Math 117: Methods of Analysis

**Professor:** Katy Craig, SH 6507, katy•craig•math at gmail • com

**Teaching Assistant:** Aaron Bagheri, SH 6431D, bagheri at math • ucsb • edu

** Lecture/Section/Office Hours:** Attendance in lecture is mandatory. Students who do not attend lecture may be unenrolled in order to admit students who do attend lecture. Attendance in section is optional.

** Class calendar:**

** Textbook:** Elementary Analysis by Kenneth Ross, second edition

Using the above link, you can purchase a paperback copy for $24.99 and download a PDF version for free.

Do both.

** Exams:** There will be two midterms and one final exam. The examinations will be closed book and closed note. There will be no retaking or rescheduling of exams under any circumstances, as the grading scheme allows you to drop your lowest midterm score.

** First Midterm:** Tuesday, October 23rd, 9:30-10:45AM

** Second Midterm:** Tuesday, November 13th, 9:30-10:45AM

** Final Exam:** Tuesday, December 11th, 8:00-11:00AM

**Homework:**

• Homework assignments will be posted on this website and collected during lecture.

• Only problems marked with an asterisk (*) should be submitted for grading.

• At least one problem on each of the exams will be chosen from the non-asterisked homework problems.

• No late homework will be accepted.

• Homework 1, 2, and 3 will be used as a measure of class attendance and must be turned in.

• The lowest two homework grades will be dropped and will not count toward the final grade.

** Grading Scheme:** homework: 10%, highest midterm score: 40%, final: 50%

If you have questions about the grading of any assignment or exam, you have one week after it is handed back to request a regrade.

** Prerequisites:** Math 8

** Outline of Course:**

Part I: Sequences | Part II: Functions |
---|---|

the real numbers, inf, and sup | continuous functions |

limit, liminf, limsup | cts functions attain max and min on closed interval |

bounded, monotone, and Cauchy sequences | intermediate value theorem |

subsequences and the Bolzano-Weierstrass theorem |

topic | reading | due today | notes/review materials | ||
---|---|---|---|---|---|

1 | Sept 27 (Th) | N,Z,Q,R and triangle inequality | 1-2, appendix | LEC1 | |

2 | Oct 2 (T) | properties of real numbers | 3 | HW1 SOL1 | LEC2 |

3 | Oct 4 (Th) | def’n of R, Q is dense in R | 4-5 | LEC3 | |

4 | Oct 9 (T) | sequences | 7-8 | HW2 SOL2 | LEC4 |

5 | Oct 11 (Th) | limit theorems | 9 | LEC5 | |

6 | Oct 16 (T) | monotone sequences | 10 | HW3 SOL3 | LEC6 |

7 | Oct 18 (Th) | catch up | LEC7 | ||

8 | Oct 23 (T) | first midterm, over lectures 1-7 |
Mid1 Mid1SOL | PMid1 PMid1SOL | |

9 | Oct 25 (Th) | limsup and liminf | 10 | LEC8 | |

10 | Oct 30 (T) | Cauchy sequences | 10 | HW4 SOL4 | LEC9 |

11 | Nov 1 (Th) | subsequences, part 1 | 11 | LEC10 | |

12 | Nov 6 (T) | subsequences, part 2 | 12 | HW5 SOL5 | LEC11 |

13 | Nov 8 (Th) | review for midterm 2 | LEC12 | ||

14 | Nov 13 (T) | second midterm, over lectures 8-13 |
PMid2 PMid2SOL | ||

15 | Nov 15 (Th) | proofs of subsequence theorems, part 1 | 11-12 | ||

16 | Nov 20 (T) | proofs of subsequence theorems, part 2 | 11-12 | ||

17 | Nov 27 (T) | continuous functions | 17 | ||

18 | Nov 29 (Th) | intermediate value theorem | 18 | ||

19 | Dec 4 (T) | uniform continuity | 19 | ||

20 | Dec 6 (Th) | review and math movie competition | |||

Dec 11 (T) | final exam, 8:00-11:00AM |

As an opportunity for extra credit, we will hold a math movie competition. The goal is to make the best math movie, lasting three minutes or less. Submissions are due on Thursday, November 29th. The winner of the competition will receive ten points of extra credit on their final exam. Second place will receive five points of extra credit, and third place will receive three points of extra credit.

Submissions should be uploaded to YouTube, Vimeo, or a similar site. Links to the movies can be emailed to me. (Please do not send the movies as email attachments.)

Potential topic ideas for inspiration...

• Why we should celebrate square root of two day on January 4th

• Sequences and time series analysis in mathematical finance

• Uncountability of the real numbers

• The history of the real numbers

• The importance of convergence in machine learning models