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Math 240BC-Real Analysis, General Information
Winter 2023--Spring 2023



Course Description

Math 240 ABC is a year long sequence on real analysis. Math 240A of Fall 2022 is taught by Professor Ebenfelt. The topics there are mainly measure theory and integration theory covered by Ch1-3 of Folland's text. Math 240B C are the continuations. Any student enrolled for the current courses should review these materials and make sure they are comfortable with content in Math 240A since they will be assumed.

This part of 240 series is about (i) Basic functional analysis; (ii) Properties of L^p spaces; (iii) Locally compact Hausdorff spaces and Radon measures on them; (iv) Basics of distribution theory and fourier analysis which are needed for the study of PDEs and other subjects of mathematics, (v) Sobolev functions, BV functions and convex functions. The first three items form the main topics of Math 240B. The topics in (iv) and (v) are covered in Math 240C. These are very basic topics of analysis which are needed for the further studies of almost all areas of more advanced mathematics. Part (v) shall NOT be covered by the qualifying exams.

Since some basics of the set topology are needed in Math 240B, all students enrolled are required (via the announcement via canvas) to do some readings on set topology covered in Folland's text Ch 4.1, 4.2 and complete at least half of the exercises there before the start of lectures. The alternative is to take math 190A.

Almost all problems in this course require the proof. Any mathematical proof in serious mathematical textbooks as put by A. Y. Khinchin ` will undoubtedly seem very complicated to you. But it will take you only two to three week's work with pencil and paper to understand and digest it completely. It is by conquering difficulties of just this sort, that the mathematicians/or mathematical students grow and develop.' Even though none of the theorems involved in this course is a difficult one requiring the labor beyond several hours to digest, the same principle on the effort part applies. No good mathematics can be spoon-fed fast. Learning mathematics also takes time and serious efforts via many practices of solving exercises and homework problems.

Each quarter there will be a midterm and a final exam.

The complete course schedule will be available and updated weekly.


Instructors

Name Office E-mail Phone Office Hours
Ni, Lei AP&M 5250 leni@ucsd.edu 534-2704 Tu Th 3:30-5:00 pm


Course Time and Location

Section Instructor Time Place
A00 Ni Tu Th 2:00-3:20 pm APM 2402


Texts

Required Text: Real Analysis, by Folland, 2nd ed., Wiley, 1999.

Recommend Texts for possible alternate/different approach on the topics covered: (1) Functional Analysis, by P. Lax, Wiley, 2002;

(2) Analysis, by Lieb and Loss, AMS, 2001;

(3) Real Analysis, 3rd edition, by Royden, Pearson Education, 1988;

(4) Real and Complex Analysis, 3rd edition, by Rudin, McGraw-Hill, 1987;

(5) Measure theory and fine properties of functions, by Evans and Gariepy, CRC press 1992.

Further readings: (1) Functional Analysis by F. Riesz and B. Nagy, New York, Ungar, 1956;

(2) Lectures on Geometric Measure Theory, by Leon Simon, Centre for Mathematical Analysis, Australian National University, 1984.

Important Resources
Errata for Folland's text: [html]
Errata for Evans/Gariepy's text: [html]
Problem Solving Techniques in Analysis by Terence Tao: [html]
LaTeX homework template: [tex]
Everything you need to know to typeset your homework in LaTeX: [pdf]

(i) Handout1 on L^p spaces; (ii) Handout of lecture notes; (iii) Handout2 on L^p spaces;

(iv) Handout on Sobolev spaces; (v) Handout1 on BV functions; (vi) Handout1 on Fourier Transforms.

(vii) Handout1 on Distributions; (viii) Handout on general Riesz representation theorem; (ix) Handout on BV-functuions II


Exams

There will be one midterm and one final exam.

Solution to final in Fall 2014

Solution to midterm in Winter 2015

Example 240B final1

Example 240B final2 Solutions

Solution to the final of 240B

Solution to the midterm of 240C

Content covered by the Qualifying Exam


Homework

There will be weekly homework assignments. Please check weekly for the updates. Many problems will be assigned every week. The one with (*) have to be turned in by Friday. The rest problems are recommended (which means that you should think about them and know how to solve them too). The exams will be based on lectures and homework problems. The course TA is Charles 'Casey' Perdue (chperdue@ucsd.edu). For the Winter 2023 the office hours are 2-4pm on Fridays in HSS 4012.

Solutions to the HWs of 240B

Solutions to the HWs of 240C (including the all previous solutions)


Schedule

The course schedule will be updated weekly.


Grades

Grades will be based on the following percentages.
Homework 40%
Midterm Exam (for 240B, ) 30%
Final Exam (for 240B, 03/23/2023 ) 30%

Last modified: Wed November 16, 14:49:08 PST 2014