# Syllabus

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## Prerequisites

Multivariable Calculus (18.02); Differential Equations (18.03) or Honors Differential Equations (18.034)

## Text

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

## Assignments

Weekly homework is due each Friday at 3 PM. Late homework will not be accepted, but the lowest score will be dropped.

## Exams

There will be two midterms and a final exam.

## Grading

ACTIVITIES | PERCENTAGES |
---|---|

Ten Problem Sets | 40% |

Exam 1 | 15% |

Exam 2 | 15% |

Final Exam | 30% |

## Calendar

WEEK # | TOPICS | KEY DATES |
---|---|---|

1 | Sets and Fields, The Real Numbers | |

2 | Countability, Metric Spaces | Problem set 1 due |

3 | Closed Sets, Compact Spaces | Problem set 2 due |

4 | Compact Subsets of Euclidean Space | Problem set 3 due |

5 | Completeness, Sequences and Series | Problem set 4 due |

6 | Continuity | |

Exam 1 | ||

7 | Continuity and Compactness | Problem set 5 due |

8 | Differentiability, Mean Value Theorem | Problem set 6 due |

9 | Taylor Series, Riemann-Stieltjes Integral | Problem set 7 due |

10 | Integrability, Fundamental Theorem of Calculus | Problem set 8 due |

11 | Sequences of Functions | |

Exam 2 | ||

12 | Uniform Convergence | |

13 | Uniform Convergence, Equicontinuity | Problem set 9 due |

14 | Power Series, Fundamental Theorem of Algebra | Problem set 10 due |

15 | Final Review | |

Final Exam |