week 12

woo! this was our last week of classes! it is hard to believe that the semester is nearly over.

This week we learned about countability and induction. We learned about mapping which I wish we had began learning earlier since it was an easy concept for me to grasp. Countability was comparing the size of two sets which is essentially what mapping does. it compares the sets to make sure that easch x maps to a unique y, each y is mapped to at most one x and every y has some x that maps to it. This was a concept I really understood and enjoyed.

This week I also worked hard on the third assignment. This one was by far the hardest of the three (although I suppose thats what would be expected). The thing I had most trouble with were the question 3 and 4 that discussed limits. I've learned that this is definitely a concept I need to go back and study again.

Seeing as this was the last lecture and tutorial week the only thing left is the final! I am quite nervous seeing as this will be my very first final in all of university however that gives me a lot of time to study for it :)

week 11

No lecture or tutorial this week but i continued studying up and practising writing proofs 👍 🎅

week 10

This week we reviewed a lot of the materials from last week. We reviewed big-Oh proofs for polynomials (standard procedure with over/underestimates) big-Oh proofs for non-polynomials (need

to use limits and L’Hopital’s rule). We practiced doing more proofs which is always helpful seeing as it is clearly one of the most important aspects in this course. I find these practise proofs helpful in remembering to use comments and what to write in these comments seeing as we seem to get marked a lot on the comments that we include.

 This week we also began learning about computability. We learned that computers solve problems using algorithms, but some problems are not easy to solve using an algorithm. This was demonstrated through halting. It is not possible for computers to solve the halting problem because the problem leads in a contradiction. We also discussed how reductions can be used to show that other functions are non computable.

week 9

This week we did more big omega proofs and big o proofs for general function. We also discussed over estimation and under estimation tricks which mr. zhang emphasized would be very important for future tests and finals. Some over estimation tricks  were to remove a negative terms and multiply a positive term. Under estimation tricks included removing a positive term and multiplying a negative term. We discussed big oh proofs for polynomials which was the standard procedure with under and over estimations, as well as big oh proofs for non polynomials which require the use of limits and l'Hopitals rule. We also covered proofs for general big- oh statements which were picking b and c based on known b's and c's.

week 8

This week we discussed definitions of big o and omega and also the worst cases of these two algorithms. These things i found to be more difficult than things we learned in previous weeks. This is definitely something that I will need to go over more on my own and maybe visit office hours for.However I do find these concepts interesting so I am hopeful that I will pick up on them quickly.

I have also been working on assignment two alot this week which i am finding more difficult than assignment one but I think it is still going okay, There is also the second midterm for this course coming up next week so I am going to be spending a lot of my time studying and practicing more of these proofs.

week 7

This i believe was our last week working on introduction of proofs. We covered proof by cases and reviewed some proofs. Towards the end of the lecture we started on algorithms.

At the beginning of the lecture Mr. Zhang discussed the proof of "if you have a problem in your life, then don't worry"  this was used to introduce cases. the idea was if you have a problem in your life, can you do something about it? case 1 was yes and this proved not to worry about it. case 2 was no and this also proved not to worry about it. The way this was taught was quite funny and I really like the humor that is added into these lectures, it makes it much easier to learn for three hours in a row. 

This then lead to the idea of what makes up a valid proof, which was the union of the cases covering all possibilities. We also went over proofs as a whole and discussed negation introduction and also elimination. I found that  Reviewing these concepts made it easier to tackle assignments and problems in the future.

In this lecture we also began to discuss algorithms. We began by comparing bubble sort and merge sort. This was my first time seeing programs like these and I thought this introduction was good. I learned more about computer programs in general. Like for example running time. I learned that this does not mean the actual amount of time a program takes to run, it is the number of steps taken by the algorithm.

week 6

This week we mostly just reviewed more about proofs. The tutorial this week was cancelled.

We were introduced to the topic of floors and ceilings and learned about how these worked in proofs.We also went over the idea of proving things false. To prove somethings to be false, you can disprove them and to do this you can prove the negation. This week epsilon and delta were also introduced to us and were incorporated into some of our proofs. This week I was also told that if we can't solve a proof even if we write what lines we are able to write without the proof we might still be given some marks for the question which is great to know.
Finally we also discussed a bit about a backwards search. This is starting with what you wanted to prove and working backwards to what was originally given,