**Lecturer:** Kiril Datchev, room 2-173, datchev@math.mit.edu.

**Class meetings:** Tuesdays and Thursdays 9:30-11:00 in room 4-163.

**Textbook:** Walter Rudin, *Principles of Mathematical Analysis*.

**Recommended reading:** G. H. Hardy, *A Course of Pure Mathematics*. Edmund Landau, *Foundations of Analysis*. Tom M. Apostol, *Mathematical Analysis*. See also these notes on the text by George Bergman. For inspirational reading, consult *The Study of Mathematics* by Bertrand Russell.

**Grading** is based on:

- ten problem sets, worth 20 points each, due on 9/13, 9/20, 9/27, 10/11, 10/18, 10/25, 11/1, 11/15, 11/29, 12/6,
- two midterms, worth 100 points each, one on October 2nd and one on November 6th,
- one final exam, worth 200 points, on Thursday, December 20th, 1:30pm-4:30pm in Johnson Track (upstairs).

**Problem sets** are due Thursdays at 4:00 in room 2-285. Late problem sets are not accepted.

Problem set 1 due September 13th. Solutions.

Problem set 2 due September 20th. Solutions.

Problem set 3 due September 27th. Solutions.

Review sheet for Midterm 1. Solutions to the midterm.

Problem set 4 due October 11th. Solutions.

Problem set 5 due October 18th. Solutions.

Problem set 6 due October 25th. Solutions.

Problem set 7 due November 1st. Solutions.

Review sheet for Midterm 2. Solutions to the midterm.

Problem set 8 due November 15th. Solutions.

Problem set 9 due November 29th. Solutions.

Problem set 10 due December 6th. Solutions.

Review sheet for the final.

**Office hours for the final:**

- Wednesday 12/12, 11:00-12:00 in 2-173 (Kiril Datchev)
- Wednesday 12/12, 5:00-7:00 in 2-492 (David Jackson-Hanen, 18.100B/C teaching assistant)
- Thursday 12/13, 5:00-7:00 in 2-492 (David Jackson-Hanen, 18.100B/C teaching assistant)
- Monday 12/17, 2:00-4:00 in 2-270 (Paul Seidel, 18.100C professor)
- Monday 12/17, 5:00-7:00 in 2-492 (David Jackson-Hanen, 18.100B/C teaching assistant)
- Tuesday 12/18, 12:00-1:00 in 2-173 (Kiril Datchev)
- Tuesday 12/18, 2:00-4:00 in 2-270 (Paul Seidel, 18.100C professor)
- Tuesday 12/18, 5:00-7:00 in 2-492 (David Jackson-Hanen, 18.100B/C teaching assistant)
- Wednesday 12/19, 12:00-1:00 in 2-173 (Kiril Datchev)
- More office hours to be announced here.

Schedule | ||
---|---|---|

Date | Pages | Topics |

9/6 | 1 – 12 | ordered sets, fields, real numbers |

9/11 | 12 – 26 | complex numbers, Euclidean spaces, functions, finite and infinite sets |

9/13 | 26 – 34 | countable and uncountable sets, metric spaces |

9/18 | 34 – 36 | open and closed sets |

9/20 | 36 – 38 | compact sets |

9/25 | 38 – 40 | the Heine-Borel theorem, the Bolzano-Weierstrass theorem |

9/27 | 40 – 43 | perfect sets, the Cantor set, connected sets |

10/2 | 1 – 46 | Midterm on Chapters 1 and 2 |

10/4 | 47 – 54 | sequences, convergence, Cauchy sequences |

10/11 | 54 – 60 | completeness, monotonic sequences, upper and lower limits, series, comparison test |

10/16 | 60 – 65 | series of nonnegative terms, the number e |

10/18 | 65 – 72 | root and ratio tests, power series, conditional and absolute convergence |

10/23 | 83 – 90 | continuous functions, continuity and compactness |

10/25 | 90 – 97 | uniform continuity, continuity and connectedness, monotonic functions |

10/30 | 103 – 109 | differentiation, mean value theorems |

11/1 | 109 – 113 | l'Hospital's rule, Taylor's theorem |

11/6 | 47 – 119 | Midterm on Chapters 3, 4 and 5 |

11/8 | 120 – 127 | the Riemann-Stieltjes integral |

11/13 | 128 – 137 | properties of the integral, fundamental theorem of calculus, rectifiable curves |

11/15 | 140 – 148 | sequences and series of functions, pointwise and uniform convergence |

11/20 | 148 – 154 | uniform convergence, continuity and differentiation |

11/27 | 154 – 158 | equicontinuous families of functions, the Arzelà-Ascoli theorem |

11/29 | 159 – 165 | the Stone-Weierstrass theorem |

12/4 | 172 – 178 | functions given by power series |

12/6 | 178 – 184 | exponential, logarithmic and trigonometric functions |

12/11 | 185 – 192 | Fourier series |

12/20 | 1 – 192 | Final Exam on Chapters 1 – 8 |