Text: Real Analysis, by H.L. Royden, P.M. Fitzpatrick, Fourth Edition.

The class meetings to be spent on each topic are approximate.

Chapters II, III; Sec # |
Topic |
Class meetings |

9 |
Metric Spaces: General Properties |
4 |

10 |
Metric Spaces: Fundamental Theorems |
3 |

14 |
Duality for Normed Spaces. Weak topology |
4 |

17 |
General Measure Spaces |
6 |

18 |
Integration |
12 |

19,20 |
L^p Spaces; Particular Measures |
12 |

There will be three tests during the semester (100 pts.
each). Also each student will have to work on and present a project. Final exam
(notice different time!) is scheduled for **7:00
**- **8:50 AM** on Wednesday, May 9,
2018.

Text: Complex Analysis, by Lars V. Ahlfors, Third Edition.

The number of classroom hours to be spent on each topic is approximate.

Sections |
Topic |
Class meetings |

4.6.1-4.6.5 |
Harmonic functions |
5 |

5.1.1-5.2.2 |
Power series expansions |
6 |

5.2.3-5.2.5 |
Gamma function |
4 |

5.3.1-5.4.1 |
Product development |
3 |

5.4.2-5.44 |
Riemann Zeta function |
3 |

5.5.1-5.5.5 |
Normal families |
6 |

6.1.1-6.1.4 |
Riemann mapping theorem |
6 |

6.2.1-6.2.3 |
Conformal mapping of the disc onto polygons |
6 |

There will be three tests during the semester (100 pts.
each). Also each student will have to work on and present a project. Final exam
(notice different time!) is scheduled for 9:00 - 10:50 AM on Monday, May 7,
2018.