CCS Math 117: Real Analysis

**Professor:** Katy Craig, katy•craig at ucsb • edu

** Lecture:** Monday and Wednesday, 11am-12:15pm, CRST, Room 160B

** Office Hours:** Wednesday 3:30-4:30pm and Thursday 1-2pm in SH6507

** Textbook: ** Johnsonbaugh and Pfaffenberger, * Foundations of Mathematical Analysis*

** Other Recommended References:**

- Boyd and Vandenberghe,
*Convex Optimization* - Mordukhovich and Mau Nam,
*An Easy Path to Convex Analysis and Applications*

** 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 exams under any circumstances, as the grading scheme allows you to drop your lowest midterm score.

- First Midterm: Monday, May 6, 11am-12:15pm
- Second Midterm: Wednesday May 29th, 11am-12:15pm
- Final Exam: Thursday June 13, 12-2pm, CRST, Room 160B

** Homework:**

- Homework will be due Sundays at 11:59pm.
- Assignments will be posted on this website and submitted via Gradescope.

- 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.

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

- Regarding collaboration/Google:
- The solutions to most homework problems can be found on the internet. The purpose of homework is to practice solving problems. Don’t miss out on that practice, or you will deprive yourself of key preparation for the exams.
- Discussing homework problems with classmates is an excellent way to learn the material. However, be aware that it's easy to overestimate how much you actually understand individually when you solve problems in a group.

**Participation:** Participation will be based on attendance and contributions during lecture. If you have personal circumstances that make it difficult for you to attend lecture, please contact me within the first two weeks of classes to make an alternative arrangement.

** Grading Scheme:**

- Participation: 5%, Homework: 30%, Highest of Two Midterm Grades 30%, Final 35%
- All regrade requests must be received within two weeks after the graded work is returned.

**Weekly Plan:**

topic | reading | due soon | notes | ||
---|---|---|---|---|---|

- | April 1 (M) | (no class) | |||

1 | April 3 (W) | ordered fields | J&P, Sec 1-4 | HW1 | LEC1 |

2 | April 8 (M) | the real numbers and cardinality | J&P, Sec 5-9 | LEC2 | |

3 | April 10 (W) | cardinality and sequences | J&P, Sec 8-10 | LEC3 | |

4 | April 12 (F) | sequences and subsequences | J&P, Sec 10-12 | HW2, HW2_Q8SOL, HW2_Q10SOL |
LEC4 VID4 |

5 | April 15 (M) | the algebra of limits and bounded sequences | J&P, Sec 12-13 | LEC5 | |

- | April 17 (W) | (no class) | HW3 HW3_Q7SOL |
||

6 | April 22 (M) | divergent sequences and monotone sequences | J&P, Sec 14-16 | LEC6 | |

7 | April 24 (W) | monotone sequences and rational exponents | J&P, Sec 16-17 | LEC7 | |

8 | April 26 (F) | real exponents | J&P, Sec 17 | HW4 | LEC8 |

9 | April 29 (M) | Bolzano-Weierstrass, Cauchy sequences | J&P, Sec 18-19 | LEC9 | |

10 | May 1 (W) | Limits of functions, part 1 | J&P, Sec 30 | PracMid1 | LEC10 |

11 | May 6 (M) | midterm 1 - covering through monotone sequences | MID1_SOL | ||

- | May 8 (W) | (no class) | HW5 | ||

12 | May 13 (M) | Limits of functions, part 2 | J&P, Sec 31-32 | LEC11 | |

13 | May 15 (W) | One sided limits, limits at infinity, and continuity | J&P, Sec 32-33 | LEC12 | |

14 | May 17 (F) | continuity and the Heine-Borel theorem | J&P, Sec 33-34 | HW6 | LEC13, LEC13_VID |

15 | May 20 (M) | cts functions attain max/min, lower semicty | J&P, Sec 34, 20-21 | LEC14 | |

16 | May 22 (W) | liminf and limsup | J&P 20-21 | LEC15 | |

- | May 27 (M) | (Memorial Day, no class) | |||

17 | May 29 (W) | midterm 2, through cts fns attain max/min | MID2_SOL, PracMid2 HW7 |
||

18 | June 3 (M) | limsup/liminf vs subsequential limits; sequential characterization of u-semi-cty/l-semi-cty | LEC16 | ||

19 | June 5 (W) | intermediate value theorem | HW8 | LEC17 | |

June 13 (Th) | final exam, 12-2pm, CRST, Room 160B |
PracticeFinal |