CSC165 Slog 7

    This week we continued with different examples of proofs and more specifically, upper bounds of a function and lower bounds of a function. Despite it being more proofs, this week was pretty refreshing since we moved away from solely the use of symbols, but we also used some algebra in our proofs which made understanding the reasoning behind steps in the proof a lot easier to follow.

    We covered bounds because of how in comes into play when looking at how many times a function passes any given line of execution in code. I don't know where to find the symbol for the upper bound, so I'll just use the term big-oh. This upperbound method we learned was to give a fairly loose upper bound to how many line executions are performed in any function written in python (looking at how many if statements or while loops included in the code). The typical translation of finding an upper bound of any given function looks the following:

 ∃C ∈ R+,  ∃ B ∈ N, ∀ n ∈ N, n>=B, f(n) <=C*g(n) 

    Looking at this function is pretty confusing, but seems to be consistent in the format with the lower bound statements so when we focus on that it should be a bit smoother than the introduction to this complicated statement. Overall though the proof itself has been reasonably smooth to take in and understand.

CSC165 Slog 6

    This week's material covered different varieties of proofs, and how to go about writing them.
some of the different scenarios covered this week were including case by case, proof of the negative.
    Overall this week was pretty challenging with the introduction of looking at limits while also taking a look at proofs using floors and ceilings of a variable. Limits have always been a bit of a struggle for me so it was even more challenging having to look at limits and see how they translate from english to symbolic form. I also had never seen the function 'floor of x' which made the first few examples with the function pretty difficult to follow but that only lasted the first few days of this week.
    In terms of the most important stuff that I took away from this week was writing proofs using case by case as well as proving the negation of a statement since it allows you some flexibility in deciding whether or not you want to prove or disprove any given statement.
 

CSC Slog 5

    This week was introductions to full proofs, and some examples of that. overall it was not very stressful in terms of problem solving,  just becoming familiar with the content within the proof structures.
   overall not a whole lot apart from processing and becoming familiar with what different proofs looks like.

CSC165 Slog 4

This week the topic that stuck out the most as very important was the introduction to proof structures.
A few other topics were mentioned this week included:
However Heap made it fairly clear that proofs would continue on for the rest of the semester and how it was pretty important to understand structuring so most of my attention was spent on that.
    The standard format that we were taught was to go through the given statement from left to right and introduce the variables in the statement. If  ∃ of a set of variables exist ∈ in another set, you pick a variable in the set to allow it in the proof, and assume any sets that ∀ exist a set before doing the 'meat' of the proof. Once you end the proof, you show how you got to the consequent with the knowledge of the assumptions in the proof (antecedent).
    The structure has been quite easy to catch on, which is nice to know since it is also essential to doing proofs for the rest of the semester.