November 28, 2014 - Week 12
The end of the semester has finally arrived. Only one more assessment left for this class. The truth is that this is course is probably one of the most difficult courses that I have taken this semester. Reflecting back to the first weeks, I was hopelessly lost with concepts such as "if...then", "unless", and "if and only if". Now we are finishing up with the course. This week we were discussing counting and induction. I was extremely confused with the concept that that was shown in class. Although there were many similarities such as the the base case, I was confused with the multitude of for-all and there exists that existed in the statement. To me, it look like the course was repeating itself and had many differences with what I had already learned in MAT137.
We also discussed the idea of diagonalization. The professor showed us that it is impossible to count all the outputs; therefore it is imperative that we apply induction to generate a hypothesis so that if it work for n = k + 1 then it will work for n = k. Sounds counter intuitive right? We are basically assuming the thing we want to prove and using it to prove for k + 1 greater.
Although this resembled the proof statements found in MAT137, after looking at examples, I still had no clue what was occurring. Guess that is what studying is for before the final exam is...
Thank you for sticking through and reading my posts. Until next year.
Tuesday, 2 December 2014
CSC165 - Week 11 - Wrapping things Up
November 22, 2014 - Week 11
This weeks lecture mainly focused on halting and reviewing the big Oh, Omega definitions.
The end of the semester is finally approaching. Time to wrap things up and study for final!
This weeks lecture mainly focused on halting and reviewing the big Oh, Omega definitions.
We
then defined the terms "well-defined" and "computable".
What I learned:
What I learned:
- reduce a function F to another function G, by returning G in the definition of F, then we get two implications:
- G computable => F computable, because if we can compute G, and F can be represented with G, then F is computable, and
- F non-computable => G non-computable, because if F is non-computable, there is no way of writing a G that is computable, since F can be written with G.
- to prove something is non-computable, we just have to reduce a non-computable function, in our case, halt, to that function.
CSC165 - Week 10 - Solving Problem with Big Oh!
November 15, 2014 - Week 10
This week we began to apply calculus to the big Oh notation. I was completely confused by the 2 statements listed below.
It was only after I realized that the limit definition is considered to be a know statement was I able to substitute the fact that f(n)/g(n) < e = c into the big Oh definition. After realizing this, I was able to the proof for assignment 3.
This week we began to apply calculus to the big Oh notation. I was completely confused by the 2 statements listed below.
It was only after I realized that the limit definition is considered to be a know statement was I able to substitute the fact that f(n)/g(n) < e = c into the big Oh definition. After realizing this, I was able to the proof for assignment 3.
Looking at this students slog: http://ilikecakecsc165.blogspot.ca/, I was able to understand taking limits with big Oh. I completely agree with his/her approach to the problem and in many way it resembled what I had done in the picture above. We both understood the meaning of what it meant to be bounded by another function and to use the definition of limits to satisfy a big Oh statement.
I would like to thank this fellow student for making it more clearer for me with his detailed slog post. I completely agree with his approach to the problem.
CSC165 - Week 9 - Finally! Midterm Confidence!
November 8, 2014 - Week 9
I took midterm on Wednesday and I was confident that I had done well. Unlike the first test, where I had uncertainties about various questions, I left the test centre feeling that I knew how to do all the questions before hand. However, all this fortitude belongs to the posting of assignment 2's answer key. Although I had completed the assignment, I felt that there were still many situations in my proof that I had left out or ambiguous. I was happy to note that the what I had done on the assignment was directly implemented on the term test.
The main issue for me was that I felt that the assignment had a big jump from the course notes and the lecture slides. Without any physical references to questions, I felt that I was doing some statements without a single idea of its meaning. I would find it more helpful to have full solutions to a multitude of proving questions instead of relying on assignment 2 and the term test to teach me the material. I like to learn when I have the sample questions with me when I prepare for terms test or complete an assignment. That way I would be able to learn the material through the sample questions instead of "making stuff up" on the assignment.
