Math 140A: Foundations of Real Analysis I, Fall 2013

Time and Place: MWF 1:00pm-1:50pm in PETER 103

Instructor: Adrian Ioana
E-mail: aioana@ucsd.edu
Office: APM 5210
Office Hours: M 8:30-10:00am and W 4:00-5:30pm.

Section A01: M 6-6:50pm in APM B412
Section A02: M 7-7:50pm in APM B412
Teaching Assistant: Xiaolong Li
E-mail: xil117@ucsd.edu
Office Hours: Monday 3-5pm in APM 5412

Announcements:

The second midterm will cover Chapter 3.

The first midterm will cover all the sections from the textbook covered in class up to (and including) the section on compact sets.

TED

Welcome to Math 140A!

Prerequisites: Math 31CH or Math 109, or consent of instructor.

Course description: First course in a rigorous three-quarter sequence on real analysis. Topics include: the real number system, basic topology, numerical sequences and series, continuity. (Students may not receive credit for both Math 140A and Math 142A.)

Textbook: W. Rudin, Principles of Mathematical Analysis, 3rd edition, McGraw-Hill, 1976. We will cover most of chapters 1-4.

Homework: Homework will be assigned weekly. Homework is due every Wednesday by 12:00pm (except for the first homework, which is due Friday, October 4th by 12:00pm ). There will be a total of nine problem sets and you should attempt to complete all of them. No late homework will be accepted. If, for any reason, you cannot turn in a homework assignment, keep in mind that the lowest two scores will be dropped.

Midterm Exams: There will be two in-class midterms: the first on Monday, October 21st, and the second on Friday, November 22nd. There will be no make-up exams. If, for any reason, you cannot make it to one of the midterms, you will automatically receive grading option (2).

Final exam: The final exam is scheduled for Monday, December 9th, 11:30am-2:30pm.

Grading: Your final score will be calculated as the maximum of the following two schemes:
(1) 20% Homework + 20% First Midterm + 20% Second Midterm + 40% Final Exam
(2) 20% Homework + 20% Best Midterm Exam + 60% Final exam

In addition you must earn a passing grade on the final examination in order to pass the course.

Regrades: Homework and midterm exams will be returned in the discussion sections. If you wish to have your homework or exam regraded, you must return it immediately to your TA. Regrade requests will not be considered once the homework or exam leaves the room. If you do not retrieve your homework or exam during discussion section, you must arrange to pick it up from your TA within one week after it was returned in order for any regrade request to be considered.

List of homework assignments:

Homework 1, due due Friday, October 4th : pages 21-22, problems 1, 2, 3, 4, 5, 6.
Homework 2, due October 9th: page 22, problems 8, 12, 13, 15, 17, 18.
Homework 3, due October 16th: pages 43 and 44, problems 2, 3, 4, 5, 6, 8, 10 and 11.
Homework 4, due October 23th: pages 44 and 45: problems 12, 14, 16, 22, 24 and 29.
Homework 5, due October 30th: page 44, problems 19, 21, and page 78, problems 1, 2, 3.
Homework 6, due November 6th: pages 78-82, problems 4, 5, 20, 21, 22, 23, 25.
Homework 7, due November 13th: pages 78-80, problems 6, 7, 8, 11 (ab) and 14 (abcd).
Homework 8, due November 20th: pages 79-81, problems 9, 10, 15 (show that two of the theorems listed are true), 16 (abc).
Homework 9, due December 4th: pages 98-102: problems 2, 8, 9, 12, 13, 20, 21.