Syllabus

Homework

Class Date |
Book |
Pages/Sections |
Topics |
---|---|---|---|

Oct. 30 | Bak and Newman | Ch. 1 and 2 : pp. 1-32 | introductions, complex differentiation |

Nov. 2 | Bak and Newman | Ch. 3 and 4: pp. 35-56 | analytic functions, complex line integrals |

Nov. 4 | Bak and Newman | Ch. 5 and 6: pp. 58-66, 77-88 | analytic functions as power series, Cauchy integral formula, uniqueness theorem, minimum modulus theorem, open mapping theorem |

Nov. 6 | Bak and Newman | Ch. 7 and 8: pp. 93-115 | analytic functions as power series, Cauchy integral formula, uniqueness theorem, minimum modulus theorem, open mapping theorem |

Nov. 9 | Bak and Newman | Ch. 9 and 10: pp. 117-140 | singularities, Laurent expansions, winding numbers, Cauchy residue theorem, meroorphic functions |

Nov. 11 | Manetti, Lee | Ch. 1: pp. 1-19, Ch. 1: pp. 1-17 | finish up complex analysis discussion, big picture of topology/manifolds |

Nov. 13 | Manetti, Lee | Ch. 3 pp. 39-57, Ch. 2,3: pp. 19-31, 33-35 49-55 | topological spaces, homeomorphisms, metric spaces, subspace |

Nov. 16 | Manetti, Lee | Ch. 3,4: pp. 58-61, 63-75, Ch. 2,3,4: 31-32 pp. 60-63, 64-65, 85-100 | product space, Hausdorff, connectedness, compact spaces |

Nov. 18* | Miranda, Manetti, Lee | Ch. 3: pp. 75, Ch. 4: pp. 79-82, Ch. 3: pp. 77-81 | group actions, topological groups |

Nov. 20 | Manetti, Lee | Ch. 5: pp. 87-97, Ch. 3: pp. 65-73 | identifications, quotient topology, projective space |

Nov. 23 | Manetti, Lee, Cavalieri & Miles | Ch. 6: pp. 105-108, Ch. 2: pp. 36-45, Ch.2: 14-31 | second countable, manifolds |

Nov. 25 | Miranda, Cavalieri & Miles | Ch. I.1, I.2: pp. 1-4, 7-9, Ch. 1.4, 3.1, 3.2: 9-13, 32-35, 38-41 | riemann surfaces definition, first examples: projective line, complex tori, and kth roots, inverse function theorem |

Nov. 30 | Miranda, Cavalieri & Miles | Ch. I.2, I.3: pp. 10-18, Ch. 3: pp. 35-37, 41-46 | graphs, affine plane curves, projective curves |

Dec. 2 | Miranda | Ch. II.1, II.2: pp. 21-38 | holomorphic and meromorphis functions on Riemann surfaces, singularities |

Dec. 4 | Miranda, Cavalieri & Miles | Ch II.3: pp. 38-42,, Ch. 4: pp. 47-54 | maps between Riemann surfaces |

Dec. 7 | Miranda, Cavalieri & Miles | Ch. II.4, III.1: pp. 44-53 and 57-65, Ch. 4: pp 54-61 | degree, (Riemann-)Hurwitz formula, hyperelliptic Riemann surfaces, maps between complex tori |

Dec. 9 | Miranda | Ch. III.3: pp. 75-83 | quotient Riemann surfaces, ramification, Hurwitz's theorem on automorphisms |

Dec. 11 | Cavalieri & Miles, Miranda | Ch. 5: pp. 63-79, Ch. III.4: pp. 84-86 | homotopy, fundamental groups, coverings |

Dec. 14 | Miranda, Cavalieri & Miles | Ch. III.4: pp. 86-93, Ch. 6, 7: pp. 80-96 | monodromy, Riemann Existence Theorem |

Dec. 16 | tie up all the loose ends |

HW | Due Date | Problems |
---|---|---|

# PS 1 | Nov. 13 | Complex Analysis |

# PS 2 | Nov. 25 | Topology |

# PS 3 | Dec. 9 | Riemann Surfaces #1 |

# PS 4 | Dec. 18 | Riemann Surfaces #2 |