TENTATIVE SYLLABUS, GRADUATE ANALYSIS

Homework 4 Solutions

Prerequisites and Overarching Goals

Prerequisites: Math 506

Mathematical goals: Continue with Measure Theory and Lesbesgue Integration.

Information

We meet MWF 10:50AM-11:50AM in LN2205. Office: LN-2224, Extension: 7-3506, Email: loya at math (put appropriate dots in) binghamton edu, Office Hours: ?  and by appointment. (I'm in my office quite a bit.)

Textbook and lecture notes

The class will be based on my personal lecture notes:

Lecture notes: Loya-old.pdf. This is basically last year's version of the book. This book will be revised during the semester with new versions appearing below. All comments are welcome.


Here are sections for the newest version of the book, which will be posted as the semester progresses. I will correct typos and reword various parts to make the presentation clearer. (Depending on the section, the material could be quite different from Loya-old.pdf.).
  1. Differentiation

Homework

  1. Homework 1 Due ?.

Schedule of Topics

We hope to cover the following topics:

1) Simple applications of the DCT. 3 weeks.
2) Fubini's theorem.
3) Change of variables formula
4) Banach Spaces, Hilbert Spaces, L^p spaces, Dual spaces. Central limit theorem.
5) Differentiation.

Grading

Homework
 30%
Midterm 1 (?)
20%
Midterm 2 (?)
20%
Final (?)
 30%

We shall use the following approximate grading scale.

A: Complete mastery of the material. 90 - 100
B: Mostly understands everything with some gaps.
 70 - 90
C: Basic understanding of what's going on.
 55 - 69

Drop Deadline

Sept. 9

General Comments

Class attendance is required. Questions are welcome at anytime. Please visit me in my office whenever you have a question or if you just want to talk.