Review for the Final

I completed the student ratings for this course.

Which topics and theorems do you think are the most important out of those we have studied?

Bijections, set notation, the introduction to analysis stuff, induction. Probably the triangle inequality, considering how frequently it has come up.

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 think I primarily need to review definitions. Also it would help if I slowed down when doing problems. I need to remember that sets can go to infinity and that my intuition breaks when this is the case. Also, I should review negation rules.

What have you learned in this course? How might these things be useful to you in the future?

I think I have primarily learned how to format and structure solid proofs. This will come in useful in the future. I also learned some cases in which my intuition breaks. Further, I feel that this class improved my ability to think logically, and helped to solidify some of the things I learned over the summer at my math camp.

Thanks for a great semester!

-Batman

Math Talk due 10 December

I read Dr Jarvis' devotional.

I really like how he talks about accepting imperfection. I have found that perfection can be immensely paralyzing, and that settling for "good-enough" is often far, far better than striving for perfection.

At church the other week someone discussed how failure is the Plan of Salvation. The Atonement was there because we would fail, not as a backup plan in case we did. Mistakes are part of the plan. Dr Jarvis seems to be saying this as well.

This guy taught swim lessons and lifeguarded, just like me.😊

Test Prep due 7 December

Which topics and theorems do you think are the most important out of those we have studied?

I think the material surrounding bijections is very important. Also the basics of the delta-epsilon proofs including limits, continuity, sequences, and partial sums.
What kinds of questions do you expect to see on the exam?

I expect to see questions regarding all of the aforementioned things.
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.

The practice tests went very well for me. But there is a lot of material listed on the study guide that was not covered on the practice tests. Thus, I am most worried about the most recent stuff (limits, continuity, sequences, and partial sums), as I have had the least practice with it. I would like to see examples worked out, but I want a variety of problems so that I can get used to identifying which techniques go where. 

Section 36 due 5 December

Theorem 36.7 is cool.

I feel like I have some deep insight about this on the tip of my brain (is that a phrase?), but my conscious mind can't put words to it. So I will think about it and maybe I'll have something cool to say tomorrow. I think it has something to do with the facts that functions are closed under multiplication and addition and that domains can be bounded weirdly. I'm not sure.

Random question in preparation for the midterm: If f: A \rightarrow B and g: A \rightarrow B and we know that f is injective and g is surjective and f \not= g, can we conclude that a bijection must exist? I think so, though we can't conclude what said bijection is based off of the given information. I will try to remember to ask this during office hours.

-Batman

Section 35 due 3 November

There is a problem with my grade. My grade for homework 25 got put in twice (once as assignment 25, once as assignment 26). As such, all of my homework grades since then have been shifted by one. Hence, I have a grade for homework 34 despite not having turned it in yet.

This looks like a delta-epsilon proof.

I like the proof "sketch" descriptions. They are very handy.

"Thus we want 3|x 2| < ", or in other words |x 2| < "/3. This tells us what value for delta we should use. "

How does this tell us what value for delta we should use? Upon further reading, I think I might have figured it out. But it'll be good to review. ...Yeah, I figured it out.

This is really cool. I saw a delta-epsilon proof in high school calculus, but I don't think I fully appreciated it at the time.

Section 34 due 30 November

What on earth are partial sums used for?

More induction!

I have a question about corollary 34.7. If the limit does equal 0, then does a_{n} converge? Both this corollary and theorem 34.6 come very close to saying this, but not quite. Thus, is it not true?
Oh, a note later on in the section answered this. No, the limit equaling 0 does not imply that a_{n} converges.

Section 33 due 28 November

Parts of this look very similar to the material I studied in my independent study calculus 2 class. The rest of the material is new, but it looks like something that would belong in calculus 2. It makes me wonder how comprehensive my class was and just how much I should have learned but didn't...

Woah! What does the star mean? Does that mean that the scratch work is done?

Will we get docked points if the scratch work shows up in the homework?

Proposition 33.16 is weird.