Week 6: Sorting and Penny Piles

Hello Rod here,

This week we finished with proofs and we began talking about sorting. We were also assigned assignment #2 which will probably expand my ability to solve proofs, clearly and logically. Also today we were give another problem to solve, which was called Penny Piles.

Sorting
I am pretty glad we are starting sorting algorithms because it will give me more insight into the efficiency of certain sorting methods. I always heard of multiple sorting methods such as: bubble sort, insertion sort and selection sort but I am hoping to learn about the efficiency of some of these algorithms and the number of steps based on the situation.

Penny Piles
Today we started a problem called Penny Piles. Which was a problem along the lines of starting with a certain amount of pennies in one drawer and by using only 2 specific operations trying to get the one of the drawers to have a certain amount of pennies. How we went about solving this problem was by manually using the operations to get the desired result then afterwards we decided to make a tree of possibilities which made the operations more easier to visualize.

I look forward to continuing sorting algorithms more next week and the big oh.

Week 5: Direct Proof, Indirect Proof, Proof by Contradiction

Hello Rod here,

This week we only had two lectures but we started learning about the content of a proof. Last week when we only learned about the structure of a proof which I got pretty comfortable with. This week in lecture we worked on some proofs. We proved direct proofs by proving the statement that was given to us. Usually using some algebra and manipulation. We also worked on indirect proofs which required us to take the contrapositive of the statement and prove that. Also when we wanted to disprove a statement we learned that we should prove the negation of the statement in order to disprove the original. I still feel really weak in proving the content myself. Hopefully i'm just going to follow the lectures, work on the assignment an do some sample proofs on my own so I feel comfortable writing complete proofs.
One more thing I also learned this week is grounding. It was brought up in lecture but we didn't really talk about it so i had to go find it out myself. Yep that was it for this short week.

Week 4: Proof Structure and Midterm Test

Hello,

Proof Structure
This week began starting to learn about proof structure. Not necessarily the content of proving the statement, but we learned about the assumptions, indentation,  and the conclusions at the end of the proof. The tutorial was helpful this week. We went over only the format of the proof and focusing on the format is going to help me a lot in the future when I am writing full proofs.

Midterm Test
I am mentioning the midterm test because I personally learned a lot from the test. First of all the midterm test was the first test out of all my courses, so it was a little intimidating to be my first university test. Studying over the notes and looking at the past tests helped me a lot not only with the test but my overall understanding of what we have learned so far. Right now I feel really comfortable with negation, venn diagrams, converse, contrapositive, english to symbolic and understanding boolean logic in Python code.

I found this week tough but really helpful and I look forward to learning more about proofs.

- Rod Mazloomi

Week 3: Laws and Proof

Hello,

This week I learned a lot. Not necessarily all from lecture, but a lot doing tutorial exercises and the Assignment 1. 

Laws

During the tutorial I learned to used the laws we learned to prove equivalence of statements, rather than making truth tables. I found this really helpful since it takes quite some time to make a truth table and rearranging and manipulating the statement to make it equivalent to another is a lot more efficient. I got comfortable using De morgans laws, distributive laws and manipulating an implication (P implies Q <=> not P or Q).

Proof

Just today we were shown how to prove a statement. I learned about the indentation, making assumptions and putting the footnotes. Personally I found proving the actual statement not too hard. I just need to work on properly presenting my work in the format we were shown. 

Also this week doing Assignment 1 helped a lot with, negation, taking the contrapositive and converse, changing between symbolic form to english and drawing venn diagrams that will definitely help me on the upcoming test.