# MATH 418 - Honors Real Variables II (Fall 2021) MATH 516 - Linear Analysis (Fall 2021)

## Time and Location

Time: MWF 10:00 - 10:50 am
Room: CAB 365

## Instructor

Dr. Arno Berger (CAB 683, berger@ualberta.ca)

## Office hours

MWF 3:00 - 5:00 pm or by appointment.

## General information

NOTE: All information on this site also is available from the official course site on eClass.

Please see this PDF document for all relevant details concerning MATH 418/516. (An abbreviated version of this document will be distributed in class.)

## Course notes

In class, we are going to work with a set of fairly detailed notes which will be posted on eClass over the course of the semester. You may want to give the relevant section(s) of the notes at least a cursory read before coming to class. In addition, be prepared to take careful notes in class, as needed.

You are welcome to use the fine notes by Dr. Runde (PDF, 0.7MB) for background reading. Be aware, however, that notation and terminology in these notes may differ from the ones used in class.

## Material covered in class (Course Diary)

I plan to keep an up-to-date list of the topics, examples etc. covered in class.

Lecture # Date Material covered / special events Remarks/ additional material
WELCOME TO
MATH 418/516 !!

1 Wed
1
Sep
Preliminaries: linear algebra; metric topology. Preliminaries.
2 Fri
3
Sep
Preliminaries: metric topology, completeness and completion(s), compactness, convexity.
Mon
6 Sep
No class. Happy Labour Day!
3 Wed
8
Sep
Basic properties of norms. Banach spaces. Chapter 1.
4 Fri
10
Sep
First examples. Completing a normed space.
5 Mon
13
Sep
Series in normed spaces: (absolute; unconditional) convergence; summability. Quotients and products.
6 Wed
15
Sep
More examples. Finite- vs. infinite-dimensional spaces. Equivalent norms.
7 Fri
17
Sep
Riesz lemma. Characterizations of finite-dimensionality. Examples. (class on zoom)

#### Homework

There will be a total of five assignments during the term, each of equal weight. Problems and submission details will be posted on eClass, and announced in class, as appropriate. Assignments are due on Friday, at 6 pm. Please submit your work to Assign2 via eClass.

#### Midterm test

Two midterm tests will be held on Friday, 22 October 2021 and on Friday, 26 November 2021 at 10:00 am (in class). Details regarding both tests will be announced in class and on eClass.

#### Final exam

The final exam is scheduled for Tuesday, 21 December 2021 at 2:00 pm. Details will be announced in class and on eClass.

#### Other material

General information about the department's honors program is available here.