sLog Week 5: You Want Proof?! You Can't Handle The Proof!

Hi everyone, my name is Anam Alvi and I struggle with doing proofs.
I understand the structure of the proof, but what I find the most challenging about it is figuring out the actual process of coming to the result - that is to say, "the rough work". I guess it's just more difficult for me to see the connection between the initial statement and the final statement. I'm not too sure on how to approach this situation other than to just...practice. I'm sure that with practice I will be able to make connections more quickly and intuitively, as is with problem solving in general. But surely there's more I can do, right? After some discussions with classmates and reading some tips online, I've come up with a short checklist of things to help guide me through the rough work of my proofs.

1. Do you have a clear understanding of what you are trying to prove?
2. Have you clearly written out all the given information (hypothesis) and the final result (conclusion)? Do this symbolically or in full sentences. 
3. Are there statements you can write that are 'widely known' (ie. 4 is a real number)? Don't waste time proving trivial things!
4.  Have you seen any similar proofs to this one? Is there a particular strategy to approaching this kind of proof?

...and from there, just be creative and use what you know.

I hope that with some rigorous practice over the next week, I can report back with better results for my next post! If anyone has any suggestions as to how I can perfect proofs (whether that be tips for problem solving, writing comments, or a general strategy that has worked out well for you), feel free to leave a comment on this post. Any and all help is appreciated!

See you in 7 days!

sLog Week 4: Obsessive Nature & Collaboration

     This week's main goal pertaining to this course was to successfully complete the first assignment due at the end of the week. At first glance, it didn't seem too time consuming...until I actually started doing it. Something I've started noticing about myself with this course is that I can't stand not completing a problem (or a set of problems). What ends up happening is that I'll work for as long as I can on the problem, but if I don't get the answer before I have to move on to another class or another assignment, I won't be able to get it out of my mind. In every second I can spare I'll find myself thinking about a different way to approach the problem or a possible solution. I have quite a lengthy commute to U of T that approaches 2 hours on most days, and more often than not I'll be working on any sort of 165 problem I can find or reading course notes. I'm worried it's becoming something of an obsession (if that's even possible with a course). Nonetheless, it helps me keep up with my notes and tutorials, so I'd rather be obsessed than lazy.

     The first assignment allowed us to work in groups of up to 3 students, which actually turned out to be my first group project in university so far. For the sake of minimizing our time together (we don't hate each other, I swear), we decided to do the entirety of the assignment individually and then come together and compare/discuss our answers. This proved to be a really good way of completing the assignment as we all got to understand the problem individually and then get feedback from each other on whether or not we were approaching it in the right way. We struggled the most with translating English to symbols with #1a, as well as drawing Venn Diagrams and differentiating between the different meanings of symbolic statements with #4b (who didn't struggle with #4?). With a lot of really intelligent discussion and brainstorming we eventually came to a consensus. I learned a lot from my group members about problem solving and communicating my thinking, and I hope they were able to take something away as well. Overall, we probably spent close to 4 hours working together, but it was definitely worth it and we all worked pretty well together.

Thanks for reading! See you next week.

sLog Week 3: Is This True Love?

This past week of attending lectures and tutorials for CSC165 was great. Learning the concepts of disjunction and conjunction was a little challenging at first, but I found that collaborating with my peers and discussing ideas clarified a lot of confusion. I learned a lot during my tutorial as well, and I could freely ask as many questions as I wanted, not to mention that I actually enjoyed the exercises. My favorite part of this past week, however, was definitely the folding exercise we did in Friday's lecture. I really enjoyed the experience of investigating a problem and using an analytic process to try and reach a solution. I found the tips given on the back of the sheet fascinating, and I loved how creative and out-of-the-box thinking was used to arrive at a solution (ie. writing out the sequence in a certain way to visualize a physical pattern). I've looked forward to doing CSC165 course work this past week, and I hope this course continues to peak my interest in a similar fashion for the rest of the semester.

sLog Week 1 + 2: Some Challenges

         What I found particularly interesting about this week's lectures was learning about logical implications and their restrictive meanings. I believe this is an extremely important concept to understand because it shows how careful one needs to be when working with logic problems (and in turn, with solving coding problems). It's easy to say "if you get a job in the field of computer science, then you'll be rich", but "if you're rich, then you must have a job in the field of computer science" is a false statement (counter example: Justin Bieber). Although this is a fairly simple sentence, it very accurately demonstrates the need for clear and meaningful statements. However, I quickly learned that it was significantly easier for me to understand these concepts when presented in easy English rather than symbols. I struggled quite a bit to keep up with the actual meaning of some of the expressions, as direct translations of the symbols seemed to make no sense. Realizing this, I knew I would have to spend much more time learning and reviewing the material than the time just spent in the lectures.

         My first step was to spend time daily reviewing Prof. Heap's annotated slides and making additional notes to the ones I had written, which was very helpful in reviewing and ensuring that I understood the class material. Additionally, I found that diagrams and other visual representations of the problems helped me solidify concepts and (quite literally) created a much clearer picture of the concepts for me. I also opted to go into Prof. Heap's office hours and seek further help. Prof. Heap not only clarified concepts but also made observations and gave me advice with my learning styles. He encouraged me to continue using diagrams and visuals to understand concepts, but to also focus on phrases and symbols to make sure I am clear on all levels. Finally, the class notes uploaded by Prof. Heap on CDF proved to be very detailed and helpful as well.

         Much of the material in CSC165 so far (universal/existential sets and quantifiers, logical implications, symbols using for denoting sets/phrases) has overlapped with material from MAT137 which I am also taking this term. Therefore, I'm glad I have a sufficient amount of resources and the learning skills to tackle the important concepts taught this week and last in CSC165.