Join My GA Math Book Club

Last two GA math books, and the next one on my list. Oh, and my accordion. What hobbies I have...

Last two GA math books, and the next one on my list. Oh, and my accordion. What hobbies I have…

Reading is a vice for me—I can lose hours, nights of sleep, whole weekends in novels. Often I read non-fiction to keep from getting so  sucked in, and mostly that means general audience (GA) math. Everyone who has read many GA math books would probably agree that some are not good. It can be hard to strike a balance between including enough math to say something substantial and being willing to lie or speak generally enough for the book to be understandable. I think it may be really hard to do this perfectly for a truly general audience, which is the dark secret of some of these books—they are very difficult or impossible for non-mathematicians to understand, though they try very hard to be perfectly accessible and take great pains to explain concepts in non-frightening terms. However, if you are not used to reading math this can still be very dense, and who but a mathematician would care much about these topics anyway? So these books are often not good for a general audience, but perfect for someone with a PhD in a different area of math. No complaints here, as that audience is me. Presumably many writers, and certainly their publishers, want to reach more people; for example, at least undergraduate math majors. Good GA math books are actually perfect for undergraduate math majors, and I often find myself loaning out my books to students. Most are not returned.

I read two GA math-related books this fall that in fact reached much farther than the math world: Hidden Figures, by Margot Lee Shetterly and Birth of a Theorem, by Cedric Villani. These books both escape the GA trap in different ways. Hidden Figures is the true story of black women mathematicians working for NASA beginning during World War II (in case you’ve been under a rock and haven’t heard about the movie that is coming out soon). This carefully-researched book introduced me to a part of mathematical history that I had no idea existed. Many of the “West Computers,” as they were called, had originally pursued mathematics for joy, as they did not need to learn much higher mathematics to teach in high school, essentially the only mathematical path available to black women at the time. I loved reading about the pride that these women took in their work when a path was finally opened to them at NASA. I also had no idea of the major role that they played in many of NASA’s achievements, and the difficulties they faced down in the process.

How does Hidden Figures avoid the GA problem? By including very little math. Several physics/aeronautics ideas are generally explained, but it doesn’t contain a single equation. That makes Hidden Figures a truly general audience book, with additional interest for mathematicians. Which is great. I didn’t learn any math here, but I learned a lot that is relevant to my life as a mathematician, and really my life as an American, or a human in this time. Math is essential to this story, if only as the medium for these women’s undeniable awesomeness. Because they were doing math, there was some limited sense in which their correctness and in the end their contributions could not be denied. The answers were right, and the rockets flew. The importance of their contributions, however, is still being fully understood, and this book plays a big part in that.

Birth of a Theorem is in some ways a total contrast. It is the story of Villani and his collaborator Clement Mouhot’s proof of a fantastic result in mathematical Physics, after which Villani won the Fields medal in 2010, told through Villiani’s journal entries, emails, some mathematical and historical interludes, and many pages of just plain really hard mathematics. Villiani talks about his work with passion and self-awareness. He is not at all condescending in describing what he does—he explains things in a way, but also doesn’t expect to teach the reader everything. In fact, I didn’t understand much of the math from Birth of a Theorem.  If you already knew a lot about this area, perhaps you would.  But even as he uses all kinds of mathematical terms without definition, they take on the character of foreign language passages in a novel—you really don’t have to understand to get the feeling of it.   He describes the many horrifying setbacks and surges of joy that come with trying to prove something hard. He describes his favorite music and his favorite theorems with some of the same devotion. It seems to me that Villani is totally obsessed with math, in the same way artists can be totally obsessed with art. It’s basically about creativity at a really high level, in the form of mathematics.

I loved reading these books in sequence because it juxtaposed incredibly different paths in mathematics: Villani, already a world-famous mathematician before winning the Fields medal, now a figure in French popular culture and writer of a book with blurbs by Patti Smith and Nassim Nicholas Taleb. The West Computers, just now being discussed at all, 70 years after they started at NASA.

