Sec. 7, 9.5, Due February 29

This is somewhat more familiar territory in mathematics.  I'm assuming most students in the class have also had prior experience.  The trick here is remembering if you write the composition of  functions as f(g(x)) or as g(f(x)).  Once I can keep it straight I should be okay.

Sec. 7, 9.3-9.4, Due February 27

One to one and onto functions seem easy enough.  The main difficulty I foresee myself having is with onto functions.  The example in the reading that made this most clear was a function from the integers to the integers defined by 2n.  For a while I did not see why it was not considered an onto function, but then it became clear that it was due to the domain, and so the output of the function was limited to the even  integers.

Sec. 7, 9.1-9.2, Due February 24

Defining a function as the book has doesn't seem to different from what I've learned in previous math classes.  The main difference is simply in the notation (or so it currently appears).  The sections introduced a lot of new vocabulary concerning functions.  Things such as "mapping"  and "image".  The set B is referred to as the codomain as well as the range of a function.  Are they interchangeable?

Sec. 7, 8.5-8.6, due January 22

I found multiplication and addition to be well explained.  The comparison to a clock worked well.  In section 8.5 the book said that congruence mod n would yield n equivalence classes, then in the very last example there exist only two equivalence classes.  It was explained briefly, but I would appreciate a little more understanding on the example.

Sec. 7, 8.3-8.4, Due February 21

The main difficulty I foresee with this section is defining the equivalence classes.  It was easy enough with specific examples, it only became more difficult when it was a more general case.  I would appreciate a little more time spent on these during class.

Sec. 7, 8.1-8.2, Due February 17

The only confusing thing about the section was the books insistence on using R rather than the actual mathematical symbol that it represented.  It gave all of the relations the same symbol, and when multiple examples were given in the same paragraph it became ridiculous.  Hopefully we get past the usage of R quickly and to being able to just use the symbols.  I'm curious if the properties of the relations (symmetry, transitive, reflexive) will actually be helpful in future proofs.

Sec. 7, 7.1-7.3 Due February 15

There seems to be nothing new here.  The main thing is deciding if a proof is necessary or if the statement is false.  The authors seemed to enjoy making the section that revisited quantified statements as convoluted as possible.  The statements contained within were slightly confusing at first, but only required that I read slower.

Sec. 7, 6.3-6.4, due February 13

The main thing that I found difficult was the strong principle of mathematical induction.  They took some integer i such that m<=i<=k and then never really seemed to use it in the proof.  It also seems as if finding out the minimum value of k to be used in the proofs was obtained by guessing and then checking.  Hopefully there is a faster way than having to run through the first few values allowed by the domain.

Sec. 7, 6.2 due February 10

The idea behind the section seems easy enough.  Rather than making the base case n=1 we can use some m.  Some of the examples however still managed to confuse me, namely the one involving De Morgan's laws.  It seemed as if they started out assuming what they were trying to prove.

Sec. 7, 6.1 due February 6

For section 6.1 I understood the algebra that the book went through, though it was unclear to me why they sometimes did what they did in pursuit of the proof.
Of everything we've studied thus far, the most important things are probably the proof methods: direct, by contrapositive, by contradiction.
On the exam I'm expecting similiar questions to those we've been seeing in he homework.  I don't know which way they'll go on difficulty.  Possibly easier as we will not have the assistance of any notes or T.A.'s.  I'm expecting a few things from truth tables, set theory and what not, but the meat of the exam should be proofs.
The main thing I need to work on for this exam is proofs involving sets.  I know the general idea behind it, I just need more practice.

Sec. 7, 5.4-5.5 Due February 3

For the most part I was able to understand existence proofs.  The one example that was slightly confusing to me was the one that stated, "The exists irrational numbers a and b such that a^b is rational."  Disproving statements seems easy enough.  It essentially seems as if we're doing normal proofs with the intent of showing something is not true rather than true.

Sec. 7, 5.2-5.3 Due February 1

The proof by contradiction seems straight forward enough.  I particularly enjoyed the illustrations that look as if it was the author who drew them.  The story problem that went with the pictures was slightly confusing though.  The main thing I need to get this down is to simply practice it.  The review of proof methods was also helpful.