CSC165 Slog 12

    This week covered induction which is the concept of any function F(x) is true, then it implies there's an f(x+1) which is also true. The core concept of induction seems pretty clear cut but the examples in lectures were anything but that to comprehend.
    We covered diagonalization, cantors example and looked at tables that show induction. According to Heap, the topic isn't necessary for this course but will be seen throughout other Comp Sci courses so I'm going to have to look at and fully understand the examples we did in class at a later date.

CSC Slog 11

    Only 2 lectures this week, and Heap covered non-computable functions. I don't really get this at all and assignment 3 has a question related to it. I looked back at the annotated slides and those didn't help much. Not too sure what to problems related to the topic or how to solve and or prove that they are not computable.

    Went to waterloo over the thanksgiving break and didn't get a whole lot of review in for the material covered last week on Big-Oh.

CSC165 slog week 9-10

    Past two weeks have been pretty tough, and pretty repetitive. we've been dealing with a heavy amount of proofs on upper bounds and the usage of big oh statements. last week had a large portion devoted to looking at functions and counting line execution with while loops and for loops based on any given input.
    Dealt with some variations of Big-Oh including proofs with varying break points in the proof and dealing briefly with doing proofs of limits using bounds.
    On a side note, assignment 2 was due last week. the floor functions we had on that were pretty rocky overall but it's done I suppose.

CSC165 Slog 8

    This week was a more focused and complete version of last week. Just looked at functions in python and did proofs on finding the worst case and best case scenarios in quantity of lines executed in any given function. Not a whole lot of new material, just a focus on big oh, and a more formal look at worst case scenarios and visualizing how a function would execute itself given a certain input.
    Overall doing proofs with big-oh have been pretty smooth, and being able to visualize the actual executions of code to determine the worst and best case scenarios has been more fun than the actual writing of proofs.
    Not a whole lot to go over, just need to get some more practice with big oh and get used to seeing the omega pop up. In terms of topics covered, it was mostly introduced last week.

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.