To bring it back to undergraduates, I think these books could start a really good student discussion on what it means for mathematics to be important, and how we value people’s contributions to math. There are also great GA books out that do teach a lot of math along with the stories; for example, Journey through Genius by William Dunham, and The Code Book, by Simon Singh. So many big ideas in (and whole areas of) math just don’t fit into most undergraduate programs. Books like Hidden Figures and Birth of a Theorem don’t really teach much math, but do teach a lot about math culture, which is also very difficult to bring into undergraduate math classes but could give our majors a much greater sense of being part of a community. This leads to one of my current dream courses to teach: Math Book Club. This is not my idea; I heard about it from Dr. Amy Ksir, who teaches a wonderful Math Book Club class at the US Naval Academy. I sat in on her class and was really impressed.  At the end of the semester, students write up book reviews and submit them for potential publication. After talking to Amy, I started to think about my own version, which I want to develop as a course sometime in the next few years. In my dreams, Math Book Club would help students expand and fill in their pictures of the general mathematical world, as well as have these discussions about what math means.

What would you read in your Math Book Club? How do you share the broader world of math with your students? Please let me know in the comments!



Posted in books, math and art, math in the media, minorities in mathematics, Uncategorized, women in math | 2 Comments

No Electioneering Beyond This Point: Teaching stats in an election year


Election Day by Richard Yuan on Flickr, used under CC BY-NC 2.0

Election Day” by Richard Yuan on Flickr, used under CC BY-NC 2.0

This certainly was an interesting semester to teach intro statistics. My students analyzed poll data, linked to in detail on realclearpolitics, to see if jumps were statistically significant, explored the correlation between the way different states vote, and analyzed the dependence of different demographic variables or responses to opinion poll questions on preferred candidate in polling crosstabs. We talked about why online polls are unreliable, how to check the accuracy of pollsters, and how important it is to look at averages and long-term trends in polling. And after the election, once the dust settled, we talked through some of the reasons why things didn’t go the way a lot of people had expected. Those discussions continue every week or so as new information appears.

I harped on my view of the importance of voting in all my classes. I showed how few young people vote, and why it’s important for them to be registered in their new home state. I linked them to the voter registration form (we can do it online in Maryland), voting guides, ways to find their polling place, early voting hours, everything I could think of. More than a few of my students said they don’t vote despite all this, but I know I got a lot of others registered and engaged for the first time.

Through it all, I tried my best to be impartial, not even disclosing who I intended to vote for. But c’mon, look at me up there: I’m a hipster-y woman in my 30s with a Ph.D. It doesn’t take a social scientist to take a pretty good guess as to my political allegiances. One student asked who I was voting for in a contentious local school board election, and I told them, along with my reasons for my choices, but never went further than that.

I’m not sure exactly why I felt the need to act so impartial. I even start my stats classes every semester with an activity, adapted from Dave Kung, where the students take one data set and use it to argue for multiple different conclusions. I emphasize the inherent uncertainty of statistical analysis all the time: pretty much everybody’s got an angle when they’re trying to prove something, and if you dig hard enough you can almost certainly find numbers to back up your side, even if they don’t hold up to scrutiny. I teach my class how to p-hack, so they’ll know how easy it is. And they know that type I and II errors are always lurking, and you’ll never know when they’ll come out to bite you. But I do believe that I am in a privileged position there at the front of the class, and I’d like for my influence to come only through my math instruction, and not overt moralizing.

In Tuesday’s class though, I did have to lay my cards on the table a little bit: between the allegations of election fraud from the left, and voter fraud from the right, I felt obligated to dig in. I went through the results of Nate Cohn’s regressions on Wisconsin, showing that there’s no evidence of a difference between paper and electronic ballots once education level and race are accounted for. I said that I thought it was irresponsible to even appear to allege electoral fraud with no evidence. And it was unconscionable for a president elect to claim voter fraud with no evidence, and terrifying that he would propose stripping of citizenship for speech. I know I got a little passionate during this part of class, and a few of my students did too. I’m not sure if any of them thought I went overboard – guess I’ll find out in my evals.

