MATH 245B : Real Analysis


Announcements:

        (Mar 23) Final solutions are available here; final grades are available here.

        (Feb 11) Midterm solutions are available here; some souped up versions of the midterm questions are also present for those of you who found the actual midterm too easy.  Midterm grades are available here.

        (Feb 3) The midterm will be on Feb 11; see below for further information.  On Friday, Feb 6, the class will be shortened, ending at 1:30 pm instead of 1:50 pm.

        (Jan 12) Due to even more unavoidable travel delays, I will not actually be present until Jan 21.  John Garnett will administer the first homework assignment and teach the course until my return.

        (Dec 15) Due to unavoidable travel delays, I will not be present in LA until Jan 13.  The first class will be on Thursday, January 8, 1:00 pm, and will be taught by John Garnett.  There will be no class on Friday, January 10.  The classes of Monday, Jan 12 and (possibly) Wednesday Jan 14 will also be taught by John Garnett.


 

        Instructor: Terence Tao, tao@math.ucla.edu, x64844, MS 5622

        Lecture: MWF 1-1:50, MS 5138.  

        Quiz section: Th 1-1:50, MS 5138

        Office Hours: Tu 1-1:50

        TA: Jon Handy jhandy@math.ucla.edu, MS 3973

        TA Office hours: TBA

        Textbook: Folland, Real Analysis, Second Edition.  We will cover Chapters 4-6 (Point Set Topology, Functional Analysis, L^p spaces); some variation from this plan may develop depending on time constraints.

        Prerequisite: Math 245A.  The material here will rely heavily on that in Math 245A, so be sure you have a firm grasp of the material from that course.

        Grading: Homework (30%), Midterm (30%), Final (40%).  In addition, each student must present at least one homework problem at the blackboard during at least one quiz section in order to gain the Homework portion of the grade.

        Exams: The midterm will be on Wednesday, Feb 11, and consist of three questions similar to those from Chapters 4, and Section 1 of Chapter 5.  The exam is open book and open notes.  The final will be on Tuesday March 23, at 11:30 am, MS 5138, and will consist of seven questions similar to those from Chapters 5-6.  The final is open book and open notes.

        Homework: There will be eight homework assignments, due in Quiz sections.  There will be roughly 10 questions in each assignment, mostly from Folland. 

1.      First homework (Due Thursday, January 29): Chapter 4, Questions 3,5,10,11,14,16,23,24,38,39,40,43.

2.      Second homework (Due Thursday, Feb 5): Chapter 4, Questions 47, 49a, 52, 54, 59, 64, 65, 67, 68

3.      Third homework (Due Thursday, Feb 12) Chapter 5, Questions 1, 6, 7, 8, 11,13, 14, 15

4.      Fourth homework (Due Thursday, Feb 19) Chapter 5, Questions 19, 22, 25, 30, 33, 36, 38, 48

5.      Fifth homework (Due Thursday, Feb 26) Chapter 5, Questions 51, 53, 54, 56, 58, 59, 63, 67

6.      Sixth homework (Due Thursday, Mar 4) Chapter 6, Questions 1, 3, 5, 7, 12, 18, 20, 21

7.      Seventh homework (Due Thursday, Mar 13) Chapter 6, Questions 26, 27, 32, 36, 38, 39, 40

8.      Eighth homework (Due Thursday, Mar 20) Chapter 6, Questions 42, 43, 44, 45