Recursion Formulas

I'm currently studying for the first term test in 236. I'm not sure if Danny is going to include some questions regarding recursion formulas. I believe the focus of this test is to determine our ability to apply the basic rules and properties of mathematical induction. If that's the case, then there is a good chance that some recursive methods may show up since they are basically applications of the properties we learned. So I'm gonna study as much of it as I can.

Like simple and complete induction, recursion requires you to look for patterns between cases to create a general formula and prove it. However, I've noticed that these patterns can sometimes be difficult to see. I think the main reason for this may be the fact that a pattern doesn't always take the form of an equality. Many of the examples from previous weeks require us to find and prove equalities. Recursion requires you to look at questions differently. Right now, I still have the tendency to look for an equality. So I take a bit longer to figure out recursive patterns than I would others. I'm confident that I will be able to perform this kind of induction. After all, the concept is still the same. It's just going to take a little getting used to. That means I've got a lot more studying to do if I want to feel confident about writing the test.

Assignment 1 Reactions

Finally, my first post; and just in time. I just returned home from school after finishing and submitting the first assignment for this course. After struggling with the formal write -up of question 2, both my partner and I agree that it is is lot more confusing than we had anticipated. We found an algorithm for the menus and we knew what we had to do to prove that it works. The difficult part was transforming our ideas into a proof that is mathematically sound and that makes sense the first time it's read. I'll admit we would have had an easier time if we had just proved our findings in plain English. Personally, I kind of prefer to use mathematical language and symbols within proofs whenever I can. I don't know. I guess first year Calculus has sort of brainwashed me. At least no one can say I didn't learn anything.

Speaking of learning, Danny explained to me a way in which I can combine English with mathematical language to help explain difficult concepts or operations in proofs. Basically, you just create your own symbols. For instance, in question 2, my partner and I needed to write a set in reverse with a new element added to each of it's existing elements. This is an operation for which there is no notation. So, under the permission of Danny, we made our own notation. We just created an operation, A for instance, and explained what it does in English. Once established we were free to use the operation like we would use any other mathematical symbols. Problem solved. I don't know how we would have finished the write-up of this proof without this technique. This is definitely something I'm going to want to use again.