Readings are assigned in Rudin, W. *Principles of Mathematical Analysis*. 3rd ed. McGraw-Hill Science/Engineering/Math, New York, NY: McGraw-Hill, 1976. ISBN: 9780070542358.

The supplementary notes are courtesy of Prof. Todd Kemp and are used with permission.

SES # | TOPICS | READINGS |
---|---|---|

1 | Ordered sets and fields | Section 1.1-31 |

2 | Countability, Euclidean spaces | Section 1.32-38, and 2.1-17 |

3 | Metric spaces | Section 2.15-28 |

4 | Relative topology, compact sets | Section 2.29-40 |

5 | Compact sets | Section 2.36-44 |

6 | Connected sets, convergence | Section 2.45-47, and 3.1-7 |

7 | Sequential compactness | Notes (PDF) |

8 | Completeness | Section 3.8-20 |

9 | Construction of the real numbers | Notes (PDF) |

10 | Series | Section 3.20-37 |

11 | Series (cont.) | Section 3.38-55 |

12 | Continuity | Section 4.1-12 |

13 | l^p spaces | Notes (PDF) |

14 | Continuity and compactness, connectedness | Section 4.13-24 |

15 | Discontinuities, monotone functions | Section 4.25-34 |

16 | Differentiability, mean value theorem | Section 5.1-11 |

17 | l’Hospital’s rule, Taylor’s theorem | Section 5.12-19 |

18 | Riemann integral | Section 6.1-12 with alpha(x)=x |

19 | Riemann integrability and continuity almost everywhere | Notes (PDF) |

20 | Stieltjes integral, fundamental theorem of calculus | Section 6.1-22 |

21 | Sequences and series of functions | Section 7.1-17 |

22 | Equicontinuity | Section 7.18-25 |

23 | Optional material: Weierstrass function, Devil’s staircase | Weierstrass function (PDF), Devil’s staircase (PDF) |

24 | Review for final exam | No readings |

25 | Review for final exam (cont.) | No readings |