In tomorrow’s class we’ll unpack the study cited for the prevalence of non-citizen voting and maybe talk about the effect of education level on precinct results. I’m sure I’ll keep it more buttoned-up tomorrow. But like my colleague said so eloquently, sometimes you’ve got to say something.


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Saying Something

I took this the morning of November 8 because the Schuylkill river was so exceptionally still and peaceful. I was walking to the train station and looking across the river towards UPenn. The feeling in the city has changed dramatically, with many protests occurring in Philadelphia in the days since. UPenn as well as my own campus have been sites of acts of intimidation in the last weeks.

I took this the morning of November 8 because the Schuylkill river was so exceptionally still and peaceful. I was walking to the train station and looking across the river towards UPenn. The feeling in the city has changed dramatically, with many protests occurring in Philadelphia in the days since. Both UPenn and my own campus have been sites of acts of intimidation since the election.

I said nothing to my students this week about the election outcome. I just had no idea what to say. I was (and am) a strong supporter of Hillary Clinton. I know that many of my students and colleagues were also. Campus was subdued and literally dark on Wednesday the 9th, as it poured rain all day and many people in the Philadelphia area were dressed in black. My classes don’t meet on Wednesdays, but I wondered how my students were doing. Some of them were certainly very let down, fearful, and upset. Many are far from their families and some don’t have good networks of friends at college. What was the atmosphere like in the dorms? I have no idea. Once again I realized that though I feel like an integral part of the University where I work and spend many hours, in some ways the students live in a world apart.

On Thursday things had lightened a little—it was actually sunny outside, for one thing. I thought and thought about what to say to my classes. They are fairly small, and I know many of the students well. I like them a lot and I think that we have really good relationships, with lots of trust and respect. I have strong political beliefs. I also deeply value my relationships with my students and do not want to alienate those who vote differently from me, of which I know there are a few. I’m sure there are things I could have said to try to bridge the gap between the disappointed and the victorious, but as I looked in my heart for the right words I found nothing. Perhaps I myself was too disappointed. I mostly forgot my disappointment and enjoyed teaching on Thursday, as I almost always do, and I tried to be extra kind to my students. I felt that they were also being extra kind to me.

Racism and sexism are real forces in America. It is easy to think of campuses as idyllic places where these forces are held at bay. On the contrary, our students and campuses are at the center of these larger cultural conflicts. Locally, a group of over 100 black first-year students at the University of Pennsylvania received hateful racist texts on Wednesday, apparently from another college student at the University of Oklahoma. At Villanova, we received an ominous email on Saturday from our University President about “reports of members of our community using our nation’s political process as a justification for behaviors and language aimed to intimidate or humiliate other people.” This email seems to stem from an incident reported by the Philadelphia Inquirer in which one of our black female students was knocked to the ground by other students who were shouting “Trump! Trump! Trump!” This was reported on my own campus, where I have the highest regard for our students, and where I have only witnessed positive interactions among students.  This has happened since I last taught, and I am left again thinking and thinking about what to say.  I have not figured it out.

Huge racial, gender, and class disparities exist within our field, despite the fact that no mathematician I know would ever intentionally discriminate on these bases. STEM education is a social justice issue. We need to consider the disparity in numbers of women and other underrepresented groups at all levels of math, to read and debate studies about issues like stereotype threat and bias in evaluations, and think about the implications of having some groups fall behind in math in a world where STEM skills are essential to so many well-paying jobs. Academic mathematics is often perceived to be a meritocracy, in which case the numbers send a message about the relative “merit” of various groups. Math is at the center of this national discussion. This month’s issue of The Atlantic asked Why So Few Women Mathematicians? Last week’s episode of Radio Lab, entitled The Voices Inside You, discussed the work of Claude Steele and others on stereotype threat and its effect on black and women students in mathematics.

