EMM FAQs

By far, the most common type of query I get from instructors who use, will use, or might use Excursions in Modern Mathematics has to do with matters of implementation—how to organize and structure a course using the topics in the book.

In this post I will try to address some of these issues using an FAQ format. For starters, I will throw out my own ideas (based on my experiences, opinions, and prejudices) and hope that others will throw out their own ideas. Hopefully, we can get a meaningful thread going.

So, here we go.

Q: How many chapters should be covered in a semester (quarter) course?

A: My general rule of thumb is 3-4 class periods per chapter (I am assuming fifty minute class periods). Thus, in a 3-credit semester course (about 45 class meetings) I try to cover 12 chapters. In the past I have taught as few as 9 chapters, never more than 12. I don't think that covering all 16 chapters in the book is reasonable (the only reason the book has 16 chapters is to give instructors some choice).

Q: What are the precedence relations among the parts and among the chapters in each part?

A: Each of the four parts is independent, so the parts can be taught in any order. Within each part, the relations between chapters are more complicated. The following table summarizes my suggestions for each part. The columns show the suggested choices depending on whether you want to cover only two chapters, three chapters, or all four chapters.




Q: How do chapters (and parts) compare in their level of difficulty?

A: I feel that the most relevant source of information to answer this question is the aggregate opinion of the students in the course. At the end of each semester I give an exit questionnaire that includes several questions on the relative difficulty of the chapters–over the years, I have collected thousands of students' opinions on this matter. Here is a crude summary of what my students think (keep in mind that my students may be very different from your students):

(1) In ranking the difficulty of the chapters, Chapter 16 is considered the most difficult, followed by Chapters 4 and 15. The opinions on the easiest chapter are all over the place.

(2) Within each part, the last chapter in the part is consistently ranked as more difficult than the first chapter. This is true for all parts but the different is most significant in Part 4. (If you think of each part as a hike, each hike represents a slight uphill climb with Part 4 being the steepest climb.)

(3) When ranking the overall level of difficulty of the parts, my students rank Parts 1 and 3 as slightly more difficult than Parts 2 and 4, but the differences are not significant.

Q: Is there some significance to the fact that the book is organized into 4 independent parts with 4 chapters each?

A: While there is no compelling reason for a 4 by 4 organization, I like the flexibility that this format offers. In particular, I like the symmetry of having the same number of chapters in each part and the modularity of having four independent parts. For example, an instructor that wants to cover 12 chapters in a semester course can choose a 3 by 4 format (three chapters from each of the four parts) or a 4 by 3 format (full coverage of three of the four parts). The former approach offers a little more breadth, the latter a little more depth. I think that both approaches are consistent with the goals of a Liberal Arts mathematics survey course.

Welcome to the EMM blog

Welcome to the first post of the Excursions in Modern Mathematics blog. Why, you may wonder, a blog for a mathematics textbook? At the moment, I can think of three good reasons. One of my measures of the blog's success is how many other good reasons will surface after others have a chance to add their input.

Here are my three reasons:

(1) Once a book goes to the printer the contents of the book are set in concrete, at least until the next edition or, in the case of minor errors and typos, until the second printing. This is a problem for a book that places a premium on currency and relevance. I will illustrate how I will use this blog to get around this problem later in this post.

(2) In addition to updating information already in the book, I plan to use the blog to introduce facts, tidbits and resources that fall under the umbrella of "enrichment" of core concepts in the book. Typically these resources will be websites, videos or articles that I will introduce and, when appropriate, briefly discuss. In my second post I plan to start the ball rolling on this one.

(3) A blog can be a good place for networking– not as good as a social networking site but good enough for people to interact productively and share comments and ideas. As the book's author I have had some opportunities to hear from and interact with users of the book, but I would welcome much more sharing. The success of this aspect of the blog depends on you. I am hopeful that this blog will eventually take a life of its own and become a shared "meeting place" for all users of the book.

As promised, in this post I want to discuss a couple of substantive updates to information that went to press with the 7th edition and soon become dated. In one case the circumstances were foreseeable, in the other they were a bit of a shock.

Much to my regret, I had to submit the final manuscript for Chapters 1 and 2 in July 2008. Thus, by an accident of bad timing I was unable to discuss or even mention one of the most exciting presidential elections in U.S. history. My biggest regret is that I had to use the 2004 presidential election for the cartogram that illustrates the "real" Electoral College in the opening image for Chapter 2. Thanks to Mark Newman of the University of Michigan, a new cartogram with the 2008 Electoral College results (shown below) is readily available for anyone to use under the Creative Commons License (text and images may be freely distributed). I definitely plan to use it in my introduction to weighted voting and the Electoral College. To download the cartogram,
click here. In a later post I plan to discuss some of the other amazing cartograms produced by Mark and his team.
















The second piece of real-world data badly in need of updating is Example 10.4 on the ups and down of the Dow Jones Industrial Average. When I wrote the example the Dow Jones was at around 12,800. As I write this post, the Dow Jones is at 8,300. Had I known the stock market was going to tank I would have done Example 10.4 (plus a lot of other things) differently. When I cover Example 10.4 in class I plan to change the numbers to reflect current values for the Dow. And who knows, maybe by then 12,800 will be a current number again. That's a cheery thought!