CSC165H1--WEEK12

  Time is passing unbelievably fast, I can still remember the first day I had CSC165 class, but now it comes to the end of the term. This week, we had our last lecture. We talked about some proof on computability and learned about induction! Although I had learn induction from my math lectures, I still feel excited to hear that in computer science course. After a small lecture on new concepts, we reviewed for final exam. To be more specific, there is going to be around 9-10 questions no the exam, 5 of them is going to be proof question and the rest of them might be logic and other concepts.
  I just finished assignment #3 and I think some of the questions are really hard. For instance, before I went to Larry's lecture, I did not know how to solve question #3 because I don't know how to do with the limit of 0. In class, we only learned infinity. Therefore, what I firstly did was change the order of denominator and the numerator, so that instead of having 30/=0 I will get /30=, and this result would be similar to what we learned in class and I disprove the statement by exchanging the direction of previous equation. Indeed, I think this method although seems not general, it still can take a fair proof. However, according to the hint of y professor, I understood that I can only change the definition of limit from >=c to <c to represent that limit of an equation is 0. This way of thinking the question is pretty inspiring to me and it is clearer and more direct than what I did before. Therefore, I learn how to proof a limit of 0 and I believe it would be greatly helpful during the test and after courses' learning.
  This week, we also had our last tutorial and we talked about proof of Big-Oh and Omega proofs. So far, I find computer science tutorial is the most helpful and effective tutorial I have ever had. My TA explained everything really well and this helps me a lot in my learning. Last quiz, I made a math error and this made my whole proof no sense. When I was thinking about inequality transitivity I always got lost in the process, and I sometimes wrote steps that are wrong. I found this king of mistakes happens a lot during quiz and when I did assignment on my own. Therefore, I think I need to review more for the proof question and try my best to avoid math mistakes again.
  My assignment working group is going to have a meeting on Monday. Hope we can do better on this assignment and we will try our best.
  CSC165 is a great and challenging course, it is full of fun. I really like this course!

CSC165H1--WEEK11

  Due to fall break, we do not have lecture and tutorial this week. However, I still spend some time going through notes and assignment #3. Most of questions in assignment 3 are about proving the growing speed. The first two proofs are very similar to what we have done in class and starting from question #3, it is getting really confused. The hint says we need to used the concept in proving, but I don't know how to add limit. Do I just pick a random number and limits x to that equation. I believe I need further discussion with my group members.
  Unfortunately, I did not know what the symbol of F is yet. Because I did not learn that far. I think I need to speed up a little bit.
  As the course website and Markus are just ready for using, I may start my learning now.
  I have no idea what our final exam will be like, probably it will contain all the concepts we learned so far. Starting from next week, I am going to start my review for CSC165 and hope I could get a better and satisfying mark in the final test, Of course, I will need some assistance from my assignment group.
  I am hoping assignment #2 can be posted this week, because I think my group was not dining our best in this one. Need to put more effort on next one indeed!

CSC165H1--WEEK10

  This week we got our teats back. I felt really regretted that I forgot to bring a cheat sheet during the test, so I made many foolish small mistakes. Overall, I am quite satisfied with my second term test because I did my best without the help of cheat sheet and my answers were okay. The happiest point is that I finally exceed the average mark in this course! For me, I really think it is a hard course and I absolutely no background knowledge on computer science, at least, this proves that a good result comes from hard work.

  About the course this week, quite disappointing to hear, I think I am really behind the pace of teaching! I feel quite confusing with this week's lecture and the process of proving. To be more specific, I have problem reading computer code! Concepts about "return" and "loop" totally makes no sense. I just made an appointment with my assignment working group members, I want to ask them for help and maybe I would figure out something together with them. 

  As I mentioned previously, I did not understand how to read lines of computer code and this resulted in a 0 in my last quiz! This is so tragic. i can understand the tutorial problem pretty well if the question asks us to find the total number of loops we need for different inputs. However, the quiz problem was quite different and I thought in a total wrong direction. First, I don't know how to say return, I thought if an input does not satisfies the condition then the return at this point is false, otherwise is true. However, this is not correct. If the input is a number, according to the loop, the output should also be a loop. Increasingly, the number that makes the condition unsatisfied is the number returned. I just understood that and I will remember it for sure.

  The direct proof of a polynomial grows no faster than another polynomial is not very hard. Basically, we need to change the form of each side and try various ways to make then connected. However, the backward proof such as the negation of O is really hard, because we need to include more generic numbers in our statement. However, I feel like the proofs of kind of O related are although sometimes difficult, it is still within the capability of understanding.

