#5: Lecture 5, due September 2nd

Difficult- I am following what the lecture says in words, but the symbols are confusing me. I don't know what the c with an line underneath it means. I understand what each of the properties mean with the equivalence relations, but when applying them to sets I am lost. Sets were not my forte in linear algebra so I am nervous. I hope when we discuss this in class it makes more sense to me. It also helps to think of sets in words instead of symbols so some the examples make a little more sense.

Reflective- Well I like the reflective, symmetric, and transitive properties since I learned those forever ago. I like that I learned them a long time ago but they play a big part in many areas in math so when they come up I know what they mean. I also think the cross products of sets interesting because that is how you form new sets, taking elements from both sets to make a new one.

#4:Lecture 4, due on August 31st

Difficult- Okay well even though we covered this lecture in this class today, I think I am still confused on which technique to use when. I am going to try the homework for it and see if that helps because I know you said practice is what helps you master the proof techniques. I understand the techniques of proofs 1 but 2 is a bit more challenging for me. I am still worried I will not know what technique to use when I'm given an implication. The most difficult technique seems to be proof by induction. Theorem 1.7 and Example 1.8 were hard and took me a while to follow. Hopefully once I practice these I can get the hang of it.

Reflective- The most interesting part of the lecture to me is needing to prove 2 cases. I think I might like this one because it seems to be the most obvious proof to solve. The implications that require 2 cases are pretty straight forward, or so I think, so I will hopefully be able to figure these out. I also like the well-ordering axiom because I  clearly understand this one. Most of the rest of the material I have to think about for a little longer but the 2 cases and well-ordering axiom are interesting and I understand them.

#3:Lecture 3, due on August 29th

Difficult- In symbols and descriptions I follow exactly what the lecture is saying. Our applied linear algebra class started out learning a little bit about contrapositives so that came back to me. However when it comes time to prove a contrapositive and the examples are in sentences, I struggle. This is weird to me because with lectures one and two it was easier to think in sentences than in symbols. I can do the contrapositive example but it took me a while.
I am wondering on a test how will I know when to use the contrapositive, are there words that signal to use it? The contrapositive example given is an "if => then" problem and an example of deductive reasoning is an "if => then" so how will I know which is way is the correct way to prove a problem? Trial and error?

Reflective- The most interesting part of the material to me is that the inverse of the implication is equal to the converse of the implication, therefore the inverse is the contrapositive of the converse. I had not learned that before when we had briefly discussed this is in linear algebra but it makes sense and connected the different parts of the lecture. Making the truth table helps to solidify for me that the implication and the contrapositive are equivalent, and that the inverse and the converse are equivalent. I think I will get this even more when I do the homework questions that go along with this.

August 25th, 2010. #1 Introduction

1. Well, I am in my third year of college but am technically a senior by hours, and planning to graduate a semester early. My majors are Mathematics, Secondary Education, and Applied Critical Thought and Inquiry.
2. Linear Algebra is the only post calculus class I have taken, and this semester I am taking Abstract Algebra and Differential Equations.
3. Well besides the fact that I have to take this course, I am excited to learn about ring, groups, and fields. My pastor majored in Math and so he has told me a little bit about it. He also said that it was the most difficult math class he had to take so I am very nervous! I am not very good at proofs :/
4. Well Dr. Nicholson is the best math teacher I have had. He always had his office open so I would go in at least twice a week to get outside help. It helped me a lot to talk one-on-one and work out what I wasn't understanding. Least effective for me is not being open to help students outside of class.
5. Well something interesting. Hm, I am from Kansas and my family and I are HUGE Jayhawk fans. Rock Chalk!
6. Unfortunately, I cannot come during your office hours. I have from 10:15-1:30 open MWF so I hope sometime in there works for me to come get help because I am telling you now I will need it!! I hope this is okay. 

I am excited for this semester and getting to know you!