3rd week journal

This week, we learnt more symbols of the language of Math. ‘And’ and ‘or’ are two words that we use very often in daily life. In math, ‘and’ is called conjunctions, which has a similar meaning to natural language. ‘Or’ is called disjunctions and has a different meaning from natural language. In natural language, we usually give two choices and use ‘or’ to connect them, this is an exclusive or. But in language of math, ‘or’ is an inclusive or. Negation is easy to express when it is in natural language because I just need to add a ‘not’, but it becomes a bit more complicated when it comes into language of math. Since adding a negation to a sentence with a combination of conjunctions, disjunctions and implications, we need to apply laws to change it properly.

It’s hard to memorize all the laws, and understanding the laws will make me remember them better and longer than just memorizing them. To me, using different examples is the easiest and most efficient way to understand the laws.  From my experience from PHL245(modern symbolic logic), practice is the key. I am going to do lots of practice during the weekend. And I found out that the interaction in class is pretty important too. Because it will help me to think more if I interact more in class. 

CSC165 2nd week journal

In the first two weeks, I knew that programming language is very precise and logical symbols are used to prevent ambiguity. The two quantifiers in logical notation are universal quantification and existential quantification.  To disprove an universal quantification, there simply needs to exist one exception. To show that something exists, simply find one case where the property applies to one instance. Implications is one of the forms of a sentence. If I study hard, then I will do well in this course.  And the converses, contrapositive of the implications have different meanings from the original implications. While equivalence means antecedent implies consequent and the meaning is the same the other way around.

These are techniques we are building up to solve proofs later on in this course. Proofs will be formalized and presented in not only a precise and accurate manner, but also logical.  

Although human language may be ambiguous at times, it is more intuitive for solving problems. It is then translated into symbols to reason more precisely. This is the background I come from, as I took PHL245 (modern symbolic logic) before, that was when I found myself really interested in symbolic logic. I am not a computer science student, but I am looking forward to learning more from this course because it is interesting. From this week’s materials, since I have learnt the logical notations from PHL245, so converting English sentences to symbols is something I am familiar with. Different from PHL245, this course is more towards mathematical expression and reasoning.  This is something I have to work on more. I am going to review the related material from the course notes during weekend and try to understand the material better.