**MATH 131A-2-Analysis-Fall 2016-UCLA**

**Lecture:** MWF, 9:00am-9:50am, at Geology Room 4645.

**Discussion:** Tu, 9:00am-9:50am, at Geology Room 4645.

**Professor:** Wenhao Ou (wenhaoou-at-math.ucla.edu, MS 5346).

**Office Hours:** M 3:00pm-5:00pm, W 4:00pm-5:00pm, or e-mail me to make an appointment.

**Teaching assistant:** Assaf Shani (assafshani-at-ucla.edu, MS 2344).

**TA Office Hours:** Tu, 10:00am-11:00am.

**Textbooks:** Ross, Kenneth A. *Elementary Analysis: The theory of calculus, Second edition.*

**Description.** This course provides an introduction to foundations of real analysis: real numbers, limits, convergences, functions, continuity, derivations and integrations.

**Schedule.** This course consists of three parts and about 25 lectures. We will start by recalling rational and real numbers. The first part will end up with analysis of sequences. In the second part, we will commence the study of functions, and will focus on continuity and derivations. The last part is on the Riemann integral.

Weeks |
Sections | Topics |

1 |
1, 2, 3, 4 | Introduction, Rational Numbers, Real Numbers, Least Upper Bound Axiom |

2 |
5, 7, 8, 9 | Limits of Sequences |

3 |
10, 11, 12 | Monotone Sequences, Cauchy Sequences, Subsequences |

4 |
14, 15 | Midterm 1, Limsup and Liminf, Series |

5 |
17, 18, 20 | Continuous Functions |

6 |
19, 28 | Uniform Continuity, Derivation |

7 |
29, 31 | Mean Value Theorem, Taylor's Theorem |

8 |
32, 33 | Midterm 2, Riemann Integral |

9 |
34 | Fundamental Theorem of Calculus |

10 |
Review of Course |

**Holidays:**

- Veterans Day holiday, F Nov 11.

- Thanksgiving holiday, F Nov 25.

**Homework.** Homework is assigned weekly and collected at the beginning of class on Wednesday. There is no make-up homework. The lowest score is dropped from the computation of your grade. Please click here for the homework list.

**Exam Dates:**

- Midterm 1: Monday of week 4, Oct 17, during the regular class hour.

- Midterm 2: Monday of week 8, Nov 14, during the regular class hour.

- Final Exam: Thursday, December 8, 2016, 8am-11am.

**Grading.** There are two possibilities for the nal grade:

- 10% Homework + 30% Best of the two midterms + 60%Final Exam.

- 10% Homework + 25% Midterm 1 + 25% Midterm 2 + 40% Final Exam.

**Academic integrity.** Please review the regulations at the following website: http://www.deanofstudents.ucla.edu/Student-Conduct

**Notes.**

- Textbooks, Calculators, laptops and cell phones are prohibited during the Midterms and the Final Exam.

- There will be no make-up test. A missed test will count for a zero for that test.

- Students may work together to solve homework problems, but each student must write down his/her own solutions on separate copy. One should also write down the names of his/her collaborators.

- Exam grading complaint should be submitted to the instructor, no later than two weeks after the exam, and before the last lecture.