I was born in August 1946, in Washington DC, at the start of the post-WWII baby boom. I grew up in Silver Spring MD, just outside Washington, and attended public schools. I am the oldest of three boys. My parents tell me I was fascinated by math from an early age -- they say at dinner time I used to run into the dining room, hide under the table, and not come out to eat until I was given and solved an arithmetic problem -- but I have no memory of a special interest in math until later. I think it was around 7th grade that I read Gamov's book "One Two Three Infinity", the first part of which is about math. There I learned of the solitaire game Towers of Hanoi. Not having a set around, I made one by cutting different-sized squares out of the white cardboard backing inside my Father's shirts when (in those days) they came from being cleaned and starched at the laundry. I played Hanoi over and over with more and more pieces until I could solve it without a hitch for up to 10 pieces (1023 moves - same as our house number!).
Also, my 7th grade math teacher inspired me. He was disorganized and ignored the curriculum, but it worked for me. He taught the Euclidean algorithm for finding greatest common factors, and also how to find the volume of multi-sided pyramids. I remember calculating these volumes to maybe 10 decimal places and being quite excited. (Only much later did I realize my answers were inaccurate, since I had computed the factors to fewer places.) It was also in this class that I found I enjoyed, and was good at, explaining math to others -- other kids asked me because almost none of them could understand Mr Grant. From then on I planned to be mathematics professor (though I had no role models: my father was a lawyer, my mother a local elected official (later Treasurer of the State of Maryland), and other adults in my extended family were lawyers or businessmen, or in the case of many of my oldest relatives, immigrants without much formal education). In addition to the puzzle aspect of math, and my talent for it, I was attracted by the black-white certainty of mathematics in what otherwise for me was a grey and confusing world. Only much later did I come to appreciate grey, both outside mathematics and within it.
I went to Swarthmore (!), attracted by its small size, beautiful peaceful campus, and coeducation (the Ivies were still single sex). Actually, Swarthmore was my second choice. My first choice was Princeton. It too had a relatively small enrollment and beautiful campus, and I was willing to give up coeducation, and put up with Princeton's then snobby reputation, for its world-class mathematics. But Princeton rejected me.
I majored in math, though at times I was discouraged and thought of switching to philosophy, which became my minor. While I had been the best math student in my high school class, I expected to be just average at Swarthmore. Somewhat to my surprