CSC165 WEEK11

This is the last week of this semester, and I want to make a summary of what I learned in CSC165.

First, we learned some basic elements related to the logic such as some logic symbols including quantifiers.Also we learned conjunction, disjunction, implication, which are useful to combine statements.

After that, we started to learn the proof, which I think is the most important part. We learned a lot of techniques of proofs, such as using contrapositive and contradiction. We also learned to prove a lot type of problems, such as the proof for existence, the proof about a sequence and the proof for Big-oh.

The last part is about halting problems and computability. This part seems not related to the previous parts, and also a bit confusing for me. So I think I should review the content of this part more carefully for the final exam.

In conclusion, I think CSC165 is a really good course for me since it improves my critical and logical thinking.And my professor and TA are both really kind and always answer my questions clearly.

CSC165 Week10

This week we learned the countability, and the content is a bit abstract and complicated : it requires some skills of math , which in particular include the ability to identify the 1-1 and onto functions. A typical example is X = {natural numbers} Y = {even natural numbers}, and we are required to prove |X| = |Y|. It seems impossible at the first sight, since I think Y should definitely contain less elements than X and is a subset of  X. However,after the lecture, I realized that the infinity of the elements' amount of both sets lead to the equality of them. More exactly, every element of X has a unique corresponding element in Y , which implies X and Y have the same size, which is infinity.

And we also learned a little about the induction. In fact, I learned it in MAT137 last year, and found it is an effective and logical way of proof. And I feel kind of disappointed as it's not included in the final exam.

Anyway, the final is approaching. And I hope I can do my best to get a satisfying grade.:)

CSC165 Week9

We got our test papers back this week and I found the outcome is actually not as bad as I thought before. It seems like I've acquired basic skills of proofs but maybe hadn't attached enough importance to some details such as writing comments and how to convert the given condition to essential steps of the proof step by step.

This week we finished the Chapter4 and started Chapter5. For Chapter4, we extended our proofs of big-O to general functions. The basic skill of this type question is the same, which is to pick the B first, then fund the c to make the right side an upper-bound. And after a week's practice, I started becoming familiar with the process of this kind proof. However, I sometimes I am not totally sure whether I should break a certain step into two to make sure others understand. I think I should find more standard examples so that I can makes sure.

CSC165 WEEK8

I felt really depressed after taking the CSC165 term test2. I have to admit that I didn't make sufficient preparation for it and ignored some details of the concept tested. First, we are not required to write the commentcof every step in proofs in quizzes, I actually didn't realize we had to write comments in this test until few minutes before the test. Secondly, I didn't read the sample answers of assignment#2 and the past test carefully. I thought I'd already obtained them, but I didn't in fact, especially those "floor" problems. More exactly, I always feel that I need to use some conclusions about the floor to prove the problem and I don't know whether those conclusions should be proved first and how to prove them.( For example, the floor of an integer is equal to itself. )I think I really need to track back the recent concept carefully to understand them better.

This week’s lecture looks harder than before.We learned prove big-oh using limit techniques. It requires technique to pick c properly, which is the core of solving these problems. I know we should fix a B first, then find some polynomials which are greater than the left-side function in problems and less than the c times the function in the bracket of big-oh so that we find the c which connect the two bounds. But it's still difficult to find c sometimes in practice. I think I should practice more.

CSC165 WEEK7

This week we recapped the formal definitions of asymptotic notations O(f(n)) and Ω( f(n) ).I think they are not difficulty to understand, and the core of solving related proofs is to find the C and B(breakpoint)so that we can get the upper or lower bound. But I am wondering that why we paid so much attention to them. I know we can use them to analyse the running time of the programming code, but I think we don't care to much about the method of calculation of the running time in csc165, since I remember it is required in CSC108. 

And we are gonna take a test again next week! OMG I just finished my midterms on this Friday! Hope it won't be too challenging.

CSC165 WEEK6

We finished the study of proofs and started to learn algorithm analysis this week.  
 
By taking this week's lecture , I  learned that sometimes we need to discuss different situations in a problem and prove the problem by cases.For example, we need to assume a number n as both odd and even numbers, which splits the proof into two cases. Just as many math problems, we need to consider all possible cases to find the result. And the professor gave us an extreme example of proof by cases: the four colour theorem, which states that four colours are enough to colour any map, so that no two adjacent regions will have same colour. Although it seems not difficult to prove since the four colour map shows the feature visibly, it actually takes a computer 1000 hours to solve it and all counter-example of proof  can be at least 1936 cases! And this makes me understand that we need to be really careful to find all cases in a proof. And I feel fortunate that most  problems in csc165 only  require up to 3 cases.

The professor also showed us a ' funny' video titled as "the right emotion about finding a proof'. The man who found a difficult proof felt so agitated and can't help crying. It looks funny, but I understood we should enjoy the sense of achievement of finding out a proof so that we can take those proof problems seriously.

CSC165H1 Week5

We got our term test paper back this week and the average score is so high which really surprised me! Although the test is not very hard , I still have a strong sense of competition, feeling  hat everybody works hard in CSC165! I think this feeling can also encourage me to work harder and do better in next exam.

This week we learned more about proofs. Just as what I guessed last week, these questions look like mathematical problems and require us to understand those functions completely. We even learned the proof of limits！Actually I found they are not as difficult as I thought after listening the lecture, however I still feel chaotic when I tried to prove some questions. A friend who learned CSC165 last semester told me more practice is needed to improve the ability of proof. But I am so busy recently since I have two tests next week and another two the week after next week .(TOT) So I do hope next lecture won't be too hard and I can understand those proofs better after it.