# 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 self-contained. 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, 2.12.13-2.12.19.
• 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