  Next week of school is going to be relatively relaxing in comparison with previous week. I feel like I need to make time more valuable and work more on computer science and proving problems.

CSC165H1--WEEK9

  Time is passing so fast and it is the ninth week of my first university term. We had our second term test this week! wow! The test is about proof and there was only three proof questions on the test. Overall, I think I was doing pretty well on this test because I felt confident to my proof when I was writing it.
  However, there is only one small problem I did not understand throughout the test. The first proof has an antecedent to something like m=5j+2. Because there is a existence antecedence, therefore, I used another number k to replace j, and using k throughout my proof and let k=j in the end. This is what I remembered my TA told us that we needed to make assumption on what we assume. However, from the sample solution for our assignment, it does not give this kind of assumption. Now, I am feeling pretty confused and I do not know how TA will mark this proof.
  In addition to this, we had another proof based on the concept of "when y is bigger or equal to c and y is also smaller and equal to c" than it implies y=c. The last proof question is based on this concept and all I have to do is to make some changes in the definition to get the result. I found it was not very hard and I wrote as many comment as I could during the test. Hope it will help me explain my steps
well. Overall, I found this test was not very hard and I think I can do well, praying, praying, praying.
  Assignent group working is really helping e to understand the concept well, I always learn from others and I understand how to proof existence with the help of my group members.
  This week's lecture if based on the proof of O. Personally, I found this kind of proof harder the before, or maybe I should say I still do not have a clear understanding on the concepts and I should work on them later on.
  The tutorial problem this week was really hard and I barely understood what the question is asking me to do even even after my TA explained it. I kind of feel confused on loops and how it returns. Similarly, the quiz was so hard for me and I felt I was somehow behind the course schedule in comparison to others.
  I need to work harder in week and go through all the in-class problem be my self. I have any question, I will ask my TA or my assignment group members.

CSC165H1---WEEK8

  I have been working on my assignment throughout this whole week. Some of the questions in the assignment are easy because we have done several example in the class and tutorial, such as the problem asks us to prove n=5k=2 and n^2=5j+4. i am pretty confident with these direct proofs. However, problem #1.2 and #1.3 pre ally confused me! The only difference between the claims is the "existence" and "for all' symbol. I think I need to work on these problems with my group members in next week.
  In the lecture of this week, we talked about the formal definition of O and Ω. O means the set of functions which grow no faster than N^2. In addition, we also learned insertion sort and I think this is a little confusing to me. Especially, when it is hard to combine the concept of insertion with O. After this, we learned about maximum slice using the symbol of input L. The concept is pretty easy but I feel uncomfortable to use it within the proof.
  In addition to this, about this week's tutorial, we got our last quiz back which I think I did pretty well. However, I still made some careless mistakes and I need to be careful next time. The tutorial problems of this week was pretty hard, but I can understand them after my TA explained them to me.
To be more specific, the first problem is every similar to what we did last week. There is one problem I found pretty interesting is the usage of sub-cases to discuss the possibility of 0. Indeed, I have never seen this kind of discussion before. During the tutorial I learned how to prove a existential case. All I have to do was to give an example and prove the previous cal aim wrong through this evidence. For instance, I just need to take x=1 and y=1 to prove the addition of square root of x and y is not equivalent to the square root of the addition of x and y.  In addition to this, I believe the contrapositive proof is also an effective way to make proof.
  We are going to have another midterm next week and the test will be based on proof. I hope I could do better in this test than the previous one. I will review past tests and assignment to prepared for this test.

CSC165H1--WEEK7

  In this week's lecture, we talked about more on proof and introduced a new concept of introduction rules. These rules are new to me, indeed.
  Until now, I am feeling relatively confident in writing proof structure, however, I still think the hardest part is to actually find a way to complete the proof. Sometime, I could not think of that particular way and got confused or massy during the process of proof. For example, when my professor talked about the proof of when n=6, T(n^2)=T(n). If change this into a mathematical proof, I may be able to do it because I can involve simple calculation. When I first saw this question, I found it was not so hard and I had the idea putting 6 into the assumption. The biggest problem is that I did know where to start with the prove. It is always a hard proceed when I had to think about setting a n' or some other number to help me with the proof. Well, I finally understood the proof process and it seemed pretty obvious to me.

