Thinking Outside the Box

My one true weakness in math. I guess that explains why I enjoy computer science more than math and logic. With computer science you generally understand all the instruments you have at your disposal when solving problems. As long you understand the commands you can give in your programming language, there won't be any crucial method or tool that you can miss that will prevent you from solving your problem. Computer science is pretty flexible in terms of solutions; while it not be super efficient at least your program can still work. Math for me at least not so much. Sometimes when an answer in given in class, I think to myself "there is no way I could have ever thought of that solution on my own". I just probably haven't even considered thinking that way in terms of solving the problem. For example regarding question 2 on the test, my mind was not analyzing the problem the way that the answer was given (the great Heap has tested me, and I have failed). Assigning delta as a function that uses epsilon never struck me, but I'll definitely catch that in the future. As I've said before, I really need to get into a mathematical mindset and estrange myself from interpreting symbols through language when they only just represent symbols. My main frustration with myself is when I am posed with something new and abstract, I just fall into this state of mind that I can't do it. I can't understand the problem because I'm not viewing from different perspectives or can't remember a useful equation. It's not until I actually see an answer that I perceive I can keep that mentality when dealing with a problem.
 
On the bright side I do believe that I am getting the hang of proofs, there's just a few things that I need to keep reminding myself. Like if the statement of a variable is actually posed in the statement that needs to be proved, one must prove somewhere that the variable is in fact an element of its set. Also it is very beneficial sometimes to bring in extra variables (I don't really understand where it would be useful though), setting up y' can help with proving a statement with y in it. But there are still some things I need help clearing up. If you're supposed to prove something such as  P(x) ^ Q(x), are you supposed to reformat the statement so it becomes an implication? Or are there other ways to directly or indirectly prove such statements?

Seriously Dude, Hear Me Out

Okay before you ask anything... wait why would you ask me anything, I'm a blog. Before you want to know what I thought about the test (though I have no idea why you would EVER want to care about that), I believe our supreme leader Heap is reading our minds (by this I mean blogs). While this may seem like a no brainer, he appears to be using the information against us. With this blog we write all our deepest math related secrets, aspirations and fears (sooo intimate). By effectively talking about all of our troubles and questions we have in the class, we have given him an extensive list of all our weaknesses. Thus he has the potential to pose questions on tests and assignments that will bring us to our knees in an attempt to break our spirits. I suspect this to be true because in one of my previous blogs, I was explaining my confusion over the interpretation of multiple quantifiers and the importance of their order when they are not similar. And to my chagrin guess what was on the test, a question that required the interpretation of multiple different quantifiers! The question was also very abstract in the sense that the symbols were nothing more then symbols. It would have been easier for me if they represented something or anything, but then I guess I wouldn't be able to suffer then (I could try to learn so I can fix my mistakes, but accusing people is a lot more fun). Complaining aside, I felt that the test overall was fair and I did well on most of the questions. I will however how to brush up on my understanding of quantifiers.  

Now that we're well into our way for solving mathematical proofs, I would like to see some general tips on how to understand how to solve the problem (so meta, but not really). As mentioned in the lecture slides, one thing we will have to master for writing proofs is understanding why you believe the thing is true. Welp, easier said then done. I personally see that sort of telling me "yeah in order to do well on a test just write down all the correct answers". I would really enjoy more specific pointers here and there. For example, something like think this way y mathematically when posed with x type of proof. I guess the only way to have serious improvement with solving proofs is to practice with them more. I should bring up some facts in the old dusty attic that is my brain, keeping facts on my mind such as odd natural numbers can be represented as 2k + 1. I feel it would also be useful if all these random math facts could be gathered and presented to us so the tools become more obvious for solving proofs. So basically I welcome any anything that makes it easier for us to solve these pesky proofs. I'M NOT A THERAPIST MATH SOLVE YOUR OWN PROBLEMS!!!

I Can't Think of a Witty Title

Just bare with me alright? I'm in my shorts sitting here waiting for my laundry to be done wondering what the heck I'm going to write in this soggy blog. One thing I didn't get (which won't be the last) was the example for why the order of different quantifiers matter. The whole enemy picking a specific region in a graph flew completely over my head. The math classes I've taken in university have not taught me anything about that kind of a definition of a limit, so I had no idea what was going on. I also have trouble considering quantifiers when translating to english, so I really understand how they differ in definition.

So I guess I don't have a good conceptual grasp on that sort of thing but whatever, I've got bigger things to worry about. Like oh dear Heap we're going to start actually doing proofs next week. So far it hasn't been too hard on me, I felt like I did well on the assignment (please have mercy T.A.'s), and I understand the content we've learned so far. I think that the proofs require a large leap in thinking processes if someone has never done them before. I feel that in order to do well one must have this certain spark of ingenuity and abstract thinking when it comes to math. I like math just as much as the other guy in computer science, but we have a strictly business relationship. I don't do math in my spare time or learn new things outside of what is required because I'm just not one of those people. So I'm a little worried that I wont be able to think understand what is required of me. From the steps for solving proofs given to us in the first week, I feel I'll just be stuck with step 1 with understanding the problem. Then step 2 is just figuring out a plan??? Yeah, easier said then done.

Scepticism aside, I felt good about the assignment #1 (mercy, I beeeggg you). That sense of ego was slightly deflated when looking at the answers, but I know that I got the gist of it. I did get confused with the translation from symbolic to english, and I probably will need some clarification but it was never like I didn't understand what was going on. If the  If the upcoming test is like the assignment and tutorial handouts, I will definitely be ready for it. This class is really interesting so far, but I shudder in anticipation of what is to come. May Heap have mercy on our souls.