## Schedule

Lecture |
Date |
Topic |
Reading* |
Notes |

1 | Aug 29 | Natural numbers and Mathematical Induction | 1 | |

Sept 1 | Labor Day (No Class) |
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2 | Sept 3 | Field Axioms and Rational Numbers | 2 | |

3 | Sept 5 | Real numbers | 3 | HW 1 due |

4 | Sept 8 | Completeness axiom and infinity | 4,5 | |

5 | Sept 10 | Sequences and Convergence | 7 | |

6 | Sept 12 | Proofs | 8 | HW 2 due |

7 | Sept 15 | Properties of sequences | 9 | |

8 | Sept 17 | Monotone and Cauchy sequences | 10 | |

9 | Sept 19 | Subsequences | 11 | HW 3 due |

10 | Sept 22 | Bolzano-Weierstrass Theorem | 11 | |

11 | Sept 24 | limsup and liminf | 12 | |

12 | Sept 26 | Series | 14 | HW 4 due |

13 | Sept 29 | Series | 14 | |

14 | Oct 1 | Convergence tests | 15 | |

Oct 3 |
Midterm I |
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15 | Oct 6 | Metric spaces | 13 | |

16 | Oct 8 | Metric spaces | 13 | |

17 | Oct 10 | Metric spaces | 13 | HW 5 due |

18 | Oct 13 | Continuity | 17 | |

19 | Oct 15 | Properties of continuous functions | 18 | |

20 | Oct 17 | Uniform continuity | 19 | HW 6 due |

21 | Oct 20 | Uniform continuity | 19 | |

22 | Oct 22 | Limits of functions | 20 | |

23 | Oct 24 | Limits of functions | 20 | HW 7 due |

24 | Oct 27 | Differentiation | 28 | |

25 | Oct 29 | Mean Value Theorem and Rolle's Theorem | 29 | |

26 | Oct 31 | The Riemann Integral | 32 | HW 8 due |

32 | Nov 3 | The Riemann Integral | 32 | |

Nov 5 | Midterm II review | |||

Nov 7 |
Midterm II |
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28 | Nov 10 | Properties of the Riemann integral | 33 | |

29 | Nov 12 | Fundamental theorem of calculus | 34 | |

30 | Nov 14 | Power series | 23 | HW 9 due |

31 | Nov 17 | Uniform convergence | 24 | |

32 | Nov 19 | Uniform convergence | 25 | |

33 | Nov 21 | Differentiation and integration of power series | 26 | HW 10 due |

34 | Nov 24 | Taylor series | 31 | |

35 | Nov 26 | Weierstrass function | ||

Nov 28 | Thanksgiving (No Class) |
| ||

36 | Dec 1 | Taylor series | 31 | |

37 | Dec 3 | Metric spaces | 21 | HW 11 due |

Dec 5 | Metric spaces | 21 | ||

Dec 10 | HW 12 due | |||

Dec 12 | Exam review session | |||

Dec 18 |
Final exam |

*The numbers in the reading column refer to chapters in the course textbook

Ross, Kenneth A.

**Elementary Analysis.**Springer, 2013.