Summer 2010
MATH 312: Proofs in Elementary Analysis
Branko Ćurgus
 Tuesday, August 17, 2010


I am posting the proof presented today. I made the proof completely selfcontained. That is I am not citing any exercises from the notes. I just use the definition of continuity.
Here is the "zero theorem".
 Monday, August 16, 2010


Our goal tomorrow is to prove Exercises 4.6.2 and 4.6.5.

The current total presentation
scores are 35, 32, 31, 30, 26, 25. The average is 29.75
and the standard deviation is 3.437.
 Wednesday, August 11, 2010


Remaining sequence problems for presentations 3.13.5, 3,13,8,
3.15.1, 3.15.2, 3.15.3, 3.15.4.

Read 4.1, 4.2, 4.3. Any of the exercises can be presented
tomorrow.

The current total presentation
scores are 32, 30, 29, 25, 24, 21. The average is 26.75
and the standard deviation is 3.739.
 Tuesday, August 10, 2010


Remaining sequence problems for presentations 3.8.6, 3.8.7, 3.10.1, 3.10.2, 3.10.3, 3.13.5, 3,13,8, 3.15.1, 3.15.2, 3.15.3, 3.15.4

The current total presentation
scores are 32, 28, 26, 25, 21, 14. The average is 24.25
and the standard deviation is 5.655.
 Monday, August 9, 2010


We need to move quickly through the sequences section.
Read 3.1, 3.2, 3.3, 3.4 and 3.5. I did 3.5.1 today.
Work through the solved exercises and examples, read and
understand the meaning and importance of remaining exercises.

For presentations try 3.7.1, 3.8.1,
3.8.3, 3.8.4, 3.8.5, 3.8.6, 3.8.7.

For more presentations try 3.11.4.

The current total presentation
scores are 29, 28, 23, 22, 19, 14. The average is 22.42
and the standard deviation is 5.119.
 Wednesday, August 4, 2010


The class average for two exams is 66 with the
standard deviation 10.71. The current total presentation
scores are 27, 25, 19, 17, 17, 11. The average is 19.25
and the standard deviation is 5.383.

Two more chapters of the class notes.
 Monday, July 26, 2010


Tomorrow I will do the remaining proof from Section 2.11.

We should also do Exercises in 2.13. These have a priority: 2.13.4, 2.13.5, 2.13.6, 2.13.7, 2.13.8, 2.13.9, 2.13.11, 2.13.12, 2.13.17.
 Wednesday, July 21, 2010


This is Lesley's solution of Exercise 2.9.5.

Tomorrow I will talk about Section 2.11. Read this section and do exercises from Section 2.12: 2.12.1, 2.12.2, 2.12.3, 2.12.7, 2.12.8, 2.12.9, 2.12.10, 2.12.11, 2.12.132.12.19.

On Monday we should do Exercises 2.9.5 and 2.9.6. We will then proceed to Exercises 2.10.1, 2.10.2 2.10.3, 2.10.6.
 Thursday, July 15, 2010


The following exercises from Section 2.8 might appear on the next exam: 2.8.12, 2.8.13, 2.8.14, 2.8.15, 2.8.18, 2.8.19, 2.8.21 and Proposition 2.8.20. Also, make sure that you know all the definitions.

On Monday we should do Exercises 2.9.5 and 2.9.6. We will then proceed to Exercises 2.10.1, 2.10.2 2.10.3, 2.10.6.
 Tuesday, July 13, 2010


The exercises to do from 2.7 are 2.7.3, 2.7.5, 2.7.7, 2.7.8, 2.7.9, 2.7.10.

Read Section 2.8. The only exercise related to finite sets that we will do is 2.8.6. In the proof of this exercise you can use the previous exercises even if they are not proved.

Do the following exercises about infinite sets: 2.8.12, 2.8.14, 2.8.18, 2,8,21.

There are several proved statements in Section 2.8. Read them carefully. If something is not clear ask.
 Wednesday, July 7, 2010


This is Chris' solution of Exercise 2.3.6.

The problems for tomorrow are 2.5.12, 2.5.13, 2.5.14, 2.5.15, 2.5.16, 2.5.17, 2.5.18.
 Tuesday, July 6, 2010


This is Lesley's solution of Exercise 2.4.4.
 Read and do exercises in Section 2.5.
 Thursday, July 1, 2010


This is Mike's solution of Exercise 2.3.3. This proof is missing one detail. Can you figure out what?

This is Lesly's solution of Exercise 2.3.4. This proof is also missing one detail. Figure out what.
 Read and do exercises in Sections 2.4 and 2.5. Pay attention to details in your proofs.
 Tuesday, June 22, 2010
