Proofs Summary

We covered the basic rules for proofs and did the "penny piles" problem during lectures. The list of basic rules was kind of like a summary on Chapter 3 --- Proof. Accompanied with tutorial exercises and quizzes, it gave me a deeper and more systematic understanding on this chapter.

Basically, I divided my working on proofs into four steps: 

1. Determine whether the statement is true of false. If the statement is false, write down the negation of it.

Sometimes it's a good idea to draw a graph when the whole statement seems too abstract. And I found   this method really helpful when I was doing 1.2 and 1.3 on assignment 2.
To prove a statement is true, instead of proving itself, we choose to prove the contrapositive occasionally. To write a negation for the original statement, first we change the quantifiers, then we negate the if-then statement. Be careful when using De Morgan's law. And parentheses are always helpful.

2. Write down the assumptions.
These include universal quantifiers and the antecedent.

3.Start from the antecedent. Reach the consequent.
If we come across an existential quantifier, we will need to give specific names and then continue the proofs. As for me,  make sure to complete the whole structure for each different case in the proof.(examples are Week 6 Tut Q3 and Q4).

4. Complete the whole structure.
These include introducing the =>, quantifiers , etc.

More on Proofs

There were only two lectures this week and we've been talking about proofs in class.

During this week's lectures, I learned that when we are working on a proof, we don't have to know what to write from the beginning to the end at first. Instead, we can write down the assumptions and conclusions first, then go inward until we have to give an explanation on a statement. This method applies to problems from MAT137 as well.

Also, I found proving the contrapositive of a statement quite helpful sometimes, especially when I apply this method to problems in my Linear Algebra course.

The midterm results were announced this week. Though I got a good mark, I'm not satisfied because I made an unnecessary mistake in the paper. Maybe I should keep a record of my past mistakes so that I can do better next time.

Midterm's over Yippee!

I was upset about the midterm and finally it's over!

In fact, what made me upset before the test was the solution to assignment 1. I did spend time on it, but I still noticed some stupid mistakes when I went through the posted solution. So I was worrying that I would make a lot of mistakes without even knowing. When the result for the test came out, once again I found that I lost marks on mistakes due to carelessness, but much less this time. But how can I avoid such errors? Checking is not enough for me. 

The good thing is at least I've become more confident for everything we've covered after reviewing for the test. 

This week we learned the structure of proofs and the tutorial was quite helpful for me. We talked about how to write a proof and how to make comments. 

Working on Assignment 1

I focused on Assignment 1 the past whole week. Having discussed with my partner, I found there were some problems I thought I had understood actually  puzzled me. The discussion with my friends was quite meaningful, it revealed some problems I had barely noticed and gave me a hint what to review for the midterm. Having my answers refined, I went to Danny's office hour to make sure I was clear about the problems. It shocked me when I saw about thirty students waiting outside, but it made sense since the assignment due the day after. So, I went to see Larry and fortunately there were a few students then. He was so patient and explained clearly to me about my questions. And he also pointed out some details I had overlooked, like the "three sets" in question 4.  Now I totally get it and feel much better!

Midterm is coming, I had better work harder now. Hope everyone will get a good grade!

First Problem Solving

There was a change on Friday's class, we worked with peers on a Folding problem. We were asked to take out a strip of paper and fold it with its left end on top of right end, then repeat this several times trying to find the creases pattern. I folded the strip, and my partner recorded the creases. At the beginning, the problem seemed complicated and the record of ups and downs wasn't that helpful. After a brief discussion, we decided to change our way  to record how exactly each fold added creases to the strip like this:

It's easy to find the pattern now.
Copy the arrows from the previous row and there will always be an up, a down, an up, a down, an up, a down... in the intervals. Besides, the left side and right side is symmetrical.

We predicted the pattern after the fifth fold first,  then folded again. And it turned out as we expected.  When we saw the hints on the other side, we knew our method was correct.

The experience of working with a peer in class was valuable. I hope there will be more classes like that.

I've been trying to write a program in python this weekend, but with only a few week's python classes, I found it really challenging. Maybe I'll drop in office hours next week.

Week 1 and Week 2

 I loved those mathematical logics we've discussed in class so far! This course went beyond my expectation. Though I had been admitted into computer science program, I was worried about the coming computer science courses.  To my surprise, I found myself kind of immersed.

       
 In the first week, we talked about sets, quantifiers and proofs for universal statements and existential statements. Those were pretty easy. And in this week we learned implications and negations which also been taught in MAT137.  

        
To be honest, I've already learned the above things in junior high and senior high. However,  I still felt uncomfortable occasionally during classes. Since English is not my mother tongue,  I'm not that familiar with some English terms and some logics behind the language. Besides,  the "if only" and "unless" statements indeed frustrated me for quite a long time, but I actually enjoyed the process of trying to understand it. To learn more efficiently, I plan to set aside some time to preview, maybe just go over the course notes for next period. I'll start this weekend and see if it will work.