Honors Analysis II  Spring 2013
MWF 10:40am  11:30am, Jordan Hall of Science 322
Course website:
www.nd.edu/~gszekely/HonorsAnalysisII.html
Instructor:
Gábor Székelyhidi
Email:
gszekely (at) nd.edu
Office: 277 Hurley
Tel: (574) 6317412
Office hours:
Wednesdays, Thursdays 4pm5pm.
Textbook:
Kolmogorov, Fomin  Introductory Real Analysis
Grading:
Homework 30%; Quizzes 20%; Midterm 20%; Final 30%
Quizzes:
There will be a short quiz roughly
every second Friday,
starting Feb 1. Each quiz will be on the proof of a result from
the lectures. The proofs of the theorems in the course contain many
useful techniques in analysis and so it is important to know them
well. The goal of the quizzes is to help you keep up with learning
the proofs throughout the semester.
The lowest quiz grade will be
dropped.
Midterm:
There will be one midterm exam during class, on
Wednesday February 27.
Final:
I will give a take home final, on the last day of class. You will be able to spend 2 hours on it, and you can return it to me by
Monday May 6, 6:15pm.
Homework:
There will be fortnightly homework assignments from the textbook, which can be found below along with the due date and time.
 Late homework will not be accepted.
 The lowest homework grade will be dropped.
 Please staple or paper clip your work.
 Don't forget to write your name on it!
 You may ask others for help with your homework. However, it is
unwise to do the homework exclusively in a group; there is no substitute for
the insight and self confidence that comes from successful individual study.
Honesty:
This class follows the binding
Code of Honor at Notre Dame. The graded work you do in this class must be your own. In the case where you collaborate with other students make sure to fairly attribute their contribution to your project.
Syllabus
List of theorems:
Theorems(4/13): This is a list of theorems you should know, and which you might need to prove on a quiz/exam. The list will grow as the course progresses.
Here is the same list, with some sketched proofs for some of the theorems.
The dates given below for specific topics is only meant as a general
guide, and the syllabus is likely to change as the course progresses.
Date 
Reading in KolmogorovFomin 
Homework/Quizzes 
Jan. 16, 18 
Measure in the plane 
Homework 1
due 1/25 in class 
Jan. 21, 23, 25 
Lebesgue measure; Measure on a semiring 
Homework 2
due 2/8 in class 
Jan. 28, 30, Feb. 1 
Countably additive measures; Extension of measures; Measurable functions 
Quiz 1 on Friday 2/1 
Feb. 4, 6, 8 
Measurable functions; Lebesgue integral 
Homework 3
due 2/22 in class 
Feb. 11, 13, 15 
Convergence theorems; Lebesgue vs. Riemann integral 
Quiz 2 on Friday 2/15 
Feb. 18, 20, 22 
Monotonic functions; Differentiation of monotonic functions 
Homework 4
due 3/8 in class 
Feb. 25 
Differentiation of an integral 

Feb. 27 
Midterm 

Mar. 1 
Functions of bounded variation 

Mar. 4, 6, 8 
Hilbert spaces 
Homework 5
due 3/27 in class 
Mar. 11, 13, 15 
Spring break 

Mar. 18, 20, 22 
Operators on Banach and Hilbert spaces 
Quiz 3 on Friday 3/22 
Mar. 25, 27 
Banach algebras 
Homework 6
due 4/12 in class 
Mar. 29, Apr. 1 
Easter break 

Apr. 3, 5 
C*algebras 
Quiz 4 on Friday 4/5 
Apr. 8, 10, 12 
The Gelfand transform and GelfandNaimark theorem 
Homework 7
due 4/26 in class 
Apr. 15, 17, 19 
Spectral theorem for normal operators 
Quiz 5 on Friday 4/19 
Apr. 22, 24, 26 
Harmonic analysis on groups 

Apr. 29, May 1 
TBD 

May 8 
Final exam due 6:15pm 
