due on October 31

• Which topics and theorems do you think are the most important out of those we have studied?
• The stuff about onto and one-to-one, induction, and equivalence relations
• What kinds of questions do you expect to see on the exam?
• Proofs about these topics
• 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 would like to see more proofs with bijective functions.

9.6-9.7, due on October 29

1. I'm really not sure what exactly permutations are for and why they are important.

2. Inverse functions are kind of interesting. It seems like one-to-one is just onto backwards.

9.5, due on October 27

1. I don't really understand why the proof makes a point of saying that the functions are both injective and surjective instead of just bijective. Does't it mean the same thing?

2.I think it's interesting how they got the derivative rules.

9.3-9.4, due on October 24

1. I'm not really sure what bijective is and why it is important.

2. I remember learning about one-to-one and onto functions, but I don't remember ever hearing the name "surjective."

9.1-9.2, due on October 22

1. I don't really understand what it means to say all the functions from A to B.

2. Functions are familiar. It's interesting to learn more about them.

8.5, due on October 17

1. I didn't really understand the proof to show that it was symmetric.

2. This kind of broadens the definition of equality. Before, I had only thought of the equals sign, but there are other equivalence relations.

8.3-8.4, due on October 15

1. The proof of how to show that something is reflexive is confusing. I'm not sure where they are pulling the numbers from.

2. I think it's interesting that they explained what equivalence is. It seems so basic, but it's still an important concept to understand.

8.1-8.2, due on October 13

1. It's not really clear to me why these properties are important. What can be done other than just prove that they have a certain classification?

2. Domain and range are familiar terms that always seem to pop up in math classes.

6.4, due on October 10

1. I am unsure of when to use regular induction as opposed to this strong principle of induction.

2. I think it's interesting that from what I can tell, this technique is just regular induction backwards.

6.2, due October 8

1. I'm not sure why the name of the set had to switch in the inductive step. It looks like we're using completely different sets.

2. It's interesting that it's just about the same thing as the last section, but a little bit more useful as you can use it with any number m.

6.1, due on October 6

1. I'm not sure what the point of induction proofs is. Or exactly how they work.

2. I liked the story about Gauss. Very smart person.

due October 3

• Which topics and theorems do you think are the most important out of those we have studied?
• I think the properties of sets are important because they seem to come into play in a lot of proofs. Also the stuff about odd and even numbers.
• What kinds of questions do you expect to see on the exam?
• I expect to see proofs with odd and even numbers, proofs with sets being even, and the three different kinds of proofs.
• 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 work on problems like the proof that sqrt(3) is irrational, to get down all of the steps that lead up to the contradiction. I also need to look more at congruence of integers. I think I would like to see more of the problems about how to prove that two sets are congruent, especially those that involve cross products.