CSC165H1 SLOG3 BY MINGYU LIU

Mingyu Liu @ CSC165H1 SLOG3

This is the third time of writing SLOGs for CSC165, in this week's lecture, we have finished talking about the language of MATH which is called 'Bi-implication'. Initially, professor posts some slides in order to review the former lecture which is a means to place a foundation for further lecture as well as recall my memories. For example, P => Q is equivalent to -/P v Q and -/(P => Q) is equivalent to P ^ -/Q. I believe this part provides me a great tip which I can be used for exercises in the lecture after. Then our professor talks about bi-implication which can be utilized to translate from conjunction of two disjunctions and also from disjunction to conjunction. The method of doing that requires mathematical ways which are distributive way. After bi-implication, the lecture also covers the negation of bi-implication which is a little difficult than bi-implication because it requires 'De Morgan's law'; therefore, I believe this part is what I grasp well in this week's lecture.
Moreover, transitivity and proof which I believe to be not that difficult. For example, the transitivity of this expression (P(x) => Q(x) ^ (Q(x) => R(x)) is P(x) => R(x). the reason why it is not difficult, because professor uses a visual way to teach us the definition of transitivity which means that if P implies Q and Q implies R, then Q must include P and R must include Q; therefore, R includes P for sure. For the proof part, professor teaches us about how to find the chain with ^ and v. For example, if there are no particular features in the expression, you will just have to start from downward to upward; otherwise, you can start from upward.
The interesting part of this week's lecture is that the professor makes a small activity of lecture which requires a group of three people and thinks the problem together. This is absolutely interesting because it improves the interaction between the lecture and students.
In conclusion, we have finished the language of math in this week's lecture and the difficult part which I encounter is mixed quantifiers. According to the professor, the language of math is not only for using symbols but understanding and expressing in a logical way. Finally, I hope my first test will be good.

Third slog
Mingyu Liu

CSC165H1 SLOG2 BY MINGYU LIU

Mingyu Liu @ CSC165H1 SLOG2

In the lecture of this week, Professor Danny Heap continues to teach us about language of math which mainly concentrates on conjunction, disjunction, negation and Demorgan's laws. i will start with the first topic which the Professor has covered in the lecture. Conjunction is news to me; therefore, my primary aim is to understand it by knowing its definition which is combining two statements by claiming they are both true. For instance, there are for two statements which are both true. The first statement says that car 'X' is red and the second statement has a saying which is car 'X' is a Ferrari; therefore, the conjunction of these two statements is called Car 'X' is a Ferrari and red. This is a case which is told by using human language, but using mathematical language is far more different to express. in human language,  we use 'and' to combine two statements while we use symbol '^' to combine statements in Math. This means that 'statement 1' and 'statement 2' is the same as 'statement 1' ^ 'statement 2'.

After the introduction of conjunction, professor also talks about disjunction which we use 'v' to describe it in Math and 'or' in human language. i understand it in a different way which is that treating disjunction as a set of 'union'. For example, 'Statement 1' V 'Statement 2' equals to 'Statement 1' U 'Statement 2'. Negation is what I grasp well in this week's lecture which using 'not' and the symbol '-\' to prove statements that are negative. For example,'Not all red cars are Ferrari'can be written in this way: '-\(Axec,R(x)=>F(x)).

Professor also teaches us some useful tips which are changing 'not all... ' In 'There is one that is not... 'and 'there does not exist... 'to 'all...are not'. These tips are useful because we can understand what the question requires us to do both quickly and efficiently; therefore, the way of solving the problem is just change the word simply.

There are no difficulties of this week's lecture, but the exercise of TUT is a little bit difficult for me. For instance, question number two of exercise which makes me encounter some problems which is that I initially write all the answers to get true, but the correct answers are different. After the teaching of TA, I find out during TUT.

In conclusion,lectures and tutorials of this week continue the topic of how to change human language into mathematical expression. Professor does superb work to help me understand the lecture and TA  helps me to resolve the problems of exercise with patience. Next week, I will continue to collaborate hard in both lecture and tutorial.

Second slog
Mingyu Liu

CSC165H1 SLOG1 BY MINGYU LIU

Mingyu Liu @ CSC165H1 SLOG1

I will start at something I have leaned something new in this week's lectures.
Professor begins with visualization with Venn Diagram contains two essential symbols which are "X" and "O". The meaning of first symbol "X" is that there is no element in this area, for instance, if there is no element in the intersection area of "P" and "Q", "X" is what you need to indicate this situation. The second symbol "O" contains meaning which is there are some elements exist in somewhere, for example, if there has some elements in the intersection area of "P" and "Q", writing "O" in the intersection area indicates there are elements in the intersection area.

Predicate and implication is what I grasp well in this week's course. Predicate simply indicates that you can use the easy way to write "X" is in the set "L" into "L(X)" which is exactly the same. Moreover, "L(X)" without specifying "X" is an open sentence which means that "X" can be substituted for specifying the "X". Implication contains assumption and conclusion which can be submitted in "P=>Q". The most important thing of implication is that assumption requires conclusion, but the assumption does not cause conclusion.

The most difficult part in the lecture of Tuesday is statement and sentences. The reason why it is difficult because the difference between sentences and statement is confusing. For example, A statement is a sentence but it is a sentence that is not open. However, sentence is not always a statement. Due to the confusion, when I am facing exercises, I cannot really determine which one is the sentence and statement.To solve this problem, I will do some exercises and ask professor if necessary.

The teaching style is exactly what i enjoy the most during this week's lecture, because instead of using tedious definition to teach students, professor replaces traditional course material by using an idiom which is called "Sometimes there are more than one way, even in math. Some ways are more commonly used than others." In my opinion, students are more attracted by interesting instead of boring teaching style. Professor uses idiom which to make students focus on course; therefore, students grasp knowledge better in course when they are interested in course.

When I was doing my exercises this week, I first confused about where should I put each letter which is A, T, P in the correct posion into Venn Diagram. The tutorial actually is really helpful which helps me to understand my question. For example, A be the set of all possible python programs which mean that A indicates the rectangle of the Venn Diagram.

In conclusion, lectures and tutorials of this week were superb experience which taught me how to utilize a mathematical expression to transform human language into simple mathematical language, and also, use Venn Diagram to verify statements. Difficulties did occur in this week which are the differences between statements and sentences. Overall, CSC165 is an interesting course which definitely deserves time to study hard.

My very first Blog
Mingyu Liu