On Saturday, we got our first real tourist exposure to Portland. We went to the arboretum to see some massive trees, to the rose garden because Portland is the Rose City, and to one of the highest points in the city to see this:
In addition to being the Rose City, Portland is also known as beervana, so we went to a brewpub for lunch, after which was the real highlight of the day: Powell’s City of Books. Powell’s is a book store that takes up a full square block. The rooms are color-coded so you know where you are, and it takes a map to get around. The best part is that they carry both new and used books, which means you can find some great things if you have the time to look. I made a beeline for the math section, which was three full aisles of books. I had something in mind when I went there, and I actually got lucky and found it pretty quickly:
I don’t know how long the Schaum’s Outlines series has been around. This one was published in 1958. They still publish these books today, but the current editions pale in comparison to older editions. I have a Calculus edition that is 50 years old, and I’ve found some great, challenging problems that I’ve used over the years in my multivariable calculus class. I was hoping to find a similar resource that might prove useful in our upcoming work on integrated math, and this book looks like it will fit the bill.
Consider, for example, this question, which is one of the last ones in the section on ellipses: “Prove: The locus of the midpoints of the chords of an ellipse drawn through one end of the major axis is an ellipse.” (pg. 351) Compare that to this one, the last question on ellipses in the third edition of Schaum’s Outline of Precalculus, which was published in 2013 : “Use the definition of an ellipse PF1 + PF2 = 2a directly to find the equation of an ellipse with foci at (0,0) and (4,0) and major axis 2a = 6.” (pg. 1087).
The first question above is a challenging one, requiring an understanding of both the algebra and geoemtry of an ellipse as well as a more general familiarity with geometry. The second question is little more than a plug-and-chug question, one only a little more challenging to, “If AB + AC = D, and B=2, C=3, and D=6, find A.” It does require a geometric understanding of ellipses, but there is no request to prove any relationship, recall other material previously presented, or synthesize ideas anywhere.
While I understand why textbooks have moved from questions like the former to ones like the latter over the last fifty years, I think we’re really lost something in the process. I was thrilled to find this book, along with a few others, and I can’t wait to start finding some integrated math inspiration in them.