Week 1

  This week I learned the importance of mathematics for all Computer Science applications. In order to make compelling and interesting programs, mathematics is required. From artificial intelligence, to graphics, mathematical applications are needed (i,e, probability, linear algebra, and geometry).
      I also learned about precision and ambiguity in computer languages. I learned that computers are not only extremely precise, but they require a certain type of mathematical precision. (By mathematical precision I mean a certain type of precision where the meanings of the words put into the program are restricted.)  Then, I learned about the relationship between human language and computer language, and how they translated into one another. Professor Zhang managed to include both human language and computer language into his examples with python code and Venn diagrams, which helped me understand the relationship between the two aforementioned elements better. I also learned how human language has an adequate level of precision and ambiguity (or intuition) to help us solve problems effectively.
     I then learned about more problem solving with quantifiers. First, Professor Zhang gave us useful steps to follow in order to solve problems effectively. These steps include: Understanding the problem, trying more than one plan, executing the plan, and then reviewing the plan by convincing a doubtful peer. I then learned about universal and existential quantification, their respective symbols, and how to prove and disprove each statement (To prove universal quantification: Prove that all elements in the domain satisfy the quantification, to disprove show one counterexample that does not satisfy the quantification. To prove existential quantification show that there is one example that satisfies the quantification, to disprove show that all the elements of the domain are counter examples that do not satisfy the quantification.) We did a few examples with a table of employees that had different salaries to demonstrate both types of quantification and their vocabulary. Vocabulary words that correspond to universal quantification are: all, every, or any word that describes the entirety of a population (ex. male and female.) Vocabulary words that correspond to existential quantification are: Some, there exists, at least one, where not all members of the population correspond to the quantification.
      I enjoyed the examples Professor Zhang included in his explanations this week, since not only did they apply to real world situations, but they were also humorous. I particularly enjoyed the problem where two people meet on the street, and one is trying to figure out what the ages of the other person's children are. We solved this particular problem algebraically as a class, assigning values of x,y, and z to each child and using inequalities. This showed me the importance of problem solving with mathematics not only in computer science, but in day-to-day situations.  I found this problem compelling, and the humorous aspect of its presentation decreased my anxiety caused by not grasping the entirety of the information being presented.
     I initially found using the universal quantification and existential quantification symbols in problems slightly challenging, which led to a slight frustration, but as did examples of a class, I started to grasp the material. Currently, I feel confident about the material covered this week, but in order to remember the information I will review Professor Zhang's slides and the course notes throughout the rest of the week.
   There were no tutorials or assignments due.