Week 6

Week 6 Slog:

This week's lecture focuses on completing proofs with proof structure. The first part of the lecture focused on the new non boolian function "floor" and "ceiling". Initially, I found it very difficult to understand the proofs Prof Zhang showed us because I found it very difficult to create logical links between mathematical statements full of symbols. Yet, as the lecture goes on, I realized that the reason for such confusion was due to that fact that I was unfamiliar with the definitions. After spending the break rereading the definition of floor and ceiling function, I felt much more comfortable with understanding the proofs. Furthermore, to start a proof, I realized the importance of beginning from the basic definition because these are the only information we know from a mathematical statement. This was something I found very useful and can be applied in my mathematics courses.

The second part of the lecture focused on methods of disproving statements and proving sequences. From this part of the lecture, I understood the importance of learning logic statements as now I grasped the idea that to disprove something, we would just have to prove the negation of the statement true. We applied this technique to disproving statements about sequences and I was able to follow the proof completely since I spent time digesting the meaning of the statement given. The final part of the lecture was the most challenging aspect as we had to prove limits. Fortunately, I learnt the concept of delta and epsilon in MAT 137 which enabled me to focus on the prove structure mainly instead of the concept. Using the skills learnt from previous lectures, I was able to reproduce these proofs by going step by step slowly and state the quantifiers respectively. Noticing how we were starting to use the ideas learnt previously to prove practical problems, I felt very satisfied as I was able to make all the logical links together and write organized proofs.