**Instructor:** Alena Erchenko

**Course on canvas.dartmouth.edu.**⇗

## Syllabus

Date |
Topic |
References |

01/03 | Introduction. Basic Set Theory. |
(R) Chapter I |

01/05 | Bijections, invertible maps. Cardinality. Cantor's theorem. |
(L) Introduction, Section 0.3 |

01/08 | Ordered fields |
(R) Chapter II, Section 1-2 |

01/10 | Least upper bound. Existence of square roots |
(R) Chapter II, Section 3-4 |

01/11 (block 10X, 12:15pm - 1:05 pm ET) |
Metric spaces |
(R) Chapter III, Sections 1-2 |

01/12 | Ball neighborhoods. Open sets |
(R) Chapter III, Section 2 (L) Section 7.2 |

01/15 | No class -> Moved to X-hour on 01/11 | |

01/17 | Open and closed sets. |
(R) Chapter III, Sections 2 (L) Section 7.2 |

01/19 | Convergence. |
(R) Chapter III, Section 3 (L) Section 7.3 |

01/22 | Complete spaces. |
(R) Chapter III, Section 4 (L) Section 7.4 |

01/24 | Compact sets |
(R) Chapter III, Section 5 (L) Section 7.4.2 |

01/26 | Equivalent definitions of compactness. |
(R) Chapter III, Section 5 (L) Section 7.4.2 |

01/29 | Heine-Borel. Connected sets |
(R) Chapter III, Section 6 |

01/31 | Continuous function. Functions on connected spaces. |
(R) Chapter IV, Sections 1, 5 |

02/02 | Intermediate Value Theorem. Limits | (R) Chapter IV, Section 2, 5 |

02/05 | Rational functions | (R) Chapter IV, Section 3 |

02/07 | Functions on a compact | (R) Chapter IV, Section 4 |

02/09 | Sequences of functions | (R) Chapter IV, Section 6 |

02/12 | Derivatives | (R) Chapter V, Section 1-2 |

02/14 | Mean Value Theorem | (R) Chapter V, Section 3 |

02/15 (block 10X, 12:15pm - 1:05 pm ET) |
Taylor's Theorem | (R) Chapter V, Section 4 |

02/16 | Riemann Integral | (R) Chapter VI, Section 1 |

02/19 | Properties of integral | (R) Chapter VI, Sections 2-3 |

02/21 | Integrable functions | |

02/23 | Fundamental Theorem | (R) Chapter VI, Sections 4-5 |

02/26 | Interchange of limit operations | (R) Chapter VII, Section 1 |

02/28 | Power series | (R) Chapter VII, Sections 2-3 |

03/01 | The fixed point theorem | (R) Chapter VIII, Section 1 |

03/04 | Review | |

03/08 (11:30am-2:30pm ET) |
Final exam |