Section 2 due on September 7

I do not understand the point of attempting to graph the unions between sets. Is it meant to be purely a visual representation of the concept of unions, or will graphs of unions play some significant role later on? I'd imagine it is probably the former, though I find that visual representations can provide an alternate way of viewing problems that can prove enlightening.


I find it very exciting and fascinating when I learn math that provides context for simpler math I learned at another point in time. For example,

"The set R2 = R × R is called the Cartesian plane. We view elements in this set as points {(x,y) : x,y ∈ R}."

This is a perfect example of the way the math curriculum simplifies math to make the basics easier to understand. Sometimes I think it is a good idea to simplify the content. After all, why would you learn about sets before you can add? Other times I wish I had been exposed to the "big picture" of math much earlier. When I was a senior in high school I began to witness this bigger picture behind math for the first time. That was ultimately what convinced me to switch from my plans to be a physics major. It makes me sad that so many of my peers will never see the bigger picture because they did not progress far enough in math. It makes me think that we need to drastically rethink the primary education math curriculum to ensure that all students have had enough exposure to math to truly understand whether or not they want to pursue it. Most of the math I learned up until my senior year of high school were merely tools for exploring more complicated subjects; they didn't even address the meat of the subject. (How on earth are you supposed to phrase that sentence correctly? Is "math" inherently singular or plural?)