The Final Stretch

We did more on computability in lecture this week and I think that I still understand it. I am still having trouble seeing how exactly to formally show computability because everything I come up with looks very informal and doesn't look like work I would want to submit. I am going to as Danny about this in lecture and hopefully know exactly what I need for the last question of Assignment 3. When reading other SLOGs, I noticed that Damon made a really good point in saying that the halting problem is a lot like recursion. Although he didn't quite understand the concept fully, I think that this idea of relating it to recursion makes a lot of sense.

This will probably be my final SLOG, and I will be busy over the next week trying to make sure I understand everything for the exam. I am still having a little trouble with delta epsilon proofs but hopefully I can understand them well enough to get a good mark on the final.

Week 10 and 11

The thing I found most difficult in the past 2 weeks was disproving that functions are in Big Oh of other functions. Even after reviewing the slides I was still confused, and since there was no tutorial this week I ended up having to look online. I was able to find a document which really helped me to organize my thoughts and see what I knew in a very structured format. This helped me quite a bit, but I am still having trouble with this. I may ask about this in tutorial next week if I still don't understand it.

We looked at the halting problem and computability in lecture this week and it made sense to me. I had seen a Computerphile video on the topic a few months ago and now that we've covered it in more detail in lecture I understand what the video was saying and more.

Week 9

Assignment 2 was due this week and I still had trouble with the questions involving Delta Epsilon proofs. I was unable to complete them on the assignment but I am going to keep trying. The other questions on the assignment made sense and I think that I did well on those questions.

We had a term test on Wednesday and I think I did alright. One of the questions was a Delta Epsilon question and I wrote a proof structure for it but I was unable to complete it. The other two questions made sense and I think that I got them mostly right.

In lecture we looked at proving Big Oh and I had a little bit of trouble but I haven't had a lot of time to review it because I was studying for the test so I think that once I practice more I will be able to do the proofs.

Week 7

I'm still having trouble with Delta Epsilon proofs after tutorial this week, but I am continuing to try to do practice questions to get a hang of them. We started to learn about Big Oh and looking at the number of steps different sorting algorithms take. I think that the way we learned to count steps is fairly simple as I have quite a bit of programming experience and don't really find it difficult to determine how many times each line will run.

In lecture on Friday we did a problem about Penny Piles which I am going to work on writing a program to solve, as it interests me.

Week 6

This week we looked at proofs of limits which I found difficult to grasp. Even after reviewing the slides and looking some examples up I still didn't really understand what was going on. I understand the concept of being able to manipulate certain variables and not others but whenever I try to do a problem I encounter issues picking a value for delta. I will continue to try to work on the problems in the sample problems to try to understand better. There were also no tutorials this week so hopefully tutorial next week will help me to understand better.

Week 5

This week was the term test. I studied quite a lot for this test and I think I did alright. Some of the questions regarding proofs made me sort of scratch my head, but I think in the end I understood them. My only worry is whether or not my answers had sufficient proof, as I did was not exactly sure how much I needed to say to answer some questions. In tutorial we went over proof structures. When I looked at the tutorial sheet the weekend before tutorial I was thoroughly confused and did not really have a good idea of how to complete either of the questions. Once we went over them in tutorial I understood them (hopefully), although I feel like I definitely need more practice with these questions before I will be confident in my answers.

Week 4

We covered some more about the differences between the universal and existential quantifiers at the beginning of this week, and although this made sense I found it interesting to see exactly what can happen when wrong assumptions are made. In tutorial we went over some simple negations, proofs, and guarantees. At first the guarantees section did not really make much sense to me, but after seeing Gal go through every step I was able to grasp the concept a lot better. This week the first assignment was also due. I think that I did fairly well on this assignment, as I understood how to do all the questions. Any marks off would simply be for me making a mistake and not because I did not know how to do something. Hopefully this assignment will serve as a good indicator of my progress and whether or not I actually understand things fully.

Week 3

This week we learned about conjunction, disjunction, implication, and negation. Everything we did made sense as I was able to think about it in terms of programming, with which I am more familiar. The conjunction and disjunction are exactly the same as the ‘and’ and ‘or’ which are used in almost every program. Danny put stress onto the fact that logical or is not exclusive, giving another way in which it is similar to programming. Implication to me seems simply like an if statement in programming. After looking at the truth tables from lecture, the fact that P implies Q is the same as not P or Q makes sense even though it was not immediately apparent to me. Negation made sense to me conceptually from the beginning, but I had trouble with using it in practice. As with all science courses, I was able to fully grasp how to use negation and DeMorgan’s Law after doing practice questions using it.

Week One and Two

The first week of the course served as an introduction and did not really teach any completely new concepts but instead took concepts which everybody knows and put them into a mathematical form for everybody to be able to discuss and understand each other. The intro to the course reminded me of Plato's Meno in that nothing really new was taught, but instead students were shown something that they already knew but didn't know that they knew.

The second week brought on many new topics, the most interesting of which to me was vacuous truths. The idea did not really puzzle me at all but presented an interesting way of thinking which has never really concerned me in my previous schooling and everyday life. The idea of the implication being true if the antecedent is false reminds me of the idea in programming that as soon as one part of an if conditional is false the rest of the conditions will not even be checked. This at first appears to only be a technicality but actually tends to help out in programming, and I think that the same applies in the use of logic.

I feel that I did well on the quiz this week. The use of Venn diagrams to convey logical thoughts made sense to me, and the fact that the empty set always has to be considered added an interesting element to what I would otherwise consider to be a somewhat simple task. I look forward to the increase in difficulty of the problems and the new concepts which we will consider soon (although I'm sure that once they are introduced I will be scratching my head).