Week 3

This week, my professor taught us some more complicated, logical concepts. I learnt about concepts all the way from expressions that restricted domains of items in two sets when they are combined together, until a concept known as De Morgan's Law. The course content is still challenging for me, but I try to understand it by rereading over the information and repeating it to myself. At the extra help sessions, I try to further clarify my doubts with teaching assistants through explanations and diagrams. It has helped me and I am confident that I will succeed in this course if I continue to attend these sessions regularly.

Other concepts that I have learnt this week are conjunction (combining two statements by claiming them as true with the word "and"), disjunction (combining two statements by claiming that at least one of them is true with the word "or"), and negation (reversing the truth values of statements using Ø). Negation involves changing a statement so that true becomes false and false becomes true. It is a very tricky concept to grasp because it involves changing certain conditions to fit the negation statement. For example, there is a statement that implies "for all x belonging to a set of real numbers, P(x) implies Q(x). The statement that says this is "xeX, P(x) -> Q(x). When this statement is negated, we get the statement "for certain x belonging to a set of real numbers, P(x) is true and Q(x) is not true". This is symbolized by $xeX, P(x) and ØQ(x). At first, I was confused at why this happened as I thought that the inverted A could not be changed to a mirror-image of E just because of a sign. However, through extra help and rereading, I was able to make sense of the concept. Furthermore, I was unaware of what the word parse meant, despite it being used several times in class. I researched its definition and I saw that it was just the breaking down of a statement into components to make sense of it.

I also learnt that Venn diagrams were necessary to represent conjunctions, disjunctions and negations in an easier and a more visual way, but there were some limits as to how many predicates or functions the Venn diagrams can represent. This is where truth tables can help. Truth tables are tables that have variables and functions as headers and T and F in the tables to signify if the eventual condition will be true or false. This was one of the concepts that I enjoyed learning the most this week as it was easy to find results of expressions using this way. Other new terms that I learnt this week are tautology (when a statement is true in all cases), satisfiable (when a statement is true in certain cases), and unsatisfiable (when a statement is false in all cases). Lastly, De Morgan's Law states that the roles of "and" and "or" are switched. For example, Ø (P or Q) <-> ØP and ØQ. At first, I couldn't understand this, but later I understood the logic by rereading it: if P or Q cannot be true, it means that both of them will be untrue.

On Friday, my professor conducted a unique activity. He told his students to take a strip of paper and keep folding it into half from the left. Each time we folded, we had to open up the folded paper and record how many times the paper folds pointed upwards or downwards. Then, we were to find some kind of logical pattern as to how the number of upward or downward folds increased. I came up with a math equation for the increment of the total number of folds for every fold leftwards. This was the most interesting and enjoyable activity for me this week as I not only learnt something, but had fun at the same time. At the moment, I am looking forward to and a little apprehensive of the upcoming course material for next week.

CSC165 - Week 1 and Week 2

I am a first-year student in CSC165, which is a course that covers mathematics in terms of computer science and logic related to it as well. While this course may be interesting and detailed, it can also be very challenging and overwhelming for beginners, like myself. At this point, I have learned quite a lot about the logic involved in this course, and it has turned out to be quite challenging for me as a student. A main reason why I find the course challenging is because of the language used to convey logic. An example of this is when a statement asks to return all elements in a set if they do not correspond to the elements in another set. I think the wording for this is not all. I found this wording quite confusing and thus, I didn't understand it. Additionally, we had to draw Venn diagrams to show how certain elements in one set related or didn't relate to elements in another set. I struggled to do this as well because of my lack of understanding of the logic in the phrases. Likewise, a tutorial exercise consisted of drawing Venn diagrams based on statements that declared whether all, some or no python programs passed all, some or no test suites. This was confusing for me as well because I could not interpret the statements' meanings well enough to draw correct diagrams for them.

As well, I did not understand other phrases which imply multiple meanings in logic, such as 'If you eat your vegetables, then you can have ice-cream'. My professor explained that the antecedent, which is the first part of this sentence before the comma, could not happen and the entire phrase would evaluate to true. I did not understand why this was. This is because I interpreted the sentence literally and thought one could not have ice-cream without eating vegetables. Another concept I struggled to understand to the point of frustration was the idea of contrapositives. I was confused of how and why the end result of certain statements were the way they were after reversing their implications. Furthermore, I kept struggling to retain the information that I had learned and not get confused at the same time. To clarify my doubts, I asked the teaching assistant to explain the use of Venn diagrams in my tutorial session. I also attended and plan to continue to attend the help centre for computer science to clarify my doubts about concepts learned in class.

One thing I enjoyed in this course is the professor explaining to students whatever concepts they find confusing. He also understands that they find this course challenging and overwhelming and knows that it will take time for them to fully absorb and understand the course material. To help his students, he incorporates simple, real-life phrases and situations to convey the course concepts to them. Right now, I am still confused with certain concepts, but I will take the initiative to improve my understanding of this course and its wonderful logic. I do believe that if one takes the time to practice and absorb the material in the course, it will become more manageable and easy.