### Course Meeting Times

Lectures: 2 sessions / week, 1.5 hour / session

### Prerequisites

*18.02 Multivariable Calculus*; *18.03 Differential Equations* or *18.034 Honors Differential Equations*

### Text

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

### Assignments

Weekly homework is due on the second day of class each week. There are 10 homework assignments; the lowest two scores will be dropped.

### Exams

There are four in-class 30-minute quizzes, and one 3-hour final exam. The worst quiz score is dropped.

### Grading

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

Problem sets | 20% |

In-class quizzes | 25% |

Final exam | 45% |

Discussion | 10% |

### Calendar

SES # | TOPICS | KEY DATES |
---|---|---|

1 | Ordered sets and fields | |

2 | Metric spaces | |

3 | Relative topology, compact sets | |

4 | Compact sets (cont.) | |

5 | Connected sets, convergence | |

6 | Sequential compactness | Quiz 1 |

7 | Completeness | |

8 | Construction of the real numbers | |

9 | Series | |

10 | Series (cont.) | |

11 | Continuity | |

12 | l^p spaces | Quiz 2 |

13 | Continuity and compactness, connectedness | |

14 | Discontinuities, monotone functions | |

15 | Differentiability, mean value theorem | |

16 | l’Hospital’s rule, Taylor’s theorem | |

17 | Riemann integral | |

18 | Riemann integrability and continuity almost everywhere | Quiz 3 |

19 | Stieltjes integral, fundamental theorem of calculus | |

20 | Sequences and series of functions | |

21 | Equicontinuity | |

22 | Optional material: Weierstrass function, Devil’s Staircase | Quiz 4 |

23 | Review for final exam | |

24 | Review for final exam (cont.) | |

25 | Final exam |