  The tutorial problems of this week is very hard, I spent a plenty of time on it but I could not figure any of them. Again, I was stuck in setting numbers like n' or k'.
  This week's tutorial was good and I understood concept throughly.  The first question was not so hard after my TA explained that. The main point it to choose z=x such that it can stratify the given condition, in addition, it is also important to suppose a z' in stead of z in the first place. What's more, the second question was relatively hard because I did not thought of "closure under multiplication and addition" although I remembered I learned this when I learned linear algebra transformation this year. Still, I am pretty slow when writing the proof question. One because of I can not come up with a thorough process right after I looked at the question and secondly, I may need to practice more to become more familiar with the proving method and structure.
  I made some small mistakes in this week's quiz because I did not understand the process totally. I would review these stuff this weekend and start working on our second assignment problems.

CSC165H1--WEEK6

  We got our tests back on this Tuesday. I can believe the average mark is so high, 83%! My mark, in comparison, is not good and I think I need to work harder from now on. I went through the test, the errors are basically from unclear understanding of the concept and stupid mistakes. For instance, I have a unclear understanding of the output of python and I can not distinguish the difference between false and counterexample. Therefore, I got all the determination of python right but some counterexamples wrong. I might ask my group member for help next time when I met them. Overall, I am not satisfied with this test result, there are a lot for me to improve such as doing assignment on my own instead of giving it to my group members, understanding the concepts and asking questions.
  The lecture of this week we talked about floor and its definition. The definition is pretty long and hard to remember. Because we did not have tutorial this week, I did not get a chance to do problems associated with proof methods. I can understand the proof process when my professor do the question step by step, however, when I try to do questions on my own, I found it is so hard to start the proving process. This the actually the biggest problem I usually face when I did proof questions, I did not where to start and it is hard to find a link between hypothesis and conclusion.
  For instance, the first proof question on floor the professor proved the contradiction with definition #3 of floor to get the conclusion. When I first looked at the example, I had no idea of what to do. However, following the steps my professor took, first we need to compare the given condition with definition of floor, trying to find similarity and difference. Then we need to do a scratch work which can lead us to the result (this is the most difficult one!). We move minus 1 to the left side and this becomes plus 1 and this corresponds to definition #3. Then we let X belongs to Z and change the original element in the definition, thus we can disprove the failure of its negation.
  About the concept of proof, I think I need to do more problems and conclude some usual proving method, thus I can be more adept in solving questions.

CSC165H1--WEEK 5

  This is the fifth week of my fall term study and the most importantly, we had our first CSC165 term test on this Tuesday evening! To be honest, I felt really nervous because some questions from class and assignment are confused my a lot. It is normal that I spent over one hour to figure out or even understand the question. 
  I prepared a lot for this test as I reviewed in class ppt, tutorial questions, assignment past tests and quizzes. Fortunately, the test was not as hard as I thought, although I had a little problem with answer the second and last question. Overall, I felt pretty stratified of what I had accomplished and I will continue trying my best on this course. One funning thing was that I grew lazy when solving question no.4 on the assignment and let my group member dove for that. Unfortunately, the same question appeared on the test! It was so SAD! I promise I will compete and understand all of the questions from the assignment next time. So, I saw this misfortune as a lesson to myself.
  Because of test, this week's lesson was pretty short, we basically went though some method of proof such as proving a statement to be truth be proving its contrapositive to be false, backward proof and direct proof. The most interesting question was the proving that when boxes and balls problem. First we I looked at the question felt confused and somehow it doubt the validity of the statement. It was so wise to write the contrapositive statement first and them continuers with this assumption to reach a conflict statement. It is admittedly that this process of proof seemed awkward to me sometime and I might need to re-write the proof again and again to really understand its meaning. However, everything needs practice, I believe I can become more adept after more classes and exercises.
  About this week's tutorial, we learned the structure of proof and it was pretty easy. I can remember and understand pretty well. I did really bad on last week's quiz because I did not know I need to remember those implication, conjunction laws! Thus, when I wrote the quiz last week I had totally no idea on what I needed to do. Next time, I will do what professor asks m to do and be fully prepared to other coming quiz.

  Looking forward to next week's CSC165 class.

CSC165H1-WEEK 4

Time is pasting so fast and we are going to have a test next week, it is really stressful.

This week we learned about bi-implication, transitivity, mixed quantifiers and prove. In my opinion, they are all pretty hard concepts, especially bi-implication and prove. I don't quite understand the transformation for implication to conjunction because I miss first part of my class. However, later my classmate explained it to me and I can understand them pretty well now.

About proving skills, I kind of felt confusing because I usually don't know where to start y proof. Some examples need us to write the proof directly but some of them need backward proof. I believe this requires exercise and more thinking.

The tutorial of this week was pretty hard for mw and I felt I was left behind although I attend every lecture. The equations from not 2.17 are so many and I never see them before, they are somehow hard to memorise and apply. Quiz problem of this week was not hard, but I still can do it, I am feeling not very good about that.

