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. 

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. 

4.5 4.6 5.1

I feel like this section won't be that difficult to do.  I remember talking about the fundamental properties of operations like Commutative Laws, Associative Laws Distributive Laws and De Morgan's Laws.  So I'm excited to learn how to do proofs using them.  I also think the proofs with counterexamples will be a fun section, when reading over the examples I could figure out a bunch of the solutions with out reading them.  The part that I think will be the most difficult is the Cartesian Product part, I understand what they are, but I don't quite understand how to use them in proofs, so I'm excited to learn how to do that. 

4.3-4.4+ questions

I liked that 4.4 used the Venn Diagramms to explain different intersections of A and B, it really helped me see clearly what the book was talking about.  The part I thought was most difficult was when using real numbers in proofs seeing how we use the techniques we already learned, but they are much harder.  After tomorrow when these get explained in class, I think they will make sense just as the other ones did. 

Answers: I probably spent an hour - two hours on each hw assignment.  The lecture helps me understand the hw a lot better than the reading does,  I really understand the way you teach, but at home when doing some homework it is nice to have the book in case I need to look at more examples to understand what is going one.  Doing the homework assignments is what helps me the most in understanding what is going on in this class.  My goal will be to just continue doing the assignments and not falling behind. 

4.1-4.2

I love that we are learning even more ways to solve proofs, and we are getting so many new ways to look at problems.  I'm excited to have you explain these in class because I'm having a little problem with the symbols and terms that were introduced in these chapters.  I think proofs are fun!

3.4-3.5

What I learned from this reading is if two integers x and y and both even or both odd they are of the same parity, and if one is odd while the other is even they are of different parity.  I always thought this was something but I didn't know the specific name that it had assigned to this property.  Another tip I thought was important was when you are evaluating a proof you need to solve it for the general case, and you can't just assign a specific number that works for the proof, or you haven't solved it for all cases. 

3.1-3.3

Something I thought was neat from this reading is the three properties of integers, since they are basically common sense, when writing a proof you don't have to justify them.  What will be most difficult for me from this reading is the proofs, I have always struggled with proofs, and I hope after we talk about this is class I will feel more confident. 

cHaPtEr 0!!!!

I think this reading section had lots of good advice in it for not only mathematical writing but for all types of writing.  For example, know your audience and give yourself enough time to finish the assignement.  It also talked about "spirals" and I feel like that is something I will need to work on because I think I have problems with that sometimes.  It will be most difficult to remember when to use words that are usually interchangeable, such as that and which.  They have very different meanings in mathematical writing. 

2.5-2.8

I was having kind of a hard time understanding the examples when only numbers were being used, but as soon as they used visual examples, like the isosceles and equilateral triangles, I not only  understood better, but when I went back I understood the previous ones better as well.  I thought it was very interesting that when dealing with biconditional statements, both statements can be falst, but when put together the combined statement is true because both parts are false. 

2.1-2.4!

I thought a lot of stuff from this reading was interesting.  The first thing being that statements are either going to be true or false, but that they can not be both.  And the more statements you compare together, the more possible outcomes you have.  All the tables really helped in understanding the different ways writing and comparing statement is possible.  The last thing I found very neat, is how the different ways there are to write if P, then Q, some of them are much more unique that they book mentions, and there are many more ways that they book doesn't mention. 

Assignment 2

Reading Assignment 2:

Sections 1.1-1.6

I really enjoyed the reading in this section, and learning about sets.  I feel like sets are just like a whole other language.  It is the language of math.  After reading this I understood much more of the notation that my teachers have been using in my past math classes for years.  I thought the Venn diagrams really helped me understand what the book was talking about.   What I learned in this chapter will really help me in my math as I continue to progress. 

Assignment 1

Reading Assignment 1:

I am a sophomore in school, and my major in math education.

I have taken Math 112 and I am currently taking Math 113, both Honors sections. 

I am taking this class for my major, and because I’m excited to learn more about math.

Best Math teacher: The best teacher I had was my math 112 teacher I had last semester.  She really cared about us as students, and tried really hard to answer our questions.  And helped us see how this would apply to our lives. 

Worst Math Teacher: the worst teacher I’ve ever had is my teacher from high school, he taught us how to do everything in our calculators, which made it very easy, but I never really learned how to do any of it.

Something interesting and unique about me is I just got my mission call yesterday, I will be serving in the California San Jose Mission, Spanish Speaking. And I will be entering the MTC May 30.

I have a class during your office hours, so I won’t be able to come but anytime time any day before one works for me.