Lectures |
Contents |

Lecture 1 |
Course introduction, finite and infinite sets |

Lecture 2 |
Finite and infinite sets |

Lecture 3 and 4 |
Finite and infinite sets |

Lecture 5 |
Finite and infinite sets |

Lecture 6 |
Algebraic and order properties of R |

Lecture 7 and 8 | Algebraic and order properties of R, bounded and unbounded sets |

Lecture 9 | Suprema and infima, Completeness property of R. | |

Lecture 10 | Archimedean Property, Density of Q in R. |

Lecture 11 and 12 | Intervals, Nested interval property, Uncountability of R. |

Lecture 13 | Sequences: Definition and examples, convergent and divergent sequences. |

Lecture 14 | Tail of a sequence, bounded sequences, squeeze theorem. |

Lecture 15 and 16 | Cauchy's limit theorems, Monotone convergence theorem. |

Lecture 17 | Subsequences. |

Lecture 18 and 19 | Monotone subsequence theorem, Bolzano-Weierstrass theorem, Cauchy's sequence. |

Lecture 20 | Series: Examples and properties of convergent series. |

Lecture 21 and 22 | Comparsion test, Absolute convergence. |

Lecture 23 | Tests for (Absolute) convergence. |