THE FINAL

I already did my evaulations last week.  And to study for this exam, I am going to make sure I am very familar with all the definitions of all the terms we have learned about.  I am going to make flashcards to study over the weekend.  I really need to review the stuff from the start of the semester, although I think I will understand it better now, because I feel like I am grasping the concepts better now.  I know as I continue on all the mathematical notations and proof strategies I have learned will only  help me in being more succesful as a math education major.

12/4-12/5

I liked the section on fundamental properties of limits of functions.  It was cool to see the proofs of why the limit tricks that I learned in 113 really work.  In section 12.5 about continutity, I liked how it gave you those three specific conditions that ahve to be satisfied in order for a function to be continuous, it made it nice to know the outline when trying to prove if something is continuous. 

12.3

I loved this section! Cause I already know how to do it!  The only parts I think might be kinda difficult it when I am supposed to prove a limit doesn't exist by contradiction.  Sometimes I have a hard time with those ones.  But I think it will be more clear after class tomorrow! I hope we get our tests back. 

12.1

CALCULUS!!!
I liked this section because it was all very familar to me.  I think I understood most of it, and i've seen this kind of proof before, so I'm hoping it just becomes even more clear tomorrow in class.  I like that with a little math you can easily decide what needs to be used in order to make the proof work. 

11.5

Relatively Prime Numbers
Relavively Prime Numbers mean that two number have no gcf other than one.  So the number might not be prime on its own, but when paired with another number they are both relatively prime,  like 20 and 7.  I think that Euclid's Lemma will be very useful when working with relatively Prime numbers and make proof quite a bit easier. 

11.3-11.4

29000!!!!

Last night I went to the Hunger Games Movie, and thus I forgot to BLog, but I figured if I did this morning before class, that that would be okay. 

11.3 Greatest Common Divisors: This section was a nice review about greatest common divisors.   And it was cool to see the proofs and why this worked. 

11.4 The Euclidean Algorithm: This is a cool way to find the gcd, I liked how you just start dividing and deviding by the numbers you get, and it leads you to the gcd once you have to add 0 to get the number before. Math is cool.

11.1-11.2

The first section was simple because it was math I have been farmilar with for quite some time, Divisibility properties of integers.  The division algorithm will be a little harder to understand, but it makes sence the formula b=aq+r with a= some number, q=quotient devided by, and r=remainder after the division.  It doesn't seem too tricky. 

10.5

The Schroder-Bernsein Theorem!!  I'm so happy we are finally learning how to use this theorem.  It makes a lot of sense, that if you prove A is less than or equal to B as well as B being less than or equal to A that A=B, and thus meaning the have the same cardiality.  It is just hard for me to know the equation to pick, when deciding what to map them to.  I also liked reading the history about the earlier mathematicians.  They were smart smart men.

10.4

I was really confused yesterday in class because we talked about this section before I had read the whole thing,  But now that I have read it, It makes a lot more sense.  I wonder if the continuum hypothesis is true or false! It is kinda mind blowing that some things in math still can't be proven or disproven.  I also heard the Schrolder-Bernstein Theorem makes this stuff a lot easier, so I'm excited to read/talk about that next class.

The rest of 10.3

I feel like I really understood the rest of 10.3, I had to read over it to do the last few homework problems.  It isn't difficult to prove that it is a bijection, because we have been working on that for quite some time, what is going to be difficult is figuring out what function to use to ensure that it maps to the correct points in the set. 

10.3

I thought it was really interessting how the fraction 1/2 is equal to .50000 as well as .49999 i have never thought of that before, but it makes perfect sense.  I am still having a real hard time understanding what denumerable means exactly.  I don't understand how denumerable and uncountable are connected, or even if they are at all.  I way don't understand how every 2 denumerable sets are numerically equivalent, wouldn't that mean ALl denumerable sets are equivalent?

10.1-10.-2

I thought it was crazy the history lesson at the start of this chapter and it said Galileo was in jain the last nine years of his life! So many people didn't get the credit they deserved until after they had died.  numerically equivalent is pretty strait forward and I don't think I'll have  a problem with that, I do however have don't understand how a set can be countably infinite, you can't count to infinity. and denumerable is confusing too, I hope it is a little more clear after lecture tomorrow!

Examm # 2

I expect some mathematical induction problems to be on the exam, and I really need a review on them since we did them so long ago.  I also think the test will have a lot on = classes, as well as funtions, since we spent a lot of time on those.  I think there will be lot of proofs on the exam.  I hope it goes better than the last exam did, or I'll be introuble.

9.6-9.7

Inverse Functions was pretty easy for me to understand, one part I didn't get was when it says
R - {2} -> R - {3} ,  I know it has to do with the domain, but I don't quite get how you use then in the problem.  I thought permutations looked fun and not too bad.

Barry Cipra!

I attended the Math Lecture this afternoon by Barry Cipral.  He was a very interessting man.  Firstly I thought it was neat he used the overhead projector, with hand written notes.  It showed his personalilty.  He also told us a new word Herbetate, which means to make dull or obtuse, and he warns not to do that.  The main topics of his lecture I thought was his game "Tag Deal"  which was a game were you start with all the coins in one cup, and eventually they will all end up in the same cup.  The next thing he spent quite a bit of time on was "Gray Code Quilts" this was so cool how it worked out! and made such awesome designs when the pattern was repeated.  He also talked about a Bijective proof, and I thought that was cool since we had just been talking about that.  Over all it was a great lecture, and I'm glad that I went.  Plus we got treats before that were delicious. 

9.5!!!

I really liked this section of reading.  All of the composites fo sets are just like numbers that I have known how to work with for so long, so it should be pretty simple.  I liked how the book would compare the examples to calculus, then I totally understood.  The only thing I didn't understand was when it talked about combining the sets, the very last example of the chapter. 

9.1-9.2

Once they eplained the notation of a Function from A to B as B^A it makes total sense.  And it is so easy to figure out how many possible combinations there are from the sets.  I feel like I already knew all this imformation about function from my previous math classes. 

8.3-8.4

At first I was confused as to if lines equal each other that means they can either be parallel or coincide.  Once I realized this is was easier for me to see and understand how a line can equal another line and not be parallel.  When doing equivalence relations what I didn't understand is how to decide what numbers to use, the book always uses -16 and 16, but I don't know how they decided that. 

8.1-8.2!!!

I really liked 8.1 and understood it.  I liked how Domain has to do with X and Range has to do with Y, just like it always does.  So that makes it nice and easy to remember.  The Distance part at the end of 8.2 also made sense.  What I didn't quite understand was Transitive and how exactly that works.  I really understood the reflective property. 

7.1-7.3

I thought conjectures in mathematics was a very neat section.  I loved when it talked about palindromes as being words and numbers.  And that when you add the opposites of positive number together you will eventually get a palindrome.  FASCINATING! The last section of the reading adds a whole different angle to our proofs,  not having only proof they are true, but first deciding for ourselves if it is true or it it is false, then doing the appropriate proof.  This will call for more pre-work on problems.