Mathematics 131A-3 - Analysis - Winter 2018 - UCLA

Time: 1:00 MWF for lectures and 1:00 Tu for discussion.
Place: Lectures and Discussion: MS 5138.

Instructor: Burt Totaro.
E-mail: totaro@math.ucla.edu.
Phone: 310-433-7574.
Course webpage: www.math.ucla.edu/~totaro/131a.3.18w/index.html

Office hours: 11-11:50 M and 2-2:50 F in my office, MS 6136, or e-mail me to make an appointment.
TA: Younghak Kwon (yhkwon@math.ucla.edu).
TA office hours: 11-12:50 F in MS 3973.

Book: Kenneth A. Ross, Elementary Analysis: The Theory of Calculus, Springer, ISBN: 0-387-90459-X.

Course Description: This is a first course in mathematical analysis. We will make a rigorous study of the foundations of calculus, including limits, derivatives, and integrals. Proofs and proof technique will be emphasized. See also the course calendar.

Homework 1-8. The homework listed there is due each Tuesday, starting with the second week (Tuesday, January 16th). Assignments will be returned the next Tuesday in discussion. There will be no makeup or late homework accepted, but the lowest two homework grades will be dropped.

Midterm Exams: We will have two midterm exams. The dates are Monday, January 29 and Friday, February 23. There will be no makeup exams.

Final Exam: The final exam is on Friday, March 23, 2018 from 8 AM to 11 AM. You must take the final to pass the class! If you have a documented reason that you are unable to take the final, you will receive an Incomplete.

Course outline: My plan is to cover Sections 1-5, 7-12, 14-15, 17-20, 28-29, and 31-34 in Ross's book. The course calendar has planned dates for each topic.

Grading: Grades will be assigned based on the higher of the following two schemes:
10% homework + 25% first midterm + 25% second midterm + 40% final
10% homework + 35% (best of two midterms) + 55% final

1/15 - Martin Luther King, Jr. holiday. No class.
1/29 - First midterm exam.
2/19 - Presidents' Day holiday. No class.
2/23 - Second midterm exam.
3/23 - Final exam. The final will be cumulative and will take place from 8:00 AM to 11:00 AM on Friday, March 23.

Evaluation:

One of the main points of this class is to learn how to write proofs. This is what will be graded on the midterm and final grades. Your proofs should be written neatly, in sentences and paragraphs, and use reasonably formal English.
Every exam will include at least one problem taken from the homework, possibly with minor variations.
Part of the homework grading will be based simply on whether you hand in the problems (without copying from someone else). However, at the top of each homework, you may mark a problem you wish to be read carefully. We will read your proof carefully and give you detailed feedback so that you can get better and better at writing proofs.
It is your responsibility to know how to do the problems and how to write out proofs. Practicing that is the only way to study 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.

Miscellanea:

If you wish to request an accommodation due to a disability, please contact the Center for Accessible Education as soon as possible at A255 Murphy Hall, (310) 825-1501 (voice), (310) 825-9656 (fax). Web site: www.cae.ucla.edu.

Catalog description: 131A. Analysis. (4) Lecture, three hours; discussion, one hour. Requisites: courses 32B, 33B. Recommended: course 115A. Rigorous introduction to foundations of real analysis; real numbers, point set topology in Euclidean space, functions, continuity.