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.