Section 25

This section seemed pretty easy to understand as well. Basically you are just checking that each output appears at most once for injectivity and appears at least once for surjectivity. The proofs were a little strange and seemed like they were just stating the obvious, so I'm not sure what roles those play in the definitions.

One thing I noticed is that this chapter used the "onto" and "one-to-one" definitions that we learned in linear algebra. I didn't really understand it when I learned it in 313, but it made a lot more sense when I read this chapter. If I had read this chapter before that section in 313, I would have understood that concept much better. I've found that with a lot of concepts in this class actually. I don't know what you have planned for this cohort in the future, but I think it could be very helpful to have 290 as a prerequisite course for this cohort, in order to solidify the mathematical concepts that appear in other math classes. Just a thought.

Comments

Post a Comment

Popular posts from this blog

Midterm Review 10/2/18

I think the most important topic we have studied have been how to outline and write proofs. They are simple enough for the most part, but they have helped me to think more deeply about topics that I have understood but maybe not understood fully, and they have also helped me to think more abstractly to understand things that I haven't understood before. On the exam, I'm mostly expecting to see proofs and set theory questions. I think there will be a few logic questions but they will mostly be tied up in set problems and in formal proofs. I would like to see a few more examples of rationality proofs, like the ones from homework 11 and 10. Those were a bit harder for me to understand the theory behind the proof so seeing those written out would help me out a lot.
Read more

sec 28

this section wasnt terrible, I understood what was going on for the most part. It is a little more abstract since we are dealing with infinite sets. I also didn't really know what the new notation was for, the squiggly N symbol was very weird looking. I think it just need to hear it explained out loud to fully understand it.
Read more

12/7/18 midterm review

The most important thing that we have studied since the last midterm has probably been Schroder-Bernstein theorem and cardinality proofs. They are a little bit abstract since we are dealing with the size of infinite sets, and my intuition gets broken from time to time, but so many proofs and theorems build off of them. I also think that the limit proofs we did are very important, because it is the basis for Calculus and analysis which is what I will be doing next semester and in the coming semesters. For the midterm I am expecting to see cardinality proofs for the proof section, and for the multiple choice and true/false some basic questions about cardinality and limits. I'm a bit more concerned about cardinality proofs because that section was the hardest for me, so if you could go over some of the more difficult cardinality proofs tomorrow that would be great.
Read more