12.1, due on December 1

1. I'm not sure that I could come up with the nth term of these sequences.

2. I remember doing stuff like this in calculus with limits and converging sequences and such.

due on November 25

• What have you learned in this course?
• A lot of proofs, but also about logic and how to approach problems.
• How might these things be useful to you in the future?
• I think in the future, problems like this will be less daunting. Also, I like the logical statements. Sometimes I use them in real life.

11.5-11.6, due on November 24

1. I'm not really sure what the purpose of perfect numbers is. Why is it important to know about them.

2. The relative prime thing is interesting. But would all prime numbers be relatively prime to every other number?

Math Talk, given on November 20

1. I guess it seems kind of odd to me that black box models are so common if they don't tell you anything about the process. Maybe it there's no way of knowing what process is happening. But I think it's more useful if you can predict with changing circumstances like you can with the gray box model.

2. I thought it was interesting that he pointed out that most of science is just an imperfect model that only gives an approximation.

due on November 21

• Which topics and theorems do you think are the most important out of those we have studied?
• Cardinality of sets, schroder-bernstein theorem, division algorithm, greatest common factor
• What kinds of questions do you expect to see on the exam?
• Prove denumerability, proofs with schroder-bernstein and divisibility problems, and problems with prime numbers
• 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.
• Proofs with the schroder-bernstein theorem

1.1-1.2, due on November 17

1. I'm not really sure that I understand the consequences of the Division Algorithm

2. I can see division being useful in the future. I'm glad we can do that again.

10.5 part 2, due on November 14

1. I didn't really understand the function that appeared in the proof.

2. The story is interesting. I'm glad that I don't have to figure out all of these proofs from nothing.

10.5 part 1, due on November 12

1. I didn't really get the restriction of the domain or the whole theorem that came after that.

2. I think it's interesting that if B is a subset of A, knowing that a function from A to B is injective is sufficient to know that it's bijective. That's very convenient.

10.4, due on November 10

1. I real have no idea what the Continuum Hypothesis is or what it does.

2. It's interesting that there is no largest sets even when you can compare infinite sets.

10.3, due on November 7

1. I don't really understand the thing with the repeating decimals.

2. Very odd this concept that (0,1) is numerically equivalent to the real numbers.

10.2, due on November 5

1. It seems very odd that the natural numbers, the rational numbers, and the integers are all the same size.

2. It's cool that you can make a list with all of the numbers.

10.1, due on November 3

1. What is the point of finding numerically equivalent sets? Can they do something special?

2. I guess it makes sense that two sets related by a bijective function should have the same cardinality, but I had never thought about it before.