Week 7
This week we talked more on proofs and disproofs, and big-Oh, this is the first time I have seen this, and it is very interesting to me. I am also taking CSC148, and it is interesting to think about programs running time. Before I have never thought about running time, as the programs we make/study is relatively simple for the computer that we don't see a huge difference in running time.
However, in CSC148 we just had to make a program that simulates a course registration system, and it got me to think that it is probably not easy to write simple codes that does the job and does it quickly, as in the real world, the system needs to handle hundreds of thousands of applications and other things.
For the materials on proofs, I think I am getting better at noticing the relationships and implications, so I will just need to work more on getting the structure right.
Week 8
This week we talked more on big Oh and Omega. I think I understand the concept pretty well now, and I need to work more on how to reduce/enlarge each function so that I can pick a c in the middle. I am having a little trouble realizing myself of which part I should give up.
Also, I am having a little problem with counting the number of steps a program take, I think it's not intuitively obvious how many steps a function take, and sometimes my reasoning is actually off from the correct answer, so I think I will need to give it more attention.
Sunday 30 November 2014
Week 5+6
Week 5:
This week we talked about contradictions, implications, and existence. I am pretty confident with the proofs of existence. I think the most important thing is finding a pattern in the statement given to you, and find one example that works/doesn't work.
For implications, I think I can relate it more to the calculus I am studying as it involves a lot of assuming the negation is true, and seeing what kind of bizarre thing will happen, so I will continue using this method.
Other than that I think I need to continue working on being more comfortable with using symbols and manipulating them around brackets.
Week 6
This week we talked about floors and more proof structure, and limits.
For floors, I think I will need to work more on getting a hold with the definitions and using them in my proofs. Other than that, I think I will also look more into my math books for epsilon-delta proofs as they are similar to what we are asked here, also I think I will try writing out more empty proof structures as I am sometimes too free in writing down my proofs.
I think the main focus for me will be getting more confident with assume, let, and then. As long as I am fluent in using them I think I will be better at writing proofs.
This week we talked about contradictions, implications, and existence. I am pretty confident with the proofs of existence. I think the most important thing is finding a pattern in the statement given to you, and find one example that works/doesn't work.
For implications, I think I can relate it more to the calculus I am studying as it involves a lot of assuming the negation is true, and seeing what kind of bizarre thing will happen, so I will continue using this method.
Other than that I think I need to continue working on being more comfortable with using symbols and manipulating them around brackets.
Week 6
This week we talked about floors and more proof structure, and limits.
For floors, I think I will need to work more on getting a hold with the definitions and using them in my proofs. Other than that, I think I will also look more into my math books for epsilon-delta proofs as they are similar to what we are asked here, also I think I will try writing out more empty proof structures as I am sometimes too free in writing down my proofs.
I think the main focus for me will be getting more confident with assume, let, and then. As long as I am fluent in using them I think I will be better at writing proofs.
Thursday 9 October 2014
Week 4
This week we talked more about logics, and the mid term is coming up next week.
At first I was a little confused with how we got from P <--> Q to not P or Q. But from looking at the slides a few times I now get it and are comfortable with the derivations in them. The reference to epsilon-delta proofs was quite surprising as I was doing them in both my first year and mat237 now.
The proof section was also pretty clear to me, I will work more on bi-implications for the mid term. Lastly, I found that the hanging paradox that professor told us might have some flaw in its logic, but I don't know quite exactly which part is wrong.
At first I was a little confused with how we got from P <--> Q to not P or Q. But from looking at the slides a few times I now get it and are comfortable with the derivations in them. The reference to epsilon-delta proofs was quite surprising as I was doing them in both my first year and mat237 now.
The proof section was also pretty clear to me, I will work more on bi-implications for the mid term. Lastly, I found that the hanging paradox that professor told us might have some flaw in its logic, but I don't know quite exactly which part is wrong.
Monday 29 September 2014
week 3
This week we talked more about math languages. We also had a very interesting discussion about the relationships of the English language and the mathematical ways of interpreting a sentences in our tutorial.
The discussion in our tutorial was mostly on the cause and effect and how we interpret them. I remember the other peers were talking about an example of "all astronauts likes to eat oranges, then it must be that eating oranges is a cause for them being astronauts". There were confusions first, but at the end I think we came to an agreement that eating oranges is only one of the factor that they are astronauts, but not necessarily the determining factor.
As for me, I am having a little trouble with the negation part of the lecture. Mainly because if you bracket up a sentences full of symbols, and put a negation sign in the front, it will take me some time to switch up all the signs, so I am going to practice more of that and hopefully in assignment 1 as well.
The discussion in our tutorial was mostly on the cause and effect and how we interpret them. I remember the other peers were talking about an example of "all astronauts likes to eat oranges, then it must be that eating oranges is a cause for them being astronauts". There were confusions first, but at the end I think we came to an agreement that eating oranges is only one of the factor that they are astronauts, but not necessarily the determining factor.
As for me, I am having a little trouble with the negation part of the lecture. Mainly because if you bracket up a sentences full of symbols, and put a negation sign in the front, it will take me some time to switch up all the signs, so I am going to practice more of that and hopefully in assignment 1 as well.
Thursday 18 September 2014
Week 1 & 2
Week 1
This week we talked about some introduction things and why we need mathematical language to do well in CSC 165.
Last year I took Danny's CSC 104 in the fall and I had a very good impression on his teaching style! I hoped to get him this year but unfortunately my timetable did not work out. However, I think Larry's teaching style is just as good so far, his example is very clear and easy to understand. I was particularly impressed with his approach to lead us find the kids' age, we first analyzed the statements given and took out some unneeded parts and finally came to a result.
Since I have some backgrounds on math last year I feel pretty confident with the materials covered so far.
Week 2
This week we mostly focused on the 'for all' and 'there exists' symbols. The methods of using the venn diagram to understand them is kind of new to me, but after a while I think I can fill them out with 'X', 'O'.
We also worked on some sets symbols, and statements vs. sentences.
I am still a having a little problems with statements vs. sentences, but I am getting better at differentiating between them. My understanding so far is that you can always give a statement True/False, but for sentences you can't?
Implications and equivalences were good for me, I fell pretty confident about them.
This week we talked about some introduction things and why we need mathematical language to do well in CSC 165.
Last year I took Danny's CSC 104 in the fall and I had a very good impression on his teaching style! I hoped to get him this year but unfortunately my timetable did not work out. However, I think Larry's teaching style is just as good so far, his example is very clear and easy to understand. I was particularly impressed with his approach to lead us find the kids' age, we first analyzed the statements given and took out some unneeded parts and finally came to a result.
Since I have some backgrounds on math last year I feel pretty confident with the materials covered so far.
Week 2
This week we mostly focused on the 'for all' and 'there exists' symbols. The methods of using the venn diagram to understand them is kind of new to me, but after a while I think I can fill them out with 'X', 'O'.
We also worked on some sets symbols, and statements vs. sentences.
I am still a having a little problems with statements vs. sentences, but I am getting better at differentiating between them. My understanding so far is that you can always give a statement True/False, but for sentences you can't?
Implications and equivalences were good for me, I fell pretty confident about them.
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