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All readings are from Rudin, W. *Principles of Mathematical Analysis*. 3rd ed. McGraw-Hill Science/Engineering/Math, New York, NY: McGraw-Hill, 1976. ISBN: 007054235X.

Course readings.
WEEK # |
TOPICS |
READINGS |

1 |
Sets and Fields, The Real Numbers |
pp. 1-17. |

2 |
Countability, Metric Spaces |
pp. 24-35. |

3 |
Closed Sets, Compact Spaces |
pp. 34-38. |

4 |
Compact Subsets of Euclidean Space |
pp. 38-40. |

5 |
Completeness, Sequences and Series |
pp. 42-43, 47-69, and 71-75. |

6 |
Continuity |
pp. 83-86. |

7 |
Continuity and Compactness |
pp. 85-93. |

8 |
Differentiability, Mean Value Theorem |
pp. 103-110. |

9 |
Taylor Series, Riemann-Stieltjes Integral |
pp. 120-127. |

10 |
Integrability, Fundamental Theorem of Calculus |
pp. 128-136. |

11 |
Sequences of Functions |
pp. 143-151. |

12 |
Uniform Convergence |
pp. 150-154. |

13 |
Uniform Convergence, Equicontinuity |
pp. 150-161. |

14 |
Power Series, Fundamental Theorem of Algebra |
pp. 83-86 and 180-185. |