Indeed, I do want to have more exercise for CSC165, however, except for past exams and tests, I can't find any. The real problem was that I usually can understand how the problem is solved after TA or professor explained that, but when it comes to myself I often found hard to solve problems. Perhaps, I need to develop a deeper understanding of concepts and be prepared about course concepts.

On Tuesday, we are gong to have an term test and I am feeling afraid because I have no ides how hard those problems can be or maybe I might fail to otherwise. I will try my best to do this test.

CSC165H1--WEEK 3

  This week of school has been really busy and there will be lots of tests and assignments coming up.

  On Tuesday evening's lecture, we learned about conjunction, disjunction, negation and implication. As I went late for class for around 10 minutes, I did not catch professor's explanation on conjunction. At first I thought conjunction indicates at least one of the predicates is true. However, after my professor explained the example of red cars conjunct with Ferrari, I understood that junction means co-exist and in this case, it means a red Ferrari car. It can be summarised that conjunction is the intersection of two set which the result satisfies both condition in each set.

  The first three examples of negation is pretty easy for me. However, later ones are somehow confusing. I don't understand the last question why we need to change all symbols in previous statement to form negation, is it okay if we remain one unchanged. However, I believe I need to ask my TA for explanation on this week's tutorial.

  After this week's tutorial, I began to grow a feeling of anxiety because questions are really really hard for me to think on my own and to come up with right answer. For example, question (e) asks us to rewrite "some courses have several prerequisites" symbolically. I was really confused because I though the word "several" means infinite cases such as three, four, thirty and so on. However, this is a wrong way to understand this question, instead, what we need to write is a statement which can satisfy the minimum given condition. Therefore, we only need to indicate two prerequisites here. WOW, it was really hard and I need to get my brain work more effectively now.

  There are many questions that are really hard, however, at least I can understand them after TA's explanation. But I still think I need more practise and sometimes, I am slow in following my TA's teaching speed. The quiz I did last week was not good because I did not consider the condition of empty set, this is the point that I need to improve.

  Fortunately, I found a partner to work on assignment together. Actually, I can't image if I do assignment all by myself, it must be a disaster. At this point, I suddenly realise CSC165 is really a hard course and I need to put in more effort in my study.

CSC165H1 --Week 1-2

  It is great to be a first-year student at the University of Toronto. My first week of study had been very busy, but I feel delightful to learn many new knowledge. I chose CSC165H1, Mathematical Expression and Reasoning for Computer Science, because it interests me a lot and I want to challenge myself with its logic. In fact, the first class had proved that I made a right decision: this course is SO AMAZING!

  For the introductory section, we basically talked about the course outline, marking scheme, tutorial and how to be successful. There was a lot of information and professor’s joke always made us laugh. Then, we learnt about precision and problem-solving skills. Particularly, the question on inferring teenagers’ ages was the most interesting one. When I first read the question, I only got the product of 3 ages was 36. However, this point can not lead to a unique solution because other combinations exist. If you re-read the question, you might find other hiding information, such as “the eldest plays the piano” implies there can’t have two eldest ages at a time and “the sum of their ages can not infer about the result” implies that the sum is not unique. Therefore, with these information, it is easy to infer the answer is 9,2,2. This is indeed interesting, isn’t it?
   Increasingly, this week we learned about quantifiers, Venn Diagram, sets, predicates and implications. As a student majored in mathematics, it is fortunate for me because I learned concepts about sets and Venn Diagram before. However, in my opinion, implication is the most difficult concept because it is somehow abstract. For example, the sentence “there are no rights without responsibilities”, I firstly thought it meant: in order to gain rights, we must make the assumption of having responsibility. However, this was wrong. If we have responsibilities, it does not 100% implies about having rights. Conversely, if we assume to have rights as a condition then responsibility becomes a requirement. I believe I need to exercise and think more on these questions.
  It is important to be prepared for class because sometimes, the teaching speed is a little bit fast. For instance, I did not know where to find the lecture PPT online when I attended my first class and this made the whole lecture hard. I always got lost in professor's speaking. However, starting with the second week, I read the PPT before class and this made a lot easier for me to understand the course. Therefore, It is always important to keep the habit of being prepared for class.

  In addition, the tutorial class went pretty well, it is a small class with around 20 students. And each one of us has a chance to ask questions. Firstly, I didn't know how to convert language into mathematical expression for the question#1 on my assignment, because I didn't know how to deal with 2 elements in one expression. However, TA explained the answer very well and now I am confident in doing these kind of questions. I really like tutorial learning.

  Overall, CSC165H1 of this week was full of fun and I am really looking forward to the upcoming classes.