Slog 9

In this week’s lecture, we did several proves about the O(n^2) and Ω(n^2). First we did the prove about 3n^2 + 2n ∈ O(n^2). It was easy after seeing the answer; however the second question was really hard that I did not get it until I read the answer for several times. The second question is 7n^6 -5n^4 +2n^3∈ O(6n^8-4n^5+n^2). We need to make both (7n^6 -5n^4 +2n^3) and (6n^8-4n^5+n^2) as big as possible. So the value of c should be 4.5.The next type of question about disprove. The example is n^3∉O(3n^2). 

The next part of the lecture is about non-polynomials. We can use the limit function to solve non-polynomials. It totally confused. I hope I could do better in the next lecture.

Slog week8

The assignment 2 is difficult, and my group are confused about 1.2 and 1.3. I was really disappointed. In the beginning of the lecture the prof told us that there going to a term-exam on next Tuesday, and I was more disappointed. However, the prof gave us some hint about the assignment 2, and I felt a little bit confident about solving 1.2 and 1.3.

In this week’s lecture, I learnt about recap: O and Ω. O is the curve below the cn^2 after the break point; Ω is the curve above the cn^2 after the break point. The next part of the lecture is about algorithm.The algorithm is about the programming and the running time. The prof showed us some examples about the algorithm of the inserting sort.

Week 6

Slog Week 6 

In this week’s lecture, we learned about prove again. The prof introduced us the concept of floor of X. The floor of x means the largest integer that <= x. And the floor of x is not a variable; it is a function. After several steps of proving, we got the definition of floor of x: 

y is an integer

y is less than or equal to x

among all the integers that are <=x, y is the largest one,

The prof gave us a question: we need to prove for all x belongs to R, the floor of x is greater than (x-1). It is really hard to start the prove. But after the prof told us to look about what we already knew (the definition), we understand how to prove this statement.

Then we learned about how to disprove a statement. It sounds really tricky and confused at first. However, after using the idea of prove the contradiction of the statement, I felt confident about how to write the disprove.

Week 5

Week 5

In this week’s lecture, I learned about how to write a proof, such as how to prove n^2 is even ==> n is even. It is hard to think about how to prove P==>Q, but it is easy to find out how to prove the contrapositive of the P==>Q. And the prove about the prime number is also really confused.

After the tutorial, I think I could do better in writing a prove. The tutor told us how to write an outline of prove of P ==>Q:

Assume 

   Assume

       Then

       Then

       Then

   Then

Then

The ‘assume’ part is always the ‘P’, and  last ‘Then’ part is always ‘P ==> Q’.

After doing 3 practices, I felt confident about writing a prove outline. But it is still hard for me to write a prove, since I always get stuck in the middle part of the prove. But I will always thinking about using contradiction when writing a prove.

I am looking forward of the next lecture and I hope I could do better in writing about prove.

10/10/14

Slog week4

This week I learned bi-implication, transitivity and mixed quantifiers. I feel the review part is the most important part for me. I find it is really easy to solve equation by using P => Q is equivalent to ¬ P ∨ Q, and ¬ (P => Q) is equivalent to P ∧ ¬Q. 

In class we did some practices of bi-implication, such as translate a given implication into the conjunction of two disjunctions. I felt hard at beginning, but after using the distributive law and De Morgan’s law. I think doing the practice in class helped me understand the concepts better.

The next lecture is about transitivity and the mixed quantifiers. 

Then we learned about how to write a proof and did several practices about writing proof.

I think the most confused thing of this lecture is using the laws to write equivalent. However after doing all the tutorial questions I got a more clearly understand of using the function.

Slog week 3

This week in class I learned about the language of math, which includes conjunctions, disjunctions, negations, truth tables, and manipulation laws. Conjunction means And, which could be described as the intersection of two sets(A, B). Disjunction means Or, and it could be the element from either set A or set B. In math, disjunction means union. Negation is hard in the beginning. The prof gave us many statements and we need to negate them. The negation of ‘all’ is ‘not all’. And the negation of ‘there exist’ is always ‘all is not’. I found out the tips are really helpful: 

not all = there is one that is not

there does not exist = all… at not…

I feel doing excises during lecture really helped me to understand all the concepts. The Scope part is confused at first but after I finished the excise about T/F, I start to feel confident about that. 

The tutorial questions were all confused, especially the second part. And the quiz question was hard. I think I would get zero for it. However, after the tutor finished go over the tutorial questions, I feel a little be confident about transferring English to symbol. I think it is really interested when doing transfer; the negation actually made me feel depressed. I hope I could do better in the next quiz.

Slog week 2 09/19

     

    In the two weeks study of MAT165, I learned many new things and also reviewed some. In the beginning I thought this course is easy, but after the class on Wednesday I feel it’s hard and confused.

Last week I got the schedule of this course and I found out that the final exam is only 40% of the total grade, which is quite different from the ECO100 course. I learned about how to be precise, since the ambiguity always exist in the daily language and computer cannot understand words with doulbe-meanings. Some math samples such as for all and there exists are made the questions become shorter. Then I learned about some computer language: python. The basic structure for python, which I learned, is given two sequences: S1 a d S2. Then define q1, which is a header. Based on the python code the venn diagram could be draw. The other type of code I learned is ‘return all’ and ‘return any’. ‘Return all’ means all the elements in the sequence need to be true or all the elements are false. ‘Return any’ means that if there is one element, which satisfy the condition, exists then the code will be true. The computer codes need to be super precise to run the program. The last part of the course was problem. Professor gave us a piece to dialogue about an discussion on three children’s ages. We used the 4 steps to solve the problem. The four steps are: understand the problem, plan solutions, carry out your plan, and review your solution. By following the four steps, the problem was easy to solve. 

In the lecture of week 2, the topic about quantifiers showed again. I was amazed by the length of the sentence could be by using the math samples. Some new samples about sets were also been taught by professor. We first used those samples to answer the problems, then use quantifying functions to answer the questions such as q4( M, O). The expression for the quantifications are in four ways: quantifiers, venn diagrams, set relations, and quantifying functions. The second part the the lecture is about identifying the sentence and statements. Statement is specified. The conception of prediction could basic conclude in a function. The topic of implication is interesting. I need to distinguish the P and Q in a sentence. P implies Q. The converse of P and Q could be either right or wrong, but the contrapositive of P and Q must be right. There are some rules of finding P and Q: 

1. If P, [then] Q.

2. When [ever] P, [then] Q.

3. P is sufficient/enough for Q.

4. Can’t have P without Q.

5. P requires Q.

6. For P to be true, Q must/ need to be true/ is necessary.

7. P only if/ only when Q.

8. Not P unless/ if not Q.

Then I learned about Equivalence. P is sufficient for Q, and Q is necessary for Q.  The last part of the lecture is idiom, which is just saying the different ways to express same meaning by using math sample.

I found out I have learned too much material, however by writing this Slog I think I could understand the material better. My tutorial went well I think, some of the tutorial questions are hard, such as the drawing of venn diagram. But after the practice I feel less confused. I am thinking about reviewing the powerpoint if I have further more questions.