This week was pretty busy, first my partner and I had to hand in assignment 2 at the beginning of the week, and then I had to study for test 2. In addition to the tutorial on proofs, I really found assignment 2 helpful. Before we started a2 I had trouble with prove of limits, and I really had trouble using the definitions given to solve for proofs. My partner helped me understand many of the concepts needed to complete the proofs. One thing I found helpful was visualizing the floor of x. By drawing the graph I was able to understand claim 1.2 and 1.3 and understand which quantifier, and variable effects the other.
Graph of floor of x for anyone who doesn't know (hopefully everyone knows how to draw it though) :
Graph of floor of x for anyone who doesn't know (hopefully everyone knows how to draw it though) :
This is the graph for all numbers greater and equal to 0. It's not labelled, but hopefully you have an idea. The only reason why I made the graph was to just understand what delta was, what epsilon was, and what x, and w was according to the claim.
Next came the test, I didn't find too much time to study for the test, however I think I did decent. The first question was fairly simple, the second question was confusing. With the second question I was able to get the format and the negation quickly, which gave me more time to actually solve the proof. I am hoping that I will get part marks for my proof, but I guess I will just have to wait and see. The last question was fairly similar to one of the questions on the test.
As a result of the test, I only had two lectures. I was actually scared to go to Friday's lecture because I wasn't to comfortable with the last weeks content. But Friday's lecture went really well, I actually understood how to prove Big Oh of polynomials. The most important thing that I learned from the lecture was that when proving you have to keep the inequality consistent throughout the whole proof.
For instance this is part of the proof where we introduced a constant:
3n^2 + 2n + 5 <= 3n^2 + 2n^2 + 5 # 2n^2 >= 2n
3n^2 + 2n + 5 <= 3n^2 + 2n^2 + 5n^2 # 5n^2 >= 5
= 10n^2
= cn^2
Therefore c = 10 and this will be true if the break point was greater than 0. See how the inequalities are consistent, if it changed it will be very confusing.
The goal before this upcoming week is to review the week 8 content by going over the course notes, and by going over the tutorial questions. I also want to feel more comfortable with big Oh's and polynomials because were going to cover non-polynomials which I feel will be more difficult.
Next came the test, I didn't find too much time to study for the test, however I think I did decent. The first question was fairly simple, the second question was confusing. With the second question I was able to get the format and the negation quickly, which gave me more time to actually solve the proof. I am hoping that I will get part marks for my proof, but I guess I will just have to wait and see. The last question was fairly similar to one of the questions on the test.
As a result of the test, I only had two lectures. I was actually scared to go to Friday's lecture because I wasn't to comfortable with the last weeks content. But Friday's lecture went really well, I actually understood how to prove Big Oh of polynomials. The most important thing that I learned from the lecture was that when proving you have to keep the inequality consistent throughout the whole proof.
For instance this is part of the proof where we introduced a constant:
3n^2 + 2n + 5 <= 3n^2 + 2n^2 + 5 # 2n^2 >= 2n
3n^2 + 2n + 5 <= 3n^2 + 2n^2 + 5n^2 # 5n^2 >= 5
= 10n^2
= cn^2
Therefore c = 10 and this will be true if the break point was greater than 0. See how the inequalities are consistent, if it changed it will be very confusing.
The goal before this upcoming week is to review the week 8 content by going over the course notes, and by going over the tutorial questions. I also want to feel more comfortable with big Oh's and polynomials because were going to cover non-polynomials which I feel will be more difficult.