Graduate standing in Mathematics or Applied Mathematics, or consent of instructor

This is a rough outline of when topics will be covered and will be edited as the term progresses. The exam scheduling will not change. Homework problems will also be added with assignments collected on Fridays.

Day | Date | Section(s) covered | Homework |

Friday | September 27 | 1.1 Metric and Normed Spaces | |

Monday | September 30 | 1.2, 1.3 Cauchy and convergent sequences | |

Wednesday | October 2 | 1.5 topological spaces | |

Friday | October 4 | 1.4 Continuity | HW1 |

Monday | October 7 | 1.6 strong/weak topologies | |

Wednesday | October 9 | 1.6 Completion | |

Friday | October 11 | 1.6 Completion | HW2 |

Monday | October 14 | 1.3 RS Borel and Measure | |

Wednesday | October 16 | 1.3 RS L^1 completeness | |

Friday | October 18 | 1.7, 1.8 Compactness | Problems 1, 5 and 6 from HW3 and problems 17, 18 and 28 from chapter 1, volume 1 of Reed and Simon (handed out in class) |

Monday | October 21 | 2.2 C(K) completeness | |

Wednesday | October 23 | 4.7 Fol Stone-Wieistrass | |

Friday | October 25 | 2.4: Arzela-Ascoli | Problems 2,3 and 4 from HW3 and Problems 1 and 2 from HW4 and Problem 1.15 from Hunter and Nachtergaele |

Monday | October 28 | 3.1,3.2, 3.3: Lipschitz and Contraction | |

Wednesday | October 30 | 3.4: Integral Ops and Green's functions | |

Friday | November 1 | Review | Problems 3, 4, 5, 6 and 7 from HW4 and Problems 1, 2 and 3 from HW5 These problems are on material which will be covered on the midterm, but they will not be collected for another week. |

Monday | November 4 | Midterm | Try:Hunter's Midterm 1,3,4, Hunter's Final 1,2,3,4 and Thomases' Midterm 1,3,4,5 |

Wednesday | November 6 | 3.5, 2.5: ODE | |

Friday | November 8 | 4.6 Fol Tychonoff | |

Monday | November 11 | Veteran's Day: No Class | |

Wednesday | November 13 | 5.1 Banach | |

Friday | November 15 | 5.1-5.2 Banach | Problem 3.7 from Hunter and Nachtergaele, Problem 60 on page 132 in Folland (Use the diagonal trick to show that the product of countably many sequentially compact spaces is sequentially compact.) and Problems 1, 2 and 3 from HW6 |

Monday | November 18 | 5 Bases, Equivalence, Fin Dim | |

Wednesday | November 20 | 5 Ker, Examples | |

Friday | November 22 | 5 Closed Embedding, Duals | |

Monday | November 25 | 5 Compact Operators, Norm/Pointwise Top | |

Wednesday | November 27 | 6 Hilbert | Problem 5.3 in Hunter-Nachtergaele and HW7 |

Friday | November 29 | Thanksgiving: No Class | |

Monday | December 2 | 6 Projection and Sum | |

Wednesday | December 4 | 6 ONB | |

Friday | December 6 | 6 Sep Hilb, QM | HW8 |

Thursday | December 12 | Final Exam:6:00pm-8:00 PHY 148 | |