Structure of Proof (Week 7 sLOG)

To the 7th week of class, we have started doing more proofs, mostly mathematical proofs. On Monday, we have learnt that even though we might be able to do a proof initially, though, we can still write all the structure of the proof. Pushing the proof inward, and usually by doing some mathematic algebra on the side, we can figure out the proof easily. On Wednesday, we have learnt that there are several inference rules that can apply when doing proofs, just as manipulation rules. Then have been introduced about different ‘steps’.

Introducing Proofs (Weeks 6 sLOG)

The result of the term test from last week has been announced, and I did fairly well in it. After the first term test, we have been learning about proofs in class; what is a proof, how to proof and the structure of proof. 

In this week’s lectures, I learnt that sometimes we don’t necessarily to understand to know how to proof a statement in the beginning. Instead, we can write down the assumptions and the conclusions first, just like doing negation of a statement, we push the statement inward, until we get to a point where it has to be explained. And this method helps me a lot for understanding and showing a proof. This weeks’ classes are mostly proofing some basic algebra and definition of limits, and they are rather easy to understands, so we can focus on the basic structure.

First Term Test (Week 5 sLOG)

This is the 5^th week of class and also the first term test of this course. Everything that has been introduced in this course is fairly simple. I have learn how to use Venn diagram to show sets that is true or not; basic logic symbols to represent a statement; implications, contrapositive, converse and negate different statements; and also the basic structure of a proof.

I redo all the tutorial problems and quiz, also the past term test from last year, feeling confident with the term test. After writing the term test, checking with the model answers, I believe I should have done fairly well in it.

This week’s lecture is mostly about proofs, we learn more about the structure, what statement has to be made before showing and proofs; how to do a proof with the given materials and by using implications, we prove something to be true, or by contradiction, we could proof something to be wrong.

Easing In (Week 4 sLOG)

In this week’s lectures, we have learnt how to use different ways to represent a statement, proving if one statement is equivalent to another statement. We have also talked about the basic structure of a proof. In tutorial, we discuss even more about proving statements and negate statements.

The assignment 1 for this course is also due the end of this week. Overall, the assignment is fairly easy. My partners and me can finish it without any problem, except question 5, which is not as clear as other questions. In this question, a statement is given, and we have to decide and explain if another statement implies the given statement, or the other way around. In the beginning, we could not decide which statement implies which, because some of them have very similar properties with the given statement and both can implies each other. After talking to the TA and discuss on our own, we found that the easier way to understand and answer the question is to use examples, by using a subset of another set, means the set implies the subset. Hopefully, the assignment will goes well, and so does the next coming midterm.

Week 3 sLOG

The third week of class, the instructor has introduced us more logical symbols, also basic computing logics, such as implication, conjunction, disjunction and negation. Overall, things that taught in class are fairly understandable, and with certain amount of practice, I believe I have a moderate understanding of the material. By using Venn diagram and truth tables, it really helps understanding the situation that might be more complicated. 

The biggest issue that I had is when translating from English to logical symbols. I never notice how unclear English is until I take this course. One simple sentence, with the word “unless”, placing in front of the sentence or the back of the sentence makes a totally different argument, so does “rather”. And also, in English, the word “or” means either one, but not both; however, in logic, it could means either one, or both, which makes more sense. Attending to tutorial helps me a lot if I have class materials that I do not understand, the tutorial questions basically covers most of the things we learn in class, and the TA explains the answers very clearly.

Week 1-2 sLOG

School has started for almost two weeks already, and topics that taught in class have started to get more into the main theme of the course. For the first week, the topics are mostly introductions into computing logics, such as what sets are, if a statement is correct or incorrect in a given circumstance, and Venn diagram. For the second week, more symbols and signs are introduced to represent certain logics, which is fairly simple for me, as I have taken MAT137, which is more like a proof course, and sings and symbols use in it are rather similar.

The main problem I had was with the Venn diagram, which I was not very familiar with. When the professor first introduce it on class, I thought it won’t be useful, since it can be easily represent by writing all the statements and facts out.  However, when I was working on the tutorial exercise #1 which was asking us to create certain Venn diagram to represent different statements, I found that it is not that simple. I do know that the square box represents everything in that case, the two circles represents two different sets, and the intersection between them are the common value(s) that they have, but I was not sure what are the sets, as for different cases, we have to assign to different sets. After going to the tutorial, I have a much better understanding for Venn diagram, and be able to produce them in the short quiz. Now when I do my other programming course (CSC148), I found Venn diagram to be extremely useful, as in it can clear many things up, such as which data are in common with others, which are not; it really helps with the thinking before actually doing the coding part.