Week 1-2

Just from the introduction of CSC165 this course seems very interesting. I am really exited to learn how solve problems using mathematical expression and reasoning and apply these methods in programming. I also enjoyed seeing how a paragraph written in English could be translated into math making it easier to withe a program to complete whatever tasks or requirements that were in the program. In particular I enjoyed the example of how a user may ask a machine to find a phone with certain requirements which we can express mathematically and create a program to complete the tasks.

The next topic we discussed in class was precision and how precise or ambiguous to be in certain tasks. I found it very interesting how to successfully communicate with anyone we have to be the right amount of precise or ambiguous. For instance when we communicate to other humans we should be as precise as needed but when we communicate to a computer or when a computer communicates with us a high level of precision is needed.

Then we continued onto analyzing statements classifying elements of sets. Initially I found this a bit challenging as I could no picture the elements and the sets that a particular statement would refer to. But then when we were shown how ti show these elements in sets in the form of a Venn diagram, I found it a lot easier to picture the situations. The Venn diagrams helped me again when we started falsifying or verifying quantified claims as I could now easily picture what cases would have to occur for a statement to be true of false. Then i was also able identify what programs could analyze the quantified claims and also what input parameters to pass into the program to analyze the claims.

The last topics we went onto were sentences,  statements, implications, and predicates. I understood that sentences are phrases we cannot verify or falsify without further knowledge but statements can be verified or falsified.  In the predicates section we learns that if an element x has a property L then we can write L(x) to express this. When we continued onto implications, I was getting confused on the tricky phrases in identifying the assumption and the consequence. I plan on paying closer attention in class this coming week to get a better understanding of implications. Although I was able to understand the concept of Vacuous truth as even though logically an assumption or consequence is incorrect  if it is not possible to show that they are incorrect, the statement is taken to be true. That is where we ended off for the week.