Math 421/510
Math 421/510
- Instructor: Brian Marcus
- Email: marcus@math.ubc.ca
- Meeting time/location: MWF 11:00-11:50, MATH 126 (NOT in the Ponderosa classroom listed
on the UBC course schedule)
- Math 126 is accessed through the card-controlled Math 125. On the first day of class, Math dept. staff will be on hand to let you in to the room.
We will explain access procedures on the first day.
- Office: Math 218
- Office Hours: MWF 1:30-2:30, and by appointment.
- Textbook: Gerald B. Folland, Real Analysis, 2nd edition.
- Course Outline:
5.1: Banach spaces, including 6.1 L^p spaces:
5.2: Linear functionals on Banach spaces; Hahn-Banach theorem and corollaries:
any Banach space has lots of continuous linear functionals.
5.5: Hilbert spaces -- has many properties of finite dimensioanl spaces.
5.3: Open mapping theorem, closed graph theorem and uniform boundedness principle
5.4: Topological vector spaces, weak topologies on Banach sapces,
Banach-Alaoglu theorem, weak convergence of Borel probability measures.
Riesz representation Theorems: characterization of dual spaces (spaces of cts. linear functionals)
of certain Banach spaces (three different versions (Theorems 5.25, 6.15, 7.17 of Folland)).
As time permits:
Convexity and Krein-Milman Theorem,
Ergodic theory
- Evaluation: 50% bi-weekly homework (due on Fridays) and 50% Final Exam
- Pre-requisites:
Measure Theory (Math 420/507)
A solid undergrad course in real analysis in metric spaces (convergence, continuity, open, closed,
compact, Cauchy, complete) like Math 320-321,
Linear algebra (vector spaces, linear independence, basis, dimension, linear transformations),
like Math 223.
and, ideally, a bit of general topology
(chapter 4 of Folland); but we will introduce this as we need it)
Lecture Notes:
Lectures 3-5
(Jan 7, 9, 11)
Lectures 6-8
(Jan 14, 16, 18)
Lectures 9-11
(Jan 21, 23, 25)
Lectures 12-13
(Jan 28, 30)
Lecture 14
(Feb 1>
Lectures 15
(Feb 4)
Lecture 16
(Feb 6)
Lecture 17
(Feb 8)
Lecture 18
(Feb 11)
Lecture 19
(Feb 13)
Lecture 20
(Feb 15)
Lecture 21
(Feb 25)
Lecture 22
(Feb 27)
Lecture 23
(March 1)
Lecture 24
(March 4)
Lecture 25
(March 6)
Lecture 26
(March 8)
Lecture 27
(March 11)
Lecture 28
(March 13)
Lecture 29
(March 15)
Lectures 30-32
(March 18, 20, 22)
Lectures 33-34
(March 25, 27)
Lecture 35
(March 29)
Lecture 36 (Kyle MacDonald)
(April 1)
Lecture 37
(April 3)
Homework Assignments:
Homework 1, due Friday, Jan 18, 11AM.
Homework 1, Solutions.
Homework 1, TA comments
Homework 2, due Friday, Feb. 1, 11AM.
Homework 2, Solutions.
Homework 2, TA comments
Homework 3, due Friday, Feb. 15, 11AM.
Homework 3, Solutions
Homework 3, TA comments
Homework 4, due Friday, March 8, 11AM.
Homework 4, Solutions
Homework 4, TA comments
Homework 5, due Friday, March 29, 11AM.
Homework 5, Solutions
Information for Final Exam
Homework 5, Solutions
Past Final Exam,
Winter 2005,
Past Final Exam
Winter 2005, Solutions
Past Final Exam
Winter 2013
Past Final Exam
Winter 2013, Solutions