Final Blog Post, Due on April 14th

I completed my student ratings.

• Which topics and theorems do you think are the most important out of those we have studied?
• I believe that overall, I need to know the proof of induction, direct proof, contrapositive, and contradiction.  I feel that everything we did this semester kind of stemmed off of those, so a good review of those will help.
• What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out.
• I need to see more proofs by limits.  The whole limits thing has been difficult for me ever since we started, and it would be very helpful to get more help with that.
• I will simply need to study the proofs on limits more.
• What have you learned in this course? How might these things be useful to you in the future?
• I learned a couple of things:
• Direct proofs
• Contrapositive proofs
• Logical thinking
• LaTex
• Having a schedule for homework and blog posts that are due
• I believe these things will be helpful to me as I continue to study and learn about math.  I'm grateful I took this class.

Section 12.5, Due on Friday April 11th

Continuity

What did I find difficult?
I like continuity.  Because this is the end of the semester, this is difficult for me to focus and understand.   I read through the chapter, but will need to complete the last homework assignment to understand exactly how to prove continuity.  I come to the table with a pretty good grasp of what continuity is, from my calculus experience.  The whole concept of proving is difficult to understand with just one pass over the reading material.  I love the graph on page 291.  That helps me understand continuity.

What did I find interesting/fun?
I really enjoy the whole concept of continuity.  It's fun to think about continuity, and a line that continues.  The whole discontinuous thing is something that never really pleased me mathematically.  I understand why things are discontinuous, but I like continuous functions so much better.  It just makes more sense to be connected, and not to be disparate.  I look forward to learning more on how to prove continuous functions.

Section 12.4, Due On Wednesday April 9th

The Fundamental Properties of Limits of Functions

What was difficult for me in this section?
It is still difficult for me to understand exactly what is going on in this section.  The past two homework assignments have helped me become familiar with limits and the syntax in proving limits.  I still think this is the most difficult part.  I understand basically how to prove a limit, but I misunderstand the syntax and the details.  I'm excited to continue learning about this and making it less and less difficult.

What did I enjoy/find interesting in this section?
I enjoy limits, like I've said before.  I also feel like a true mathematician when I am proving limits.  I enjoy the use of arbitrary value such as epsilon.  I also enjoy the feeling of writing a well written proof, that flows well.  I think that the path one takes in proving a limit helps to think through other problems.  It's all good.

Section 12.3 Due on Monday April 7

Limits of functions

What was difficult for me?
It was difficult for me to understand the first vocab word of this section: deleted neighborhood of a.  For some reason, it's always been difficult for me to go through the syntax of definitions like that and come out with a clear understanding of what it means.  I have to hear it explained to me by the teacher.  Because I didn't understand the deleted neighborhood of functions,  it was difficult for me to understand the rest of the chapter.  I believe that with practice and an explanation in class tomorrow, I'll do just fine.

What did I find interesting?
I have always found limits interesting - maybe it's that whole thing where you find interesting what you don't quite understand.  I look at the first result to prove in the book, where the limit as x approaches 4 of (3x-7) = 5.  That's just so interesting to me.  There's a lot for me to understand, but I love how with limits you can get closer and closer and closer to a number, but not actually reach it.  It's just fascinating to me.

Section 12.2, Due on April 4

Infinite Series

What was difficult for me?

Even when I was back in calculus, I had trouble grasping the concept of infinite series.  It was always difficult for me to understand, and I never really got what itwas trying to teach me.  I only know that some series converge to one, some diverge, and some converge to other numbers.  Looking at the proofs, I understand the proof by induction and the other proofs, but it will be a major learning process for me to completely grasp this concept.

What did I enjoy?

I thoroughly enjoy thinking about things going on forever.  When I was a little kid, I used to add 1+1=2, 2+2=4, 4+4=8, 8+8=16, 16+16=32, etc.

I enjoy the process of series, of patterns.  It's always been very interesting to me.  And to think that some of these patterns actually converge to a number, that is fascinating.

I love patterns.

Section 12.1 Due on April 2

What was the most difficult thing for me?
I understand the limit of sequences, but for me this chapter was difficult to understand.  It is tough to understand exactly what is going on.  I remember taking calculus, and we dabbled in proving a limit.  It was difficult to understand then.  I believe it's because there is different notation, and the whole distance and epsilon thing is tough for me.  With more practice, I will improve.

What did I find most interesting?

I remember learning about limits for the first time.  I remember learning what they are, and how we can get closer and closer to something without actually ever getting there. I enjoy the concept of limits, it's just difficult for me to understand exactly what is going on.  I look forward to having a more solid grasp on what limits are.

Exam Review for Monday March 31

What theorem do I believe is most important?
I believe the whole numerality thing is going to be important for the exam.  You know, cardinality - how to prove a denumerbale set, how to prove an uncountable set.  That was a big part of the last two sections of material that we covered, and I think that a lot of what we will see on the exam will build off of this.

What kinds of questions do I expect to see on the exam?
The same kinds that there always are - for the multiple choice, I believe there will be questions that deal with the definitions of the terms that we are given.  I can see that definitely happening, as it has happened on the last two tests.

And for the other free response questions, I can see them asking us to solve example problems, similar to the ones from the homework and the book.

What do I have a question about?
I would like to review the division algorithm, that was what gave me a lot of trouble.

Particularly problems from section 11.2  Any of those problems would be great to review to help me nail down my understanding of the Division Algorithm.