MTH 431/531: Intro to Real Variables 1

Spring 2023

Instructor: Alexandru Chirvasitu

Lectures: Office: 216 Mathematics Building
Office hours: TR 08:00 - 09:20
Email: achirvas AT buffalo.edu

TA: Dakota Leonard

Recitations: Office: 131 Mathematics Building
Office hours: MW: 12:00 - 13:00
Email: dl42 AT buffalo.edu

Subject matter

The course is an introduction to the abstract machinery that underpins calculus. While some of the topics will be familiar (e.g. limits of sequences and series, continuity, etc.), the class takes a more sophisticated, conceptual and proof-based approach to them than you might have encountered in previous courses. Some of the subjects we will discuss:

Textbook

We will be using Introduction to Real Analysis (4th edition) by Bartle and Sherbert. Specifically, we will cover chapters 1-8.

Reading

I will post the reading assignments here.

You will have to do the reading before the listed due date.

Due date Assignment Remarks
week 1: 01/30-02/05 M 02/06

1.1, 1.2, 1.3

week 2: 02/06-02/12 M 02/13

2.1, 2.2, 2.3

week 3: 02/13-02/19 M 02/20

2.4, 2.5

week 4: 02/20-02/26 M 02/27

3.1, 3.2, 3.3

week 5: 02/27-03/05 M 03/06

3.4, 3.5

week 6: 03/06-03/12 M 03/13

3.6, 3.7, 4.1

week 7: 03/13-03/19 M 03/20

4.2, 4.3

No classes the whole week of Mar 20

week 8: 03/27-04/02 M 04/03

5.1, 5.2, 5.3

week 9: 04/03-04/09 M 04/10

5.4, 5.5, 5.6

week 10: 04/10-04/16 M 04/17

6.1, 6.2

week 11: 04/17-04/23 M 04/24

6.3, 6.4

week 12: 04/24-04/30 M 05/01

7.1, 7.2, 7.3

week 13: 05/01-05/07 M 05/08

7.4, 8.1

week 14: 05/08-05/14 M 05/15

8.2, 8.3, 8.4



Supplementary material

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

Homework

We exchange homework via UB Learns: I post the assignments there through the 'Assignments' facility provided by the system and you'll similarly be able to upload files.

Unless specified otherwise, the exercises are from the textbook, and numbered identically. The problems might not be exactly on the specified page; you start on that page and scroll down (or turn it) until you find the specified problem(s).

Due date Assignment Remarks
week 1: 01/30-02/05
  • p.10: 5, 11, 18
  • p.15: 1, 6, 13, 18
  • p.22: 6, 8, 11
week 2: 02/06-02/12
  • p.30: 7, 9, 19
  • p.35: 4, 11, 13
  • p.39: 4, 7, 10
week 3: 02/13-02/19
  • p.44: 1, 8, 13, 16
  • p.52: 2, 9, 12, 13

first homework due on UB Learns

M 02/20, 12 AM

This means midnight between Sunday and Monday.

The homework consists of all of the problems listed above.

week 4: 02/20-02/26
  • p.61: 1, 4, 8, 14
  • p.69: 1, 2, 9, 10, 17
  • p.77: 1, 2, 4, 11, 12
week 5: 02/27-03/05
  • p.84: 1, 4, 7, 9
  • p.91: 1, 10, 12
week 6: 03/06-03/12
  • p.93: 1, 5
  • p.100: 2, 11, 12, 15, 16, 17, 18
  • p.110: 1, 5, 7, 13
week 7: 03/13-03/19
  • p.116: 1, 2, 10, 12, 15
  • p.123: 7, 11

second homework due on UB Learns

M 03/20, 12 AM

Again: midnight between Sunday and Monday.

All of the problems listed above, after Homework 1 (so weeks 4-7).

week 8: 03/27-04/02
  • p.129: 3, 7, 8, 11
  • p.133: 1, 3, 7, 12, 13
  • p.140: 4, 6, 17
week 9: 04/03-04/09
  • p.148: 2, 3, 6, 7, 9, 11, 16
  • p.152: 1, 5, 9, 10
  • p.160: 3, 4, 10, 12
week 10: 04/10-04/16
  • p.171: 7, 8, 9
  • p.179: 2, 4, 6, 15, 17, 20
week 11: 04/17-04/23
  • p.187: 7, 9, 14
  • p.196: 1, 3, 4, 16

third homework due on UB Learns

M 04/24, 12 AM

As usual: midnight between Sunday and Monday.

All of the problems listed above, after Homework 2 (i.e. weeks 8-11).

week 12: 04/24-04/30
  • p.206: 1, 2, 7, 11, 12, 13
  • p.215: 1, 5, 6, 8, 9, 10, 16
  • p.223: 2, 7, 11, 15, 16
week 13: 05/01-05/07
  • p.233: 1, 3, 7
  • p.246: 3, 9, 19, 20, 22, 23
week 14: 05/08-05/14
  • p.252: 1, 5, 7, 12
  • p.259: 3, 4, 8
  • p.265: 2, 3

fourth homework due on UB Learns

M 05/15, 12 AM

As usual: midnight between Sunday and Monday.

All of the problems listed above, after Homework 3 (i.e. weeks 12-14).

Homework will be collected and graded four times over the course of the semester. The grader will assign each homework a grade out of 50, for a total of 200.

Do collaborate on the homework if you like, but write up your own solutions. I also strongly advise you to have a look at the UB Academic Integrity Policy, as it very much applies to this class.

And by all means drop by at office hours if you need a hand.

Exams

There are no exams; the grade is based entirely on the homework sets, graded as described above. If you prefer, think of the assignments as constituting a number of ``midterms''.

Grading

Some links

If you have any questions, don't hesitate to email me.

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