The Bumps I Hit in the Road
    The first part of the text that takes me three more reviews to consume is the terminology through all sections. Although I’ve learned those fundamental ideas in high school, I do not know their corresponding vocabularies in English. I have to look them up and link those terms to the existing knowledge I have in mathematics. Here are some of those words I’ve looked up when I studied through section 1.1 to section 1.5: trigonometry, quotient, polynomials, exponential function, logarithm and so on. Among them, there is one word that confuses me the most – conjugate. The definition of conjugate given on the website is “change the sign in the middle of two terms” (“Conjugate,” n.d.). For instance, when we have an expression x^2 – 2, the conjugate of this expression is x^2 + 2. It’s difficult for me to understand its meaning because, in Chinese, we don’t even have a term for this idea when we learn it. We only know when to use this method to solve some math quizzes like the practices we do to simplify different quotient in order to remove that h from the denominator. The word, conjugate, becomes not only a new word but also a new concept to me.
     The second part of the text that I read more than four times is the definition of a function in 1.3 Introduction to Function (Stitz, C. & Zeager, J., 2011, p. 43). The first time I read this definition I couldn’t understand what each x-coordinate matching only one y means in the graph. When I had this confusion, I tried to draw several graphs with some random points to understand how it looks like when an expression meets the definition of a function. Also, the text introduces the Vertical Line Test (Stitz, C. & Zeager, J., 2011, p. 43) to help students determine whether a relation is a function or not. I found this method very useful and handy. All I need is get the graphs of relations and draw a vertical line to see whether it crosses more than one point on the same vertical line. After several graphs and practices on the exercise quizzes in the textbook. I gradually grasp the meaning of the definition of a function.
    I also have some hard time when I learn the ideas of what a function is and how it looks like in the Cartesian Coordinate Plane. I work as a software engineer, and one of the programming languages I use the most, JAVA, has a concept of method which someone calls it function, too. Similar to the function we learn in the text, the methods in JAVA also have inputs and outputs. However, if you give an input to a method in JAVA, it’s possible that you might get different outputs. This phenomenon violates the definition of a function in mathematics. I found I cannot use the same concept to comprehend both the methods in JAVA and the function in math. Although the concepts of functions are different in math and JAVA, the definition of set is quite the same. A set in math does not list duplicate elements and the order in a set does not matter while its counterpart in JAVA also follows these rules, too. When I realize this connection, it helps me understand the content of the text and also gives me a deeper understanding of the meaning of a set in JAVA.
References
Conjugate. (n.d.). Retrieved from https://www.mathsisfun.com/algebra/conjugate.html
Stitz, C. & Zeager, J. (2011). Precalculus. Lakeland/Lorain, OH: Lakeland & Lorain Community Colleges.
words: 565