Week 1 |

1/24 |
Number Systems, Irrationality of √2 |

1/26 |
Sets, Gaps in Q, Field |

Week 2 |

1/29 |
Field, Order, Upper Bound and Lower Bound |

1/31 |
Infimum and Supremum, Ordered Field |

2/2 |
Ordered Field, Archimedean Property, Density of Q in R |

Week 3 |

2/5 |
n-th Root of Real Number, Complex Numbers |

2/7 |
Complex Numbers, Euclidean Spaces |

2/9 |
Quiz |

Week 4 |

2/12 |
Schwarz Inequality, Function, Cardinality |

2/14 |
Finite and Infinite, Sequence |

2/16 |
Set Operations, Countable and Uncountable |

Week 5 |

2/19 |
Metric Space, Interval, Cell, Ball, Convex |

2/21 |
Definitions in Metric Space |

2/23 |
Neighborhood, Open and Closed, De Morgan's Law |

Week 6 |

2/26 |
Open and Closed, Closure |

2/28 |
Convergence and Divergence, Range, Bounded |

3/2 |
Important Properties of Convergent Sequences |

Week 7 |

3/5 |
Algebraic Limit Theorem |

3/7 |
Convergence of Sequences in R^n, Compact Set |

3/9 |
Exam 1 |

Week 8 |

3/12 |
Compact Subset, Cantor's Intersection Theorem |

3/14 |
Nested Intervals Theorem, Compactness of k-cell |

3/16 |
Heine-Borel, Weierstrass, Subsequence |

Week 9 |

3/19 |
Cauchy Sequence, Diameter |

3/21 |
Cauchy Sequence, Complete Metric Space, Monotonic |

3/23 |
Upper and Lower Limits |

Week 10 |

4/2 |
Some Special Sequences |

4/4 |
Series, Cauchy Criterion for Series, Comparison Test |

4/6 |
Convergence Tests for Series |

Week 11 |

4/9 |
Power Series, Absolute Convergence, Rearrangement |

4/11 |
Rearrangement, Limit of Functions |

4/13 |
Exam 2 |

Week 12 |

4/16 |
Continuous Function and Open Set |

4/18 |
Continuity and Compactness, Extreme Value Theorem |

4/20 |
Uniform Continuity and Compactness |

Week 13 |

4/23 |
Connected Set, Intermediate Value Theorem |

4/25 |
Derivative, Chain Rule, Local Extrema |

4/27 |
Mean Value Theorem, Monotonicity, Taylor's Theorem |

Week 14 |

4/30 |
Riemann-Stieltjes Integral, Refinement |

5/2 |
Fundamental Theorem of Calculus |

5/4 |
Sequence of Functions, Uniform Convergence |