CSC165 BLOG

Early Successes and Proofs are Scary!

Hello reader, welcome back for the third entry of my SLOG! This week, we look at the early successes on my path to becoming a master logician, as well as discuss why proofs are scary!

Early Successes!:

First things first, I'm the realest. Secondly, I am happy to say, early on in the path to mastery of basic logic, I've gotten some very positive feedback for my efforts! Last week, I went to pick up my midterm and I was pleasantly surprised to find that I'd done well on it! I'm sure that my walk from Danny's office to my class looked a little bit like this to everyone else on St. George St:

    I also recently found out that my group did well on the first assignment. This is really helping me gain confidence, confidence which I am entirely prepared to lose as we dive deeper and deeper into the next item on the agenda, Proofs!

Proofs are Scary!:

    If I try to tell myself that I only started "doing proofs" this year, I think that I would be lieing. Michael Hutchings from the University of Berkely defines a proof as "an argument which convinces other people that something is true". By this definition, I've been proving things my whole entire life. In fact, I dare say that I've gotten quite good at convincing people that something is true (like my parents when I told them I was doing fine in school during first year). Formal proofs however, with assumptions, introductions and indentations, not so much.

    My main concern at this time is that I will understand the intuition behind a problem but my proofs will be structured poorly. I guess this is analagous to syntax when learning a coding language, it comes with practice and discipline.

    I am however looking forward to the practical ramifications of writing well structured proofs. I find that often times in life, I am convinced of things and I am not clearly sure why. I hope to get a grasp of my convictions in clear detail after practicing writing mathematical proofs!

Thanks for joining me this week friend! Until next time, stay strong!

Negation is not not fun, and the beauty of truth tables!

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Welcome back for the second entry of my SLOG! We are about a month into CSC165 and fortunately my brain hasn't imploded, and the emotional/mental breakdowns have been few and far between. This time around, I'd like to address two topics that have actually helped prevent my brain from imploding. These are negation, and truth tables!

Negation is not not fun!

The concept of negation is a very simple one. The idea of negation is to take a given proposition, for example "Male" and convert it into everything that is not it ("Not Male"). In other words, it moves the focus from the element, to it's complement. At first, I didn't see any practical applications of negation. I thought, well if you negate a statement to evaluate it, it's the same thing as just evaluating the statement except it's complement. Boy was I wrong! I've realized, through trying to understand the readings in the course notes, that in some cases; proving the negation is FALSE is easier to grasp then proving that the original statement is true. It also relates directly to situations I've experienced while programming.

For example, I wanted to pop off all of the elements in a stack. The stack object has a pop method and an is_empty method. We can create a while loop and say: "while not stack.is_empty():" and proceed to pop items off of the stack. This is significantly easier to conceptualize and implement then trying to get the function body to run when the "stack has elements" .

I am excited to further grasp negation and implement it in my understanding of logic. Negation has helped me better understand the course notes, but to segue into a concept that has been the MOST beneficial to my understanding, I have to talk about truth tables!

The Glorious Truth Table

If a person were to find my notebook and flip through it, they'd be surprised to find endless amounts of truth tables (as well as some semi-phallic shaped doodles that are the result of sitting beside hooligans in class).

**Bonus Points for the implication?**

I love truth tables. I was once scared of truth tables and I feel like an idiot for not learning them sooner. What the venn diagram brings in spatial representation of a problem, the truth table brings in concrete undeniability.

They were an invaluable resource as I was trying to grasp the manipulation rules in Chapter 2. For every single one of the rules, even the intuitive ones, I created a truth table. This helped me internalize the manipulation rules in a way that I know I could not have done before. I plan on using truth tables whenever I am stumped by a statement.

We've gone over negation and truth tables, and their impact on my learning. Both are tools that have increased my logical comprehension. Join me next time where we will see if these strategies will help me take on Proofs!

First Entry!

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Professor Heap, TA's, and fellow classmates,

I'd like to formally welcome all of you to my sLOG! Through this blog, I will be sharing, with you, my trials and tribulations on my path to become a master logician! In this week's entry: weird symbols and problems with problem solving!

Weird Symbols:

{∀∃∩∪⊆⊄ℕΩ¬}: the set of all symbols that looked alien to me at the beginning of the course.

In highschool, "set notation"was a domain that I shyed away from at all costs. I remember in my gr.12 Advanced Functions class, our teacher introduced two types of notation. The first, set notation, seemed incredibly complicated. Being a disastrous combination of mindnumbingly lazy and extremely impatient, I decided I preferred the second type of notation, interval notation. You know, (0,5) or [0,5].

Like all vices, eventually my laziness and impatience would come back to haunt me. This time in the form of CSC165 and MAT223.

Immediately I felt uncomfortable with some of the symbols that were being presented to me on the lecture notes or in class. My main struggle wasn't so much in defining the symbol, but being able to convert between symbols and english - understanding and parsing problems. My good old friend Salman Khan over at KhanAcademy really helped me get comfortable with sets, sample spaces and the symbols we use to describe their relations in his "Statistics" stream of videos. Since then, I feel significantly more comfortable reading and understanding the symbols we use.

Problems with Problem Solving:

Part of what really attracts me to CSC165 (besides the fact that I need to take it to get into the subject POST) is that we examine the thought processes involved in breaking down everyday problems, and analyze them in a tangible way. I often take for granted the foundational principles that govern human reasoning. It became apparent, after the first lecture, that I was finally going to examine the core of what I have so vaguely labelled "common sense". This really appeals to me because I feel as though problem solving has been one of my weaknesses and I am ready to handle that aspect of my learning!

One particular tidbit that stood out to me was when Professor Heap (in the first lecture) advised us to write down the logical steps we are taking throughout a problem. He even told us to write down "I'm Stuck! this is why..." which I had never thought of before. I can honestly say that I have been implementing this strategy in my other courses (specifically CSC148 and STA247) and it's been working out amazingly! I've been able to greatly reduce the time I spend on any given word problem. In the past I may have started to work on a problem, read it again and realized that I interpreted it incorrectly. Now, I have a concrete and directional thought process that immediately points out any logical fallacies. I look forward to working on my problem solving skills as we move through the course!

Now that I've conquered the weird symbols, and have gotten a little bit better at problem solving, I hope to write again next week with the new challenges and victories I've made on my journey to "prove 'em all"!