4.3-4.4, Due September 24

Difficult: Woah, I totally got lost when they were trying to prove |x+y| (< or =) |x| + |y|. That proof just really through me, because they would change the = to a > throughout the proof, and seeing as they considered this a pretty important proof, maybe could you go over this one or one similar in class?

When I read these chapters, it's so difficult to apply what I learn. Like when I was reading through the subsets proofs, it made sense what they were doing, but I don't (currently) have the ability to come up with it on my own. My understanding is really hazy, but then as we talk about it in class, it becomes a little clearer, and then as I start doing my homework, it becomes a lot clearer. This cycle has become really prevalent and useful throughout these chapters. So what I'm saying, I get what it's saying, but it's going to take some lecture and practicing around with before I will get it.

Interesting: It's great that we can start using all real numbers. The proofs before were great, but they were slightly limiting because you could only use integers.  Expanding the domain definitely has a lot more applications to real world situations. Off the top of my head, I can think of a lot of engineering situations where the domain would be all real numbers, so it’s important to be able to work with this set.

--How long have you spent on the homework assignments? Did lecture and the reading prepare you for them?

I probably spend two-two and a half hours on each homework assignment, including the prereading, blog, and homework. The prereading and lecture ABSOLUTELY help a lot, as I said above.


--What has contributed most to your learning in this class thus far?

I think the biggest thing is having good solid examples, and then learning by doing. I can watch people do proofs all day long, but until I actually sit down and start doing it, I never really master the concept. Since I can't do that until after class, having solid definitions and examples gives me a great base to refer to when I need help.

--What do you think would help you learn more effectively or make the class better for you? (This can be feedback for me, or goals for yourself.) 

This is mostly a goal for myself, but I would say increasing my diligence. A lot of the time I will get discouraged because I can't figure things out right away, or that I have to just sit there and think without writing anything down for a couple of minutes. Even though I often feel "stuck," those are often the moments where I grow the most, through trial and error. I really don't have any negative feeback for you, I love your class structure; it really works with me.