week 8

This week I learned something about big-oh. Some proof about W_IS is hard. And we got the definition of O(f). it is also hard to find multiplier C and breakpoint B. we need lots of practice. My group finished the assignment 2 on the weekend. The proof of claim 1.2 is really similar to the proof of the limit of a function by using epsilon and delta. The proof of claim 1.2 may be the most difficult one. By drawing a picture of the function of the floor of x, it is easy to get the proof.

week7

This week I learned something about inference and sorting. If we know A and B, we can conclude A separately or B separately. if we want to disprove a statement, we need to prove its negation. By taking csc108 and csc148, I have learned lots of ways to sort like Bubble sort or selection sort. every way of sorting has its efficiency. Some ways are fast, some are slow. Also every way of sorting has worst case. After few weeks, I will get a better idea about big-ou and deeply know how sorting works. Sorting is very important in computer science. It can help people solving things with very complex function.  

week6

This week we still learned something about proofs.  Sometimes if the origin statement is hard to prove, we can disprove it. Sometimes we need to break down the statement. For example, ‘the floor of x is the largest integer <or= x’, we need to show the floor of x is integer, it is the largest and it is <= x. sometimes we need to prove by cases. For instance, ‘for any positive integer n, n^2 + n is even’, so we need to consider the cases where n is odd and where n is even. Proving is abstract and needs every step is reasonable. 

week5

This week went so fast. We did the term test and learned many ways of proving. The term test is not difficult. Some questions are very similar to the previous. Given some python Boolean functions, and work out the output. We were also given the question about negation. By doing lots of exercises during the tutorial, all of these are easy. The lectures of this week were mainly about proof. When we don’t know how to prove the origin statement, we could prove its contrapositive.

week4

This week I learned something about transitivity, the order of ‘for all, one’ and ‘one for all’, and proof. I thought that the order of the symbols ‘for all’ and ‘exist one’ does not matter before I took the class. After this week, I know this order is important, especially when we write some programs. Computers will give us different answers with different orders. Proof is always the hardest part. Just like the math class I am taking, the structure is important, and we need to know what we want to show. Proving takes long time to think and understand every step, and we need to make our proofs convincing. The tutorial of this week is showing the equivalence. Implication rules and DeMorgan’s laws are important. Every small symbol is important.

week3

This week I learned something about conjunction and disjunction, implication and negation. Conjunction means ‘and’, and we can consider it as ‘intersection’ in the set. Disjunction means ‘or’, and we can consider it as ‘union’ in the set. This part is not difficult to understand. The toughest part may be the negation.However, negation has some rules. For example, the negation of ‘∃ a∈A, …’ is ‘∀ a∈A, ¬…’. On the weekend, my friends and I finished the assignment1. It is not too hard to solve, but it took us much time. How to write the negation of the statement in English or symbolic form needed us to do a lot works. Some questions are easy with drawing Venn diagram. Csc165 is really an interesting course.

week2

This I learned sets, existential claim, how to evaluate claims, and implication. Some of them I have learned in my high school. Changing the claim into some sets or expressing by symbols is more convenient and easy. Sometimes drawing Venn diagrams is very helpful. For example, like what we did in this week’s tutorial, the answer will be obvious if we draw two sets which are python programs and test suites, and we only need to think about the meaning for each region. It’s my first time to learn the disjunction and negation. The most difficult part in this week may be how to express a sentence into some mathematical symbols. It is also tough to negate expressions. We really need to understand every word of the expression and pay attention to the words such as ‘all’, ‘some’, ‘every’, ‘less’ and so on. These will help us to solve the problem. Negating the expression is the most difficult part for me. After class, I searched that online and discussed with my friends to make it easier.  I enjoy doing proofs of universal or existential claims which is similar to doing some mathematical proofs. Finding the counter example or showing there is no counter example. The course material is very similar to what I learned in the math courses about the logic, sets. Computer science is always connected to mathematic. This class will help me do better in math courses by learning this basis logic concept.