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!!!

Exercise 5

This weeks exercise has been the most challenging!!!
I understand the proof structures but i find really challenging to come up with the in between part, specially when it seems so obvious or when we have to use precise definitions.
I found the first question to be really helpful to check basic understanding of proofs.
The second and third questions where a bit more challenging but i liked that it gave us the chance to disprove something in  the right format instead of just presenting a counter example.
What i have not been able to fully understand was question number 4

test 1

The test was really fair for what i was expecting.
For the first part i think list comprehensions are a good way to demonstrate ones abilities to read and understand code as well as to understand the logic behind them. I got confused with the or statement, and by accident treated as a and. I also found a little bit hard to visualize the inputs and outputs for P(x).

The second part was a little bit unexpected, I was lucky to be taking mat 137 and work my way through it. Epsilon Delta questions are always challenging.

Part three was sooo easy that I mixed up the terms, I think i got it right the first time, but i found that as i reread them i started doubting my self.

Assignment 1

I found the assignment to be relatively fair. I find translating from English to logic harder than the other way around, and so for the first part of the assignment was a bit challenging. The second part although it was hard to translate from English to Logic, I found going through the first part really helped me to understand the second part. Part three was fairly easy as i got the hang of translating. Part four was the most challenging as i found that it was easy for me to get confused about which one was being implied or implying the other. I think this assignment really pushed my understanding of the concepts learned in class.

Exercise 2

part one question f, was a mind blowing solution for me, I now see the close relation between logic and linear algebra.
 second part of this exercise, since we haven't learn truth tables and i can't think of another way to solve this questions!!!

First Week

This week we learned how to translate English sentences to logical mathematical expressions, I find this very challenging. I find that the tutorial quizzes and exercises are very helpful, specially when the TA allows us to share different answers and explain our logic.

CSC165

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