I took midterm on Wednesday and I was confident that I had done well. Unlike the first test, where I had uncertainties about various questions, I left the test centre feeling that I knew how to do all the questions before hand. However, all this fortitude belongs to the posting of assignment 2's answer key. Although I had completed the assignment, I felt that there were still many situations in my proof that I had left out or ambiguous. I was happy to note that the what I had done on the assignment was directly implemented on the term test.
The main issue for me was that I felt that the assignment had a big jump from the course notes and the lecture slides. Without any physical references to questions, I felt that I was doing some statements without a single idea of its meaning. I would find it more helpful to have full solutions to a multitude of proving questions instead of relying on assignment 2 and the term test to teach me the material. I like to learn when I have the sample questions with me when I prepare for terms test or complete an assignment. That way I would be able to learn the material through the sample questions instead of "making stuff up" on the assignment.
CSC165 - Week 8 - Big Oh Confusion???
November 1, 2014 - Week 8
This week we began to learn about big Oh notation and counting steps. I was extremely confused about the big Oh notation that was defined this week. To me the notation resembled a much more complicated version of the epsilon-delta proof that I did in MAT137. However, after going over carefully in the course notes for CSC165, it made me recall what Professor Heap explained in class that the big Oh notation simply represented "one function being bounded above by another." Like the epsilon and delta proofs in MAT137, I had trouble finding "c" and "B" values that would satisfy the statement.
The main worry of this week was that I had Assignment 2 due, which was quickly followed up with a term test. However, I quickly discovered that studying for the term test was much more relaxing than completing the assignment. I found it really difficult to work by myself on the assignment 2 due to the fact that I still had some trouble with the setting values for the "there exists" part of a proof. To me, I found it really frustrating that I couldn't do any parts of the proof except for the outline.
This week we began to learn about big Oh notation and counting steps. I was extremely confused about the big Oh notation that was defined this week. To me the notation resembled a much more complicated version of the epsilon-delta proof that I did in MAT137. However, after going over carefully in the course notes for CSC165, it made me recall what Professor Heap explained in class that the big Oh notation simply represented "one function being bounded above by another." Like the epsilon and delta proofs in MAT137, I had trouble finding "c" and "B" values that would satisfy the statement.
The main worry of this week was that I had Assignment 2 due, which was quickly followed up with a term test. However, I quickly discovered that studying for the term test was much more relaxing than completing the assignment. I found it really difficult to work by myself on the assignment 2 due to the fact that I still had some trouble with the setting values for the "there exists" part of a proof. To me, I found it really frustrating that I couldn't do any parts of the proof except for the outline.
Monday, 27 October 2014
CSC165 - Week 7 - The Penny Problem and Birthday!
2014/10/25 - Week 7
This Saturday is my birthday! I am finally 18. Even though it was my birthday, I still decided to do my slog today.
This week we got another exercise that we were about problem solving and how to approach a problem.
After going through a few examples, I found myself using hint 3 to approach my counter examples to show that there is a case (0,64] such that the above steps would not yield 48 pennies.
This Saturday is my birthday! I am finally 18. Even though it was my birthday, I still decided to do my slog today.
This week we got another exercise that we were about problem solving and how to approach a problem.
After going through a few examples, I found myself using hint 3 to approach my counter examples to show that there is a case (0,64] such that the above steps would not yield 48 pennies.
CSC165- Week 6 - Part Marks are Given! Yes!!!
2014/10/18 - Week 6
Thanksgiving!!! There was no classes on Monday, which meant that we only had to classes to further my concept on the different cases to approach a proof. The classes on Wednesday and Friday went over the concepts of proving again.
However, I was still able to get something out of the week's lecture. I learned that when I am working on a proof, I don't have to write the entire proof from top to bottom. Instead, Professor Heap told me that it is better to write the assumption and the conclusion first before writing out the middle of your proof. This way I am still able to get part marks for writing the correct assumptions.
