`www.math.ucla.edu/~totaro/131ah.1.16f/`

In this class you will be required to write precise mathematical statements in a clear logical order, and present pictures or examples as necessary to illustrate your work. Acquiring these skills is impossible without steady practice: it is essential that you do the homework problems carefully and promptly.

You may discuss homework problems with other students, the TA, or me, before they are turned in. I do expect, though, that: (i) you should make a serious effort to do the exercise yourself before discussing it with anyone, and (ii) you should write up the solution yourself after understanding it thoroughly, without following someone else's written version. Otherwise, homework will not help you to prepare for the exams. Identical solutions to a source will get zero credit.

Homework 1. Due Tuesday, September 27.

Homework 2. Due Tuesday, October 4.

Homework 3. Due Tuesday, October 11.

Homework 4. Due Tuesday, October 25.

Homework 5. Due Tuesday, November 1.

Homework 6. Due Tuesday, November 8.

Homework 7. Due Tuesday, November 22.

Homework 8. Due Tuesday, November 29.

Sample Midterm 2.

- Every exam will include at least one problem taken from the homework, possibly with minor variations.
- It is your responsibility to know how to do the problems. Practicing that is an essential part of studying for the exams.
- A grade of 'F' will be assigned to any student who misses the final. Incompletes are reserved for those who have completed all of the work for the class, including both midterms, but who, for a legitimate, documented reason, miss the final.
- Exams (or copies) will be returned, but I will keep copies (or originals) of the exams, as required by the math department.

10% homework + 25% first midterm + 25% second midterm + 40% final

10% homework + 35% (best of two midterms) + 55% final

- 10/17 -
**First midterm exam**. - 11/11 -
**Veterans Day holiday.**No class. - 11/14 -
**Second midterm exam**. - 11/25 -
**Thanksgiving holiday.**No class. - 12/9 -
**Final exam**. The final will be from 11:30 AM to 2:30 PM on Friday, Dec. 9.

- If you wish to request an accommodation due to a disability, please contact the Office for Students with Disabilities as soon as possible at A255 Murphy Hall, (310) 825-1501, (310) 206-6083 (telephone device for the deaf). Web site: www.osd.ucla.edu.

Tentative schedule of lectures, in terms of the book:

9/23: Ch. 1. Mathematical logic, induction.

9/26: Ordered fields. 9/28: Axioms for

10/3: Complex numbers, Euclidean spaces. 10/5: Construction of

10/10: Countable sets. 10/12: Metric spaces, open and closed sets. 10/14: Compact sets.

10/17: Midterm 1. 10/19: More on compactness. 10/21: Perfect sets. Connected sets.

10/24: More on connectedness. 10/26: Ch. 3. Convergent sequences. 10/28: Subsequences, Cauchy sequences, completeness.

10/31: Lim sup, lim inf. 11/2: Some special sequences. 11/4: Series.

11/7: Absolute convergence. 11/9: Ch. 4. Limits of functions. 11/11: Veterans Day holiday.

11/14: Midterm 2. 11/16: Continuous functions. 11/18: Continuity and compactness.

11/21: Continuity and connectedness. 11/23: Ch. 5. The derivative. 11/25: Thanksgiving holiday.

11/28: Chain rule. Mean value theorem. 11/30: Taylor's theorem. 12/2: Review.