homework for sept 30

In this reading we see that the Babylonians are using concrete words to substitute variables we have today. For a mathematical principle, one would have to use those words (such as ush for x, square for x^2) to represent the varaibles. “=” sign would be “Result” and any square root sign would be replaced by the word “square root”. An simple modern equation would be substituted by multiple steps described with words.

I believe that math is all about generalization and abstraction. without these, math would not be able to represent / solve real life problems. We take these problems and transform them into the “math” form and solve them(using mathematical rules) , then we take it back to the real world. Without generalization and  abstraction, we could not do this. 

For more abstract areas, such as number theory, geometries, calculus, graph theory, etc., it would be hard not to use algebra. If we don’t have algebra, number theory could hardly be represented, let alone calculus.... If we have a calculus course in which every symbol and every addition/equal sign need to be expressed by words, it must be real frustrating. How many steps are there supposed to be? We would never be able to conclude from these multiple confusing steps the final answer even if we could ever find a way to represent the complicated equation.