Recursion and Introduction to Closed Form.

Now into weeks 4/5, We have began discussing recursion, which i was first exposed to in CSC148 last year, and actually did not have too difficult a time understanding (barring the Huffman Code incident).We began unwinding some sample recursive functions and a sorting algorithm Binary Sort, (i.e simplifying each run of the code into a recursive call),Then coming up with an inductive proof to substantiate our claims.Our first midterm is this Friday, and i am not as nervous as i normally am come midterm season ,because of the methodical strategy i have adapted this year with regards to the material covered in class as well as the assignments/problem sets.Finally, we began closed forms today, which in essence relates a recursive function to a closed(i.e some sort of power or simpler) definition and use induction yet again.Good luck on the midterm everyone:)

Principle of Well-Ordering

Well we are 3/4 weeks into CSC236, and we have already had 2 problem sets and the assignment due date is due soon.So far, i have been keeping up with the work by doing over the material the same day it was covered in class, contrary to what i used to do in 1st/2nd year(which contributed to sub-par grades).Coming back to new material being covered, we have learnt a new principle of sets known as the Well-Ordering Principle which states that any non-empty set has a smallest element,and have used in several examples such as a round-robin domino tournament.So all in all, things are still smooth sailing at this point, let's hope for more of the same:)

Week 2(Problem Set and Assignment#1)

We are now 2 weeks into the csc236 course, and are now covering more techniques of induction,and writing up proofs for problems that utilize these rules. Complete Induction uses the fact that it is assumed to be true for a set of elements ranging until n-1,and using that Inductive Hypothesis to show by virtue of implication that P(n) is true,thereby concluding the P(n) holds for all n.Problem set 1 was a review of simple induction, and was relatively easy to finish.Assignment #1 still looms, although i have developed a proof for the 1st question, so i'm getting there slowly.The fear i have with respect to these assignments is that i will miss some small detail,seemingly insignificant at the time, but ultimately crucial when push comes to shove.So wish me luck,and good luck to all of you on the Assignment/Problem Set.

Beginning CSC236

Since i took two very math intensive courses during the summer break, Calculus 2 and Linear Algebra, my grasp of the mathematical notions is still quite fresh, so when i stepped into the classroom for CSC236, i anticipated a substantial jump from CSC165,but i would be able to cope with it. So far, my premonition has not been falsified.The course began with an introduction to simple induction proofs, utilizing quite basic,but essential mathematical ideas such as partitioning of sets into subsets, multiplicative axioms,and algebra.The proof structure from 165 remains in use thus far, but the rigidity has so far not been as stern as it was then.We have recieved our first 2 homework assignments of the semester, and i am eager to sink my teeth into both to determine the exact nature of my understanding of early 165 concepts.