While my students may face these issues in their own lives, many have never heard of stereotype threat, had a discussion about implicit bias, or considered how strongly academic and math achievement is linked to opportunity (in both directions: more opportunity means more achievement, more achievement means more opportunity). These are issues that I believe have a place in the mathematics classroom, because the classroom is one place where these phenomena are occurring. As a professor, I have the honor of providing definitions, ideas, data, and analytic tools to my students, and helping them to ask questions and form conclusions about the world. That’s my job. I have no desire to convert my students into similar-thinking minions or to treat them differently based on their political views. I do have a strong desire to give them the information and scientific/critical frameworks to make the best informed and reasoned decisions possible, both for themselves and for the larger world. I still do not know what to say to my students about this election, or maybe more importantly about this recent reported incident on my campus.  I want to tell them that I care about and value all of them, that we need to treat each other with respect, and that we all belong here–this is our university, our community, our world.  However, I have not yet found the right words.  I am their math teacher, how can I start this conversation? Perhaps there is a conversation that begins with math and leads to all of these difficult, important places.  Or perhaps it starts with me saying simply that I care about them, and leads to how math matters in the world.  In any case, I am strengthened in my resolve to talk with them about how larger social issues can play out in the mathematics classroom, and how what happens in math classrooms affects all of our lives going forward.

I would like to emphasize that the views here are my own and not necessarily those of the AMS. I would also be very happy to hear everyone’s opinions on these issues in the comments.

Addendum:  I did finally say something to my class.  I had to write it out on paper first, because I knew I would need that crutch.  This owes something to the comments on this blog–thank you to everyone who shared there, please continue to share your experiences!  Anyway, here is what I said:

“Three years ago I moved across the country and left my family and friends behind to come here to Villanova, and do exactly this: talk to you about math.  I am not Catholic, but I believe deeply in the values that this institution espouses: love, truth, and unity.  I believe in respect for all people. in loving and caring for one another, for reaching out instead of walling ourselves off from others.

“I also care about and believe in you guys.  Not just because you’re my students, and not, despite what I just said, because of anything institutional.  Because you are beautiful human beings, alive, just as I am, lit by the same flame.

“Last Thursday, I didn’t say anything to you about the election.  I will tell you now that I was bitterly disappointed by the outcome.  I was saddened, and worried that so many of you and others in America would feel afraid, devalued, and pushed out–truly marginalized–by this outcome.  I believe that most people who voted for Donald Trump did so with no hateful motivation.  I believe that most people who voted for Donald Trump would not want this to happen.  However, reports of people across the country, and on our own campus, intimidating and disrespecting others while cheering for Donald Trump have been deeply painful and damaging, both to those targeted and to our entire community, which is left poorer and more divided for these acts and words.

“The fact that acts of intimidation have been reported on our campus breaks my heart, and I am compelled to speak now so that you know that I do not condone, and will do anything in my power to stop, acts of cruelty, hate, or disrespect.  I don’t care who you voted for.  I care about you.  If you feel afraid, pushed out, or disrespected, I care about that.  I am here if you want to talk.  If you voted for Donald Trump but you despise acts and words of hate, I care about that.  I am here if you want to talk.  At a University, we have the great privilege and honor of being around people who are not like us in many ways, who come from different backgrounds and have had different experiences.  This is an incredible opportunity for us all to grow as people and to learn about the world.  Veritas–knowledge, truth–is right here.  Will we stay walled off, or reach out to each other?  We truly have nothing to lose and everything to gain by treating each other with kindness, compassion, and respect, now and everyday of our lives.

“Freedom of expression is the most basic of all our freedoms.  Peaceful protest is a truly patriotic act.  If you feel moved to protest, I support you.  If you support Donald Trump and want to express that respectfully, I support you.  In fact, I urge you to start a Trump voters for love and kindness movement.  But above all I ask all of you to bend over backwards to be peaceful and non-violent.  Please be passionate, please speak up about your beliefs, but please be kind to each other.  Thank you for your time and attention, today and every day.”

Then, to bring it back to math, I showed them The Parable of the Polygons, by Vi Hart and Nicky Case, kindly posted in the comments by Anne Ho.  Thanks again for sharing.

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