Finally, the fall section in U of T ended. Many friends of mine highly recommend me to take CSC165. CSC165 is extremely useful in science course because it trains me how to think logically.
Topics in CSC165 were very new concept to me and they were broken down to:
1. Reading and writing with symbols
2. Logic
3. Proof techniques
4. Growth rate questions such as Big O, Big Omega
5. Counting steps of codes
6. Computable
Overall I really enjoyed learning new concepts in CSC165. It is really
well designed course with topics broken down which teaches you
mathematical reasoning and expressions step by step. Each topics, I had
to fully understand previous materials very well in order to understand
the next topic. Although it is CS course I recommend this course to
students who studies mathematics but with lack of proving skills.
Lastly, I would like to thank my prof. Danny Heap and my TA who helped me out to understand these materials.
Tuesday, December 2, 2014
Entry 9-Assignment 3
The assignment is due 1st December. The first four questions are not that hard and they are similar to the questions that Danny did in the class.
However, the last two questions are very challenging and hard. First of all, I have to decide whether to prove or disprove the statement. I pick the side of disapproval at first. I try to find two functions such that one does grow faster than and not grow slower than the other function. I try to find an equation that in some interval, one function is growing faster than the other; then in other interval, the one is growing slower than the other. Following this idea, I successfully find that trig functions fully satisfy my requirements. Now the questions becomes that how can I disprove the statement using the two trig functions, sinx and cosx.
I spend 1 hour to prove the negation of given statement. I realize the sin and cos are not good example. Therefore I give up trig function and try to come up with another examples. Trig functions are continuous functions, and one-piece continuous functions are hard to approach in this problem, so I try to find two-pieces functions that satisfy the condition.
Eventually, I find one!!!! Even though this question takes my 2 hours, I feel it is worthwhile！！！
However, the last two questions are very challenging and hard. First of all, I have to decide whether to prove or disprove the statement. I pick the side of disapproval at first. I try to find two functions such that one does grow faster than and not grow slower than the other function. I try to find an equation that in some interval, one function is growing faster than the other; then in other interval, the one is growing slower than the other. Following this idea, I successfully find that trig functions fully satisfy my requirements. Now the questions becomes that how can I disprove the statement using the two trig functions, sinx and cosx.
I spend 1 hour to prove the negation of given statement. I realize the sin and cos are not good example. Therefore I give up trig function and try to come up with another examples. Trig functions are continuous functions, and one-piece continuous functions are hard to approach in this problem, so I try to find two-pieces functions that satisfy the condition.
Eventually, I find one!!!! Even though this question takes my 2 hours, I feel it is worthwhile！！！
Entry #10 Reading my peers' slogs
I think this week's materials are the hardest ever. Danny introduced some terminologies such as computability, diagonalization, and .countability. I find these definitions are ambiguous and confusing.. When I read my peers' slog, I find that several people have same question as me. They also feel that the materials are challenging.
When I read Matt Cheung's slog, he gives some examples to distinguish well-defined functions from not well-defined function. I feel that it is very clear.
Danny said that well-defined functions have to be 1-1 and onto. The last two example violate 1-1 and onto respectively. Therefore, they are not well-defined function.
In the Lukas Frantzke's slog, he/she talked about his./her opinion about infinite loop. He/she mentioned that infinite loop is different from long running time. Sometime it is very hard to tell which one the program counters. Last year, when I took csc108, some program that I wrote took more than 3 minutes to run. In the beginning, I thought there was a error in my program; however, it eventually returned a value.
When I read Matt Cheung's slog, he gives some examples to distinguish well-defined functions from not well-defined function. I feel that it is very clear.
- well defined: x = {1, 2, 3, 4}, y = {a, b, c, d}
- not well defined: x = {1, 2, 3}, y = {a, b, c, d}
- not well defined: x = {1, 2, 3, 4}, y = {a, b, c}
Danny said that well-defined functions have to be 1-1 and onto. The last two example violate 1-1 and onto respectively. Therefore, they are not well-defined function.
In the Lukas Frantzke's slog, he/she talked about his./her opinion about infinite loop. He/she mentioned that infinite loop is different from long running time. Sometime it is very hard to tell which one the program counters. Last year, when I took csc108, some program that I wrote took more than 3 minutes to run. In the beginning, I thought there was a error in my program; however, it eventually returned a value.
Subscribe to:
Posts (Atom)