Week 5: Proving False Statements and Limits

This week, I learned the process of proving false statements and wrote my first term test. Beginning with proving false statements, it is equivalent to disproving a statement. In other words, proving that something is false is simply proving its negation. Once I found out that disproving a statement is the same as proving its negation, it became very easy to understand. The rest of the lecture was mainly on proving a statement with cases. I somewhat understand the process of proving with cases, but I need to refer to the course notes to fully understand the process. 

As with the term test, I have mixed feelings because there were a few questions that were a little hard to comprehend. The first part of the test was what I expected, but it became more difficult as I progressed through each question. Overall, I should have done better if I spent more time on the course notes rather than the lecture slides. Hopefully, this is a signal for me to spend more time on the course notes for the next term test.

Week 4: Contradictions & First Term Test

This week, I learned how to prove an existential claim as well as a sequence. Proving an existential claim very similar to proving a universal statement, except there are a few changes to the wording. As for a sequence, it is nearly identical to the proof of an existential claim. As a result, I was able to understand it quickly with no hesitation. The last part of the lecture was about the use of contradiction; it was sort of confusing at first, but once I read the notes over and over, it became clearer. Proving the contradiction of a claim shows that the contradiction is false, thus, making the original statement true. 

On the other hand, I wrote my first term test of the year! It was a little jarring at first, but I was able to complete all the questions within the 50 minute period. However, I realized that the test was very similar to the test test that was posted a few days ago. I felt very upset because I did not spend enough time with the sample test; I simply skimmed through the paper; I focused most of my studying on the course notes. Hopefully, the mark I receive on this test is somewhere in the 60-80% range. 

Week 3: Mixed Quantifiers & Intro to Proofs

There are a few things I found interesting on this week's course material. Transitivity is simply a relation between multiple cases. For instance, if driving a sports car implies driving fast and driving above the speed limit implies aggressive driving behavior, then driving a sports car implies driving aggressively. Multiple implications lead to a single conclusion, such as the example mentioned here. A few slides down, there were a few statements that were interpreted with a graph, but it did not seem clear in my eyes. I know Professor Heap said something like "if the enemy goes first, then it is possible", but I need to re-read the lecture slides as well as the course notes to improve my understanding of this concept.  

Throughout the rest of Friday's lecture, Professor Heap introduced proofs. I am not entirely excited about this because I sometimes struggle with proofs, which seem frustrating and a waste of time. Nonetheless, proofs is something I must master because it is a vital component in computer science. This introduction mainly focuses on the outline of a proof, which to me is fairly understandable. 

The first test of this course is to be held on Wednesday, October 4 and it will cover chapters 1 & 2. I plan to spend at least one day solely on preparing for it because it is worth a large portion of the course. Hopefully, doing well on this test sets the stage for doing well on my other courses.