March 27 week 9

I had some confusion about big-oh and big-omega, originally I thought in order to disprove  big-oh statement , you would have to prove big - omega. which is clearly wrong. Some function can be true in both big-oh and big-omega. it just simply means that the function is bounded above and below. I just realize from the assignment 3 question 1 and 2. I think proving polynomial statements are pretty easy, We just need to determined the highest-degree term in big-oh / big-omega . 

In big-oh , if the highest -degree term is greater or equal , then the statement is true , otherwise disprove it by negating the statement.  

In big-omega  ,is the opposite. if the highest - degree term  is smaller or equal , then the statement is true , otherwise disprove it by negating the statement.

However , I still have trouble understand non-polynomials statement and using limits , L'hopital  rule. to prove it.

March 20 week 8

I just want review the stuff during this week's tutorial .

So the definition of  O is    /Exist c in positive real number , /Exists b in natural number , /For all n in Natural number , n>=b => f(n) <= O(g(n))

During tutorial we have to proof  5n^4 - 3n^2 + 1 <= c(6n^5 - 4n^3 + 2n) , which is pretty obvious if we think in mathematical way, but we need to prove it. lets put the structure aside for now and focus on the actual prove.   

 

5n^4 - 3n^2 + 1 <= 5n^4 + 1 # when we remove negative term , we get bigger number 

                          <= 5n^4 + 1 # we want remove the 1 , so multiply  n^4 , thus n>= 1

                          <= 5n^4 + n^4

                          <= 6n^5 # we now multiply n again .

                         #now we start from the other side

c(6n^5 - 4n^3 + 2n) >= c(6n^5 - 4n^3) # we keep the negative term , so the number always smaller

                                >= c(6n^5 - 4n^5) # when the negative term gets bigger , the number itself gets smaller 

                                >= c(2n^5) # simplify 

                                >= 3(2n^5) # i pick c = 3.

                               >=6n^5

      #we we have 5n^4 - 3n^2 + 1 <= 6n^5 <= 3(6n^5 - 4n^3 + 2n)

      #implies 5n^4 - 3n^2 +1 <= 3(6n^5 - 4n^3 + 2n)   , c = 3 and b = 1 (since n>=1)

I'm not sure if I done this correctly until the tutorial solution is posted ,  for whoever reading my slog  please feel free to leave a comment to correct me.

also , http://csc165blog1.blogspot.ca/ this blog actually contains really helpful note .

11 March week 7

I still have lots misunderstanding and confusion about the recent lecture , however I rather kept it aside for now and focus on the upcoming midterm. Review all the proof example in lecture and tutorial , and probably do some previous test. When I check my assignment 2 solution , i did pretty well. The only problem might be question 6 , I understand the logic thinking behind it but couldn't express it in mathematical way. So this might be things I really need to be aware of.

March 3 week 6

 "A HUGE WAVE OF EXAMS IS APPROACHING", things are getting very busy and frustrating.
Unfortunately, I miss my tutorial last week due to dentist appointment , especially when I plan to ask few questions on the assignment.As we go deeper into the proofs , things start getting bit more challenging for me and I had some difficulty on the assignment too but I think I can manage it.  Since upcoming midterm would be mainly on proofs and the assignment likely going to worth more than the second midterm , its about time to put some hard works into these proofs.

P.S , I had some concerns about the test format. In last test, there is big chunk of mark that concentrate into  question 1. If i remember correctly , question 1 itself are worth more than 50% of the test . It seems unreasonable that if the second term use the similar  format which concentrate majority marks into one proof.      

Feb 25 ,week 5

haven't update my blog since the mid-term week plus the reading week, sorry about that. Anyway , i would like to talk about the result of my mid-term and the first assignment. I'm pretty happy with the test result , however , the assignment result just ruin my day. ( WHY !WHY BOTH RESULT AT THE SAME TIME). I think the major problem is that the combination of  "solution" part and the "explanation" part  in the assignment. In assignment question 4 , I only get half of the mark for correction solution because of my poor explanation , I should really work on how to express my thoughts to people who is reading my solution. Also  for questions like "symbol translate to English"  ,what I did is simply translate every symbol represent which clearly make no sense in English language.  the correct translation should be in simple and understandable  English.

Feb 6 , Week 4

We starting proofs this week , we learn how to construct the basic structure of a proof . Assume > conclude , then assume again >conclude , each assumption must match toward the its own conclusion. Eventually we will reach the "tricky" part in the middle of somewhere . Examples such as n^2 odd => n odd proof by contrapositive ,  n even => n^2 even , that sometime its easier to proof in the other direction. Basically, writing a proof is like solving math puzzle where you know the solution picture but you have find the pieces to match up.

Jan 31 Week 3

Not much to say during this week , rather than 3 upcoming test and 1 essay due all in NEXT WEEK!!!

little bit more about finding the negation or equivalent from statement and treat implication as disjunctions. it seems like better convert statements into symbolic form , then work these symbolic form as maths operator  which now can be easily solved.

Key note:

A => B  <=> \not A \or B