Extra Credit

So I went to the Mimematics show.  It was pretty cool andI got a free cookie.

It was hard to understand some of the acts, like the one on distance had an accordion type thing that said don't touch and measure yourself carefully.  I don't know what that had to do with distance, maybe it meant keep your distance.

The most interesting part was how they taught us how to do some simple mime tricks, like catching a ball in a paper bag, or doing the wall.  They had an interesting act where one got into some air conditioning ventilation and used it to represent a function as stuff that went in came out small.  Unfortunately, he took the wrong thing, and didn't have a miniature version of it, so it kind of threw off the act.

Student Ratings and Review due on 10 December

Definition of limit and proving limits was one of the most important things that we studied.

Before the exam it would be great to go over serjective/injective proofs, as well as strong induction, and most missed questions on past exams.

Post 12.4, due on december 8

The most difficult part of the material was simply the minor details in the proofs of these theorems.  Some of them are not too difficult to understand, but it will be difficult to remember which lemma's to prove for each theorem.  I suppose practice would help a lot.

The most interesting part is how limits are relatively easy to work with since you can add them and subtract them, multiply and divide.  It becomes less difficult if they involve infinity and zero, because what is 0 times infinity.  I remember having a discussion about this in early calculus, but my memory is long gone.

12.4, Due on 5 December

The most difficult part of the material was using the definition of the limit to prove these theorems about functions, especially choosing delta, but it seems very similar to how we choose N to define limits of series and summations.

The most interesting material was how limits can simply be added and subtracted, as well as multiplied and divided.  The other thing was how delta is used to describe a neighborhood.  In calculus and also in physics and chemistry, we mainly use delta to mean partial such as a partial charge or a partial differential.  It is interesting that we use it in two different ways.

Section 12.1, Due 2 December

The most difficult part of the material was proving that a series diverges by using a proof by contradiction.  It does not seem like an easy thing to do.  Other than that, it was simply 12.1 plus some induction, which really is not too difficult.

The most interesting part was the harmonic series.  It is weird to think that it is a diverging series, but it did remind me of a math joke, though it is not the same series.  A mathematician walks into a bar and orders 1 glass of soda, then the next mathematician comes in and orders a half glass of soda, then another comes in and orders 1/4 glass.  At this point the bartender sees a long line of mathematicians and simply pours 2 glasses.  Because of this joke I know this series converges to two.

12.1, Due on 1 December

The most difficult part of the material was proving that a series was divergent.  I understand that there is no limit, but the formatting of the formal proof seems a whole lot more difficult then it needs to be.  Especially deciding which e to choose and so on.

The most interesting part is this remind me a lot of calculus.  I remember in multiple dimensional limits, we learned how to use the definition of a limit to formally show that a limit exists, but it was always easier to show that a limit did not exist by approaching the same point along different lines.

November 25

What I learned in the course:
I learned a lot about sets, and subsets, and cardinality, and functions, and injections, and serjections, and power sets, and primes, and evens, and odds, and divisibility, and integers, and latex, and proofs, and more proofs, and more proofs...

How will they help me in the future:
They will help me to think logically, keep the goal in mind when working to solve something, and sometimes realizing things are much easier if you can prove something else first.