Honors Analysis II - Spring 2013
MWF 10:40am - 11:30am, Jordan Hall of Science 322
Course website: www.nd.edu/~gszekely/HonorsAnalysisII.html
Email: gszekely (at) nd.edu
Office: 277 Hurley
Tel: (574) 631-7412
Wednesdays, Thursdays 4pm-5pm.
Kolmogorov, Fomin - Introductory Real Analysis
Homework 30%; Quizzes 20%; Midterm 20%; Final 30%
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
There will be one midterm exam during class, on
Wednesday February 27.
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
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.
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.
List of 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.
|| Reading in Kolmogorov-Fomin
| 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
| 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
|| Quiz 4 on Friday 4/5
| Apr. 8, 10, 12
|| The Gelfand transform and Gelfand-Naimark 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
| May 8
|| Final exam due 6:15pm