Math 424 / 574: Fundamental Concepts of Analysis
Autumn 2015

Instructor: Alexandru Chirvasitu

Class times and location:
Office hours: Tuesdays and Wednesdays 10 - 11 or by appointment (so email me and we'll work something out).
Email: chirva AT uw.edu

TA: Zihui Zhao
Email: zhaozh AT uw.edu
Announcement about the week of Oct 26

I mentioned in class that I'll be away during that entire week. That means no class on Monday Oct 26 or Friday Oct 30.

The midterm is scheduled for Wednesday Oct 28, during that week; please show up at the usual time and place, where a substitute will administer the test.
Textbook

We're using the 3rd edition of Walter Rudin's Principles of Mathematical Analysis. The textbook is absolutely necessary, both for the reading and in order to do the assignments. We'll be covering the first 4 chapters.

It's essential that you do the reading. I won't have time to go over every relevant example in class, and you'll need a good grasp of the material in order to do the homework. In fact, I encourage you to regard the reading as part of your homework.

Due date Assignment Remarks
1 Fri Oct 02 'Ordered Sets' section of Chapter 1
2 Mon Oct 05 Continue Chapter 1, up to and including
'The Extended Real Number System'
3 Wed Oct 07 Finish Chapter 1
4 Fri Oct 09 Pages 24 - 28 of Chapter 2
5 Wed Oct 14 Continue Chapter 2,
stop at 'Metric Spaces'
6 Fri Oct 16 Continue Chapter 2,
stop before Definition 2.26 on page 35
7 Mon Oct 19 Continue Chapter 2,
stop before Theorem 2.36 on page 38
8 Wed Oct 21 Finish 'Compact Sets'
9 Fri Oct 23 'Perfect Sets' from Chapter 2;
study for midterm
The midterm material is everything up to
and including 'Compact Sets'
10 Mon Oct 26 Finish Chapter 2;
study for midterm some more
We're not meeting that day!
11 Wed Nov 04 'Convergent Sequences' Chapter 3
and Definition 3.5
12 Fri Nov 06 'Subsequences' from Chapter 3
13 Mon Nov 09 Start 'Cauchy Sequences' from Chapter 3,
stop before Definition 3.12 on page 54
14 Wed Nov 11 Finish 'Cauchy Sequences';
'Upper and Lower Limits'
No class due to Veterans' Day
15 Mon Nov 16 'Limits of Functions' from Chapter 4
16 Wed Nov 18 Start 'Continuous Functions' from Chapter 4,
stop before Theorem 4.10
17 Fri Nov 20 Finish 'Continuous Functions' from Chapter 4;
start 'Continuity and Compactness',
stop before Definition 4.18
18 Mon Nov 23 Finish 'Continuity and Compactness' from Chapter 4
19 Wed Nov 25 'Continuity and Connectedness' from Chapter 4 Remember this lecture's cancelled.
20 Mon Nov 30 'Discontinuities' from Chapter 4
21 Wed Dec 02 'Monotonic Functions' from Chapter 4
22 Mon Dec 07 Finish Chapter 4

Supplementary material

On occasion, I'll post extra notes, comments, etc. in this space.

Homework

I will post homework assignments in the table below. It'll be due weekly on Wednesday, in class. I might post solutions to selected problems, but certainly not to all of them.

No late homework for any reason, but I will drop the lowest score.

Because of time constraints your TA will grade a couple of problems (tops) for correctness and the rest for completeness. I won't be telling you in advance which problems are graded for correctness though..

Due date Assignment Remarks Selected solutions
3 Wed Oct 21 Download There are extra office hours as follows:
Monday, Oct 19, 10 - 11
Tuesday, Oct 20, 2:30 - 3:30
Wednesday, Oct 21, 9 - 11
No hw due week of the midterm
Fri Nov 06 Download Bonus homework; you do not have to turn it in,
but it's worth extra credit.
5 Mon Nov 09 Download Note the unusual date;
it's because we're not meeting on the 11th.
Extra office hours for this assignment:
Fri Nov 06, 12:30 - 2:30
Mon Nov 09, 10 - 11
7 Wed Nov 25 Download You're supposed to turn in the homework at my office,
in the box by the door to room C-417, Padelford Hall.

Midterm

It's happening in class (usual time and place) on Wednesday, October 28 (see the announcement at the top of this page for the schedule for that week). The material is what your first three homework assignments cover: everything up to and including the 'Compact Spaces' section of Chapter 2.

Your homework is good training for the test; it will consist of probably a couple of proofs similar in nature and difficulty to the problems on your first three homework sets.

Both the midterm and the final are completely open book. You can bring anything you want to the exam (textbook, class notes, your own past homework, etc.).

Pre-midterm office hours: There are some by myself and some by our TA, Zihui Zhao.

• Me: Friday, Oct 23, 12:30 - 2:30

• Zihui: Tuesday, Oct 27, 10:30 - 12:30 (room C-8D Padelford)

The test, with solutions.

Final

It's been set by the department, and I have no control over time and location. I can't offer you an early / late exam, so if you can't make it you should switch to the other 424 section.

The exam will be
• Wednesday, December 16 2015, 2:30 - 4:20, room 405 Smith Hall

As I said above, the exams are both open book.

• Homework : 20%
• Midterm : 35%
• Final : 45%

As mentioned above, we'll drop the lowest homework score.