Math 103: Complex Analysis, Fall 2007

All references below are to Gamelin, unless otherwise indicated.

Week | Date | Reading | Problems | Presentation Topics | Presenters | Food |
---|---|---|---|---|---|---|

1 | Thu, Sep 6 | Ch. I(all) | I.1: 1(UPick 3), 2b, 6 I.2: 1(all) I.3: 2,3,4 I.4: 3(all), 4b I.5: 2(UPick 3) I.6: 2(Upick 3) I.7: 1, 4, 7 I.8: 1(Upick 1),4,5 |
Exp and Log | Peter | |

Branches (I.7) | Thaniel | |||||

2 | Thu, Sep 13 | Ch. II(1–4) | I.7: 11 II.1: 13, 14, 17, 18 II.2: 3, 5 II.3: 2, 3, 4 II.4: 2, 3, 4, 7 |
Cauchy-Riemann equations | Rebecca | Nathaniel |

The Jacobian | Eric | |||||

3 | Thu, Sep 20 | Ch. II(5–7) | II.5: 1(UPick 3), 3, 6, 7 II.6: 1(UPick 1), 5, 6, 7 II.7: 1(UPick 3), 2, 3, 6, 9, 12 |
Harmony (Include proof of Theorem on page 57) | Adam | Peter |

Fractional Linear Transformations | Nick | |||||

4 | Thu, Sep 27 | Ch. III (1–5) | III.1: 7, 8. III.2: 3, 4. III.3: 1, 2. III.4: 1, 3. III.5: 1, 3, 5 or 6, 8. One problem in the weekly plan. |
More Harmony | Corey | Rebecca |

The Mean Value Property | Ben | |||||

5 | Thu, Oct 4 | Ch. IV (1–6) | IV.1: 1, 3, 5. IV.2: 2, 4. IV.3: 1, 3. IV.4: 1, 2, 3, 4. IV.5: 1, 2, 3, 4. IV.6: 1, 2. |
Morera's (two) theorems | Rebecca | Eric |

Cauchy's (countably many) integral formulas | Nathaniel | |||||

6 | Thu, Oct 11 | Ch. V (1–6) | V.1:∅. V.2:3, 7. V.3:4, 5, 6.. V.4:4, 8 (9 or 10), 13. V.5:1(Upick 2), 2, 4. V.6:3, 4, 6. |
V.2 | Eric | Adam |

V.4 | Peter | |||||

Fall Break | ||||||

7 | Thu, Oct 25 | Ch. V (7–8) Ch. VI (1–5) |
V.7: 2, 8, 11, 12, 13. V.8: 2, 5, 9. VI.1: 1, 2, 5. VI.2: 2, 6, 9, 12. VI.3: 1, 2. VI.4: 2, 3. VI.5: 3, 5. |
Analytic Continuation | Adam | Nick |

Laurant Series | Corey | |||||

8 | Thu, Nov 1 | Ch. VII(1–5, 8) | VII.1: 1, 3abf, 5, 6. VII.2: 4, 8, 12. VII.3: 2. VII.4: 2. VII.5: 4, 5. VII.8: 4, 5, 10, 13. UPick 2 more from any part of VII. |
Residues: Definition and generalities. | Nick | Corey |

Residues: A concrete example or two. | Ben | |||||

9 | Thu, Nov 8 | VIII: 1–6, and the thm in VIII.8 | VIII.1: 1, 4, 9. VIII.2: 2, 7. VIII.3: 1. VIII.4: 1, 5, 6. VIII.5: 1, 4, 8, 10. VIII.6: (1,2), 4, (5,6,7). |
The argument principle | Rebecca | Ben |

Winding Numbers | Peter | |||||

10 | Thu, Nov 15 | Ch IX. | IX.1: 1, 7. IX.2: (1, 2), 5, 7, 8, 9, 10. IX.3: 2, 7, 13, 14. |
Groups of conformal automorphisms. | Nathaniel | |

Hyperbolic Geometry | Eric | |||||

Thanksgiving Break | ||||||

11 | Thu, Nov 29 | Ch. XI:1,2,5,6. | XI.1: 1, 2, 3. XI.2: 1, 2, A. XI.5: 1, A, B. XI.6: 1, 2 |
Montel's theorem. | Adam | Nathanial |

The Riemann mapping theorem. | Ben | |||||

12 | Thu, Dec 6 | Ch. XIII | XIII.1: 1, A. XIII.2: 1, 6, A. XIII.3: 1, 3, 9, 10. XIII.4: 1, 2, 5. |
The Mittag-Leffler theorem. | Corey | Rebecca |

The Weierstrass product theorem. | Nick | |||||

13 | Tue, Dec 11 | Ch. XIV | XIV.1: 1, 2, (7), (3). XIV.2:4, 6. XIV.3: 1, 5, A XIV.4: 4, 11. XIV.5: 1, 2, 3, 4. |
The gamma function | Rebecca | Peter |

The prime number theorem | Adam |

Week | Date | Reading | Problems | Presentation Topics | Presenters | Food |
---|---|---|---|---|---|---|

Thu, Dec 20 | Final exam 2:00 – 5:00 |

Send questions, comments and complaints to Thomas Hunter

Last modified: 2007-12-19 14:15:12 by Thomas Hunter.