Thanksgiving!!! There was no classes on Monday, which meant that we only had to classes to further my concept on the different cases to approach a proof. The classes on Wednesday and Friday went over the concepts of proving again.
However, I was still able to get something out of the week's lecture. I learned that when I am working on a proof, I don't have to write the entire proof from top to bottom. Instead, Professor Heap told me that it is better to write the assumption and the conclusion first before writing out the middle of your proof. This way I am still able to get part marks for writing the correct assumptions.
CSC165-Week 5 - Midterm Madness
2014/10/11 - Week 5
This week was our CSC165 midterm. I had spent all weekend doing past midterms and was happy to see that this years midterm was extremely similar to last years. Over, the past weeks, I have slowly seen the overlap between proving in CSC165 and the epsilon-delta proofs in MAT137.
What I got out of this week's class was how to prove statements using:
Direct Proofs:
Proof by Cases:
Proof by cases at first seemed to be just providing examples to show that the statement is true; however, I later realized that all the cases were extremely broad and were able to cover all the cases that might be used. This furthered my understanding that this way of proving is very situational because it relies on the fact that I am able to consider all situations.
This week was our CSC165 midterm. I had spent all weekend doing past midterms and was happy to see that this years midterm was extremely similar to last years. Over, the past weeks, I have slowly seen the overlap between proving in CSC165 and the epsilon-delta proofs in MAT137.
What I got out of this week's class was how to prove statements using:
Direct Proofs:
Proof by Cases:
CSC165-Week 4 - Introduction to Proofs
2014/10/04 - Week 4
This week was when Assignment 1 was due. To be honest, I only started doing the actual work for on Monday of the the same week. For assignment, I was extremely confused with question #4. However, after looking through the lecture sides I noticed slides that went over the work to disprove a statement while keeping the other true. After that I was quickly able to draw my conclusions with the Venn Diagrams regarding implication, conjunction, and dis junction.
In class we learned about bi-implication, transitivity, mixed quantifiers. However, I was only really interested by the proof analysis. After doing so many epsilon and delta proofs in MAT137, I was curious to see what the proof write-ups look like in CSC165. At first, I was confused about the layout of the the generic and tedious step-by-step processing of the proof, however, I later realized that by thinking of the proof set up as a basic "If....Then..." statement, all the logical processes fell in to place.
This week was when Assignment 1 was due. To be honest, I only started doing the actual work for on Monday of the the same week. For assignment, I was extremely confused with question #4. However, after looking through the lecture sides I noticed slides that went over the work to disprove a statement while keeping the other true. After that I was quickly able to draw my conclusions with the Venn Diagrams regarding implication, conjunction, and dis junction.
Monday, 29 September 2014
CSC165-Week 3- The Folding Problem
2014/9/27 - Week 3
The main topic for today's lecture was how to look at a problem before starting to try and solve it.
The paper folding exercise helped further this concept. By writing down the the folds in the notation of "U for up and D for down",
After thinking about the process in which we were told to fold the paper, I was able to recognize a pattern. Since we were always told to fold the paper down the middle, then there must be a correlation if not hint that pointed us towards the middle of the up-and-down list.
Here is what I found:
After analyzing the data, I noticed that the second half of the folding process is a carbon copy of the line above with the addition of an extra D in the middle, separating the inverted first half.
In total, my group was able to find 3 different patterns in this exercise; however, only 2 of them were we able to write a python function to represent our findings. Referencing to http://brendannealslog165.blogspot.ca/. From this pattern, we were able to generate a python code that embodied the entirety of the folding pattern that we noticed in class.
From this we were able to realize that the only way for us to write the code was to follow the problem solving steps. Had we not realized that the wording in the question, we would not have discovered the hint about folding the paper down the middle and finding the middle of the pattern.
The main topic for today's lecture was how to look at a problem before starting to try and solve it.
