**Math 412:** Topology with Applications

**Time:** T TH, 10:05 - 11:20AM

**Location:** West Duke 08A

**Instructor:** Paul Bendich

**Office Hours:** Physics 210, M 1-2, TH 12-1

Course Description and Grading Policy

**Main Textbooks:** We will be using two textbooks.
They are *
Topology: A First Course*, by James Munkres and * Computational Topology *, by Herbert Edelsbrunner and John Harer.
I'll refer to them as "T" and "C," respectively, in the syllabus below.
We will also use some supplementary handouts, including journal articles.

Date | Topics | Chapters |
---|---|---|

Aug. 28 | Overview, Introduction, Motivating Examples | |

Aug. 30 | Point-set Topology: Definitions, Examples | T: 2-1,2-2 |

Sept. 4 | Product and Subspace Topologies | T: 2-4,2-5 |

Sept. 6 | Closed Sets and Limit Points | T: 2-6 |

Sept. 11 | Continuity | T: 2-7 |

Sept. 13 | Connectedness | T: 3-1,3-2 |

Sept. 18 | Compactness | T: 3-5,3-6 |

Sept. 20 | Compactness | T: 3-5,3-6 |

Sept. 25 | Quotient Topology | T: 2-11 |

Sept. 27 | Simplicial Complexes | C: III.1 |

Oct. 2 | Convex Set Systems | C: III.2 |

Oct. 4 | Point Cloud Triangulations | C: III.3,III.4 |

Oct. 9 | Simplicial Homology: Definitions, Examples | C: IV.1 |

Oct. 11 | Induced Maps | C: IV.1 |

Oct. 18 | Singular Homology, Functoriality | |

Oct. 23 | Matrix Reduction Algorithm | C: IV.2 |

Oct. 25 | Relative Homology | C: IV.3 |

Oct. 30 | Exact Sequences | C: IV.3, IV.4 |

Nov. 1 | Zig-zag Lemma | C: IV.4 |

Nov. 6 | Persistent Homology: Intro | C: VII.1 |

Nov. 8 | The Persistence Algorithm | C: VII.1, VII.2 |

Nov. 13 | Morse Theory and Persistence | C: VI.1, VI.3 |

Nov. 15 | Stability Theorems and Homology Inference | C: VII.2 |

Nov. 20 | Gene Expression Data | C: IX.1 |

Nov. 27 | Extended Persistence | C: VII.3 |

Nov. 29 | Protein Docking and the Elevation Function | C: IX.2 |

Dec. 4 | Presentations | |

Dec. 6 | Presentations | |