exam

I was looking at the past exam posted by the proof, and i was wondering if anyone had any tips of how to approach these exam. :) i'm not scare with counting steps in code as long we dont have to use summations, proves. im not too sure about questions like the graffiti in robart's library. i was also wondering if the TAs where gona have a review session
   

Diagonal Problem

Problem: find the number of squares crossed by the diagonal on a (m x n) grid.
Plan: 1) draw lots of examples to make the relationship between diagonal and grid more noticeable
         2) write common findings across examples
         3) study the differences between examples
         4) make a hypothesis
         5) test hypothesis and try to disprove it
         6) look for special cases and divide the results
carry out plan:
           m = columns
           n = rows
           t = number of squares crossed
     
 this is the table of results:
         m / 1 / 2 / 2 / 2 / 3 / 3 / 3 / 4 / 4 / 4 / 5 / 5 / 5
         n / 1 / 2 / 3 / 4 / 3 / 4 / 5 / 4 / 5 / 6 / 5 / 6 / 7
         t / 1 / 2 / 4 / 4 / 3 / 6 / 7 / 4 / 8 / 8 / 5 / 10 / 11

special case: when ever m = n  then t = m = n 
when ever m or n is even: then t = 2 ( the smallest of m or n)
 when ever both m and n are odd: then t = 2( the smalles of m or n) + 1

in conclusion there is a special case where m = n then t = m = n, the general case is where either m or n is even then t is two times the smallest between m and n. If both m and n are odd then t is two times the smallest between m and n plus one.

assignment 3

I find that using limits really reflects the true understanding of a limit and how to interpret them, what i dont get is the format in which we have to structure the proof using the limit. the indentations and the information given by the limit is hard to match the indentations and what information should we make clear from the limit definition.

Big O and Big Omega

I do not understand why im finding this material a lot more challenging than anything else, I understand the concept behind Big O and Big Omega, but I have problems trying to find the ns, bs, and cs for each proof.

Test 2

I found this test to be pretty easy, the first two question were the basics we learned and practised in tutorials and in class. the third question I found that it was really testing our knowledge and our capabilities to put everything we have learned together, even though I found it challenging, I believe this type of questions really pushes us to fully understand the material.

Assignment 2

I found this assignment very helpful, and re-assuring of our capabilities to use the material that we learn in class, I found that it really made us understand and practice. The only question i had great difficulty understanding was the last question   GCD, even though it makes sense make up the contradiction, I found that without the TAs help or the profs help i would never have been able to come up with the proof.

Counting Steps

I dont get how to count steps!!!
I understand how it depends on the size of the array, but when it comes to over estimate so that all the terms have the same variable is very confusing.
It seems like we just manipulate it so that it works!!!