Surely,
it takes more than a week to understand new concepts in university. It was a
gruesome week to go through, trying to renew myself to think and act like a
mathematician. Quicker than expected, the consequences due to the lack of
background in proofs and theoretic math caught up to me. Arithmetic is
definitely different from the computing math from calculus from high school.
The first half of the week was acceptable as I quickly grasp the understanding
of conjunction and disjunction; conjunction is the combination of two
statements that has to be true whereas disjunction is the combination of two
statements that at least one is true. However, understanding gets chaotic soon
after negation. Entering into the realm of logic, I stumble upon the different laws
of arithmetic. The complex tautology for each law makes it hard to understand
and imagine each situation. Therefore, instead of staring blank at the
different tautology, I tried to draw out Venn diagrams that help shape and
display the different probability. In addition, I used truth table to
understand thoroughly the relationships between the different laws and
tautology. It is quite astounding to find that a statement that is written
completely different from another is equal to it; the art of arithmetic is
beautiful. Despite the fact that it is hammering me, I am still very interested
in uncovering more of the logical world.
2014年9月26日星期五
2014年9月18日星期四
Week 1 - Not The Best Start...
Well, I guess I will just rant a bit for this beginning slog. :)
Needless to say, my confidence was hammered as I took the first step into the course. Expecting a course related to computer, I found myself sitting in a room teaching logical math that excluded the use of numbers.
The concept of doing math completely based on logical proof and theories baffles my mind as I am comfortable with math that is applicable and numerical. Despite the fact that I was able to ease through the week 1 course material, understanding sets and quantifiers, I surrendered to the introduction of implication in the week 2 course material. It challenged my thinking and opened up my mind; I learned that implication is not that A caused B, but if A is true then B has to be true to be valid. As a result of the lack of understanding, I was confused among the relationships of implication, converse and contrapositive. To handle the difficult situation, I resorted my old study habit; I flip through the notes I take in class to look back at the solutions and comments and word backwards in order to figure out my understanding. In each examples, I was distinguishing the relationship between the implications as different statements provide different information on a implication. Soon, I was able to understand that implication and contrapositive is identical statements that give the same boolean answer, whereas converse is never the identical of implication.
Overall in the first weeks, I retreated back to the comfortable way of facing challenges. However, I hope for a change in ways to tackle challenging questions by following the steps recommended- understand, plan and carry out- in order for a broader and a more diverse perspective.
*A similar post that regard the situation of week 1.
http://csc165judy2014.blogspot.ca/2014/09/week-02-journal-01.html?showComment=1417664282273#c3435835114479682321
The concept of doing math completely based on logical proof and theories baffles my mind as I am comfortable with math that is applicable and numerical. Despite the fact that I was able to ease through the week 1 course material, understanding sets and quantifiers, I surrendered to the introduction of implication in the week 2 course material. It challenged my thinking and opened up my mind; I learned that implication is not that A caused B, but if A is true then B has to be true to be valid. As a result of the lack of understanding, I was confused among the relationships of implication, converse and contrapositive. To handle the difficult situation, I resorted my old study habit; I flip through the notes I take in class to look back at the solutions and comments and word backwards in order to figure out my understanding. In each examples, I was distinguishing the relationship between the implications as different statements provide different information on a implication. Soon, I was able to understand that implication and contrapositive is identical statements that give the same boolean answer, whereas converse is never the identical of implication.
Overall in the first weeks, I retreated back to the comfortable way of facing challenges. However, I hope for a change in ways to tackle challenging questions by following the steps recommended- understand, plan and carry out- in order for a broader and a more diverse perspective.
*A similar post that regard the situation of week 1.
http://csc165judy2014.blogspot.ca/2014/09/week-02-journal-01.html?showComment=1417664282273#c3435835114479682321
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