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. 

6.3-6/4

I liked that 6.3 was about counter examples.  I liked when the book said if a problem can be proved using mathematical induction it can be proved using minimum counter examples.  I sometimes think contractions are more fun than the other types of proofs.  The difference between mathematical induction and the strong principle of mathematical induction is in the latter you have to proof an implication, I have always liked proofing implications so I think this section will be fun.

6.2

A More General Principle of  Mathematical Induction:

Mahematical Induction is starting to make a lot more sense to me, I undertsand thatthe statement P(n) must be true if both P(1) is true AND P(k) must imply that P(k+1) is also true.  That is the part i'm still having problems with.  Mathematical Induction seems like once I get the hang of it, will be a wonderful tool to add to my proofing problems tool box.  I also think the divides problems at the end of the chapter are somewhat tricky too.

6.1 + test review.

In 6.1 I thought the 3X3 box was interesting, I had never thought that that many squares were really inside off the box.  Mathematical Inductions seems challenging, but I'll focus on that later, I've got to study for the test now.  Out of what we have studied thus far in the class I think the definiton of odd and even will be important as well as all the methods we have learned for proofs.  I think the test will be just tons of proofs like our homework, and be really hard.  Proofs are really hard for me,  I can start them and usually see how to set it up, but I usually get stuck in the middle.  I'm going to have to do some serious studying for this exam if I want to do well.  I would like to see a problem with absolute value signs. they kind of confuse me in proofs.  I hope after tomorrow in class and i review on my own i will feel more confident about this exam. 

5.4-5.5

I liked that this reading talked about the Intermediate Value Theorem of Calculus, and I liked even more that I knew what this Theorem was.  The concept of existence The hardest part of this will be when deciding what method to use, either contradiction or not.  Also many of these existance proofs use multiple cases.   I'll have to really think over these so I do the right method and number or cases.  I also think that disproving existence statements will be easier because I think sometimes it is easier to see a way to make something not true, then multiple ways to make it true.

5.2-5.3

I really liked the story of the three prisoners, and I am happy to say I figured out the right answer before reading the paragraph below.  It was clever.  The chart in section 5.3 was a nice review of the techniques we have already learned.  The part that will be  most difficult is decided what proof method to use when the book doesn't tell you.