Problem-Solving Narrative

I will be narrating the problem titled 'products of sums'. We worked on it in class on Wednesday April the 3rd and I gained knowledge and insight about the problem in class that day and also when I went home and thought about it more.The problem states briefly, " If n is a positive integer, what is the maximum product that can be formed of a list of positive integers that sum to n?". Many approaches exist when tackling this problem, some simple and some complex.
1. First off you must understand the problem.
Many things have to be considered when looking at a solution to this problem. Only positive integers are being used so you can immediately eliminate the negative integers which helps us. The fact that we are also only working with integers also helps us because when working with real numbers we would have to consider different techniques to solve this problem. There are various ways to represent a solution to this problem, none of them which are wrong in any sense; the solution can represented by a sentence in English, by an equation or by a python program. All of which would have their benefits, disadvantages and difficulty in interpreting.

2. Devising the plan to tackle the problem.
First off, like always, I try to solve the problem using examples, or in other terms brute force. Sometimes if the problem is easy enough then this will work, but for any problem worth solving this method usually doesn't hold up. The 'best case' I would have from this problem would be that the examples from brute force technique showed a pattern in which I could derive a simple math equation from and then the problem would be solved. Maybe if the solution takes many steps to complete, the answer could be transferred to a python program. And then from there we could even translate it to English for a wider audience. After using brute force for a little while, in this problem particularly, it seems to be useless and we need to start thinking conceptually.

3. Carrying out a plan and working through concepts.
Some large idea that I thought of and that were worked on individually were:
- Splitting up your number into just 1's, having enough 1's to add up to the particular number you are dealing with. Then from there, continue adding them up from the left to the right into different combinations or somehow organize these lists. This seemed to fail though and wasn't very practical.
- One solution I found was just breaking the number in half and then the largest product would come from those two numbers. But I soon realized that it didn't work for small numbers, or odd ones at that, and your list of sums could be bigger two numbers so that idea quickly dissolved.
- Another strain of thought came form the idea that the highest product of the sum will never include the factor of itself, examples like 199 + 1 = 200, but this idea does not work for small numbers such as three and two.

After trying these techniques I thought of dividing these numbers into two sets, odd and even numbers, which came to a moving conclusion that ceiling or floors had to be used in the solution to this problem. After then thinking about this, I still could not come up with a solution for the problem unfortunately.

When it comes to other SLOGS I thought George Abu Salehs SLOG was the best one I read. He made the posts fun and enjoyable to read as they also gave insight to understanding concepts.


Alec out

2nd last post

This week we learned about the non-computable function Halt and how to reductions work. I thought this section was quite interesting actually and had an interesting time trying to understand how to worked. When I first started to dissect that a non-computable function could be manipulated and put into a proof that proved other non-computable functions existed I was very confused. Understanding exactly how a function runs every line and what each line does is very important to understanding how these kind of reductions work. When working on the proofs, I really started to understand it when I started with looking at my desired output (eg, return 42, navel_gaze) and then working backwards from there. All in all, I enjoyed this week more compared to others personally as I felt it had strengthened my practical knowledge in Python and general programming.

Week 10

Big oh and big omega are seeming to become pretty interesting topics. The thought of limits in calculus always bore me but the understanding of comparing two functions after a certain break point is a cool idea and gives into a better understanding of what limits are. I have become way more comfortable in writing my proofs from doing the assignment and the tests. I have looked at assignment three and nothing impossible seems to be on it, looking forward to working with my team to get this challenge done.
Only two weeks more to go!

Midterm 2

This week was just filled with studying for the midterm and such. It was on proofs which I do not find to be the hardest subject. I looked at the sample solution and I think I did pretty well. I have to work on my structure in the future though because I noticed I did some things wrong in that category. Overall, excited to get my mark back.

Week 8

Had a pretty good week in this course overall. I felt like chapter 3 is the chapter I have the most understanding about and the most motivation to work on. Most of the stuff we have been learning in this course did not interest me to be honest and I felt like it was not really applying to anything practical but proofs showed me something interesting you could do with proofs. The quiz in tutorial was very confusing because our TA showed us a way to count steps different from Professor Heap and most of the class was confused I think as well. Some unity over the teaching staff would be better, I will bring it up when studying the next test.

Week 7

I am having a way better experience in this course now. For some reason, this chapter on proofs just really interested me and got me excited about this course. Honestly the first two chapters were a big bore and my marks reflected my dis-interest. Now I make sure I have questions for Professor Heap every day after class or questions for the TA on Tuesdays. I seem to be paying more attention in class and am getting better at doing proof structures and such. It doesn't seem as much of a grind anymore ether. Had a great week in this class. I am also working all weekend on the assignment and making sure I do the best I can on it as I need to upgrade my mark.
Cheers,
Alec

Week 6 (late)

After receiving marks in both the assignment and the test I am not satisfied at all at where I stand in the course. I think I should put more studying time aside for this course compared to my other courses because it seems this one is the hardest. Me and my partner didnt spend enough time working on the first assignment and that can be easily fixed for the next assignment which we have started working on now. On the test I didn't do particularly well because I misunderstood some questions and didn't do them correctly. When seeing the answers though I found the answers quite easy to derive. I found the question explanations a bit to misleading for no reason. Right now this is the course that needs the most attention as I will be going to office hours and asking questions after every class from now on.