- write down information given
- relate this to another problem
- look at question in parts
- resolution to assumption instead of assumption to resolution
The paper folding exercise helped further this concept. By writing down the the folds in the notation of "U for up and D for down",
1
|
D
|
2
|
D D U
|
3
|
D D U D D U U
|
4
|
D D U D D U U D D D U U D U U
|
After thinking about the process in which we were told to fold the paper, I was able to recognize a pattern. Since we were always told to fold the paper down the middle, then there must be a correlation if not hint that pointed us towards the middle of the up-and-down list.
Here is what I found:
Folds
|
Pattern
|
1
|
D
|
2
|
D D U
|
3
|
D D U D D U U
|
4
|
D D U D D U U D D D U U D U U
|
After analyzing the data, I noticed that the second half of the folding process is a carbon copy of the line above with the addition of an extra D in the middle, separating the inverted first half.
In total, my group was able to find 3 different patterns in this exercise; however, only 2 of them were we able to write a python function to represent our findings. Referencing to http://brendannealslog165.blogspot.ca/. From this pattern, we were able to generate a python code that embodied the entirety of the folding pattern that we noticed in class.
From this we were able to realize that the only way for us to write the code was to follow the problem solving steps. Had we not realized that the wording in the question, we would not have discovered the hint about folding the paper down the middle and finding the middle of the pattern.
Wednesday, 17 September 2014
CSC165-Week 2 - Logic = Illogical?
2014/09/17- Week 2
CSC165 started on September 8, 2014. My first math course in University took place at Sid Smith Hall.
I was troubled by the True/False statements when the professor introduced the concept of "P(false) => Q(anything)" yielding a true statement. I always thought that if the antecedent was false, the statement would yield false. However, my question was quickly answered by my MAT137 lecture in which the professor gave an interesting example:
In addition, I was confused by the python codes that were listed on the lecture notes. The problem stated that we had to comment on the functions given: q0, q1, q2, q3. However, I did not understand the meaning that was enclosed by the triple quotations. Later on in CSC108, the professor promptly went over the docstrings, which solved my dilemma about the "... ->bool" statement. This statement is used to evaluate True/False statements.
I was troubled by the True/False statements when the professor introduced the concept of "P(false) => Q(anything)" yielding a true statement. I always thought that if the antecedent was false, the statement would yield false. However, my question was quickly answered by my MAT137 lecture in which the professor gave an interesting example:
"1=0 I am in love"
In the statement above, even if the antecedent is false, the statement will still yield true. The truth table furthered my understanding of "If....then..." statements by simply organizing the 4 cases into a table.
| P | Q |
| T | T |
| T | F |
| F | T |
| F | F |
In addition, I was confused by the python codes that were listed on the lecture notes. The problem stated that we had to comment on the functions given: q0, q1, q2, q3. However, I did not understand the meaning that was enclosed by the triple quotations. Later on in CSC108, the professor promptly went over the docstrings, which solved my dilemma about the "... ->bool" statement. This statement is used to evaluate True/False statements.
Tuesday, 16 September 2014
CSC165 - Week 1- The Introduction to Reasoning
2014/09/15
My First Blog Post!!!
This marks the beginning of my CSC165H1 F course with Professor Heap. In all honesty, I was pretty nervous about this course since it was something that I had never done before. Courses like CSC108 and MAT137 did not bother me due to the fact that I was pretty confident in my calculus and programming in C. For this course, I did not know what to expect. Hopefully, everything turns out fine and I would be able to understand the material of this course.
Good luck to everyone and this marks the beginning of my slog posts for CSC165H1 F 2014.
My First Blog Post!!!
This marks the beginning of my CSC165H1 F course with Professor Heap. In all honesty, I was pretty nervous about this course since it was something that I had never done before. Courses like CSC108 and MAT137 did not bother me due to the fact that I was pretty confident in my calculus and programming in C. For this course, I did not know what to expect. Hopefully, everything turns out fine and I would be able to understand the material of this course.
Good luck to everyone and this marks the beginning of my slog posts for CSC165H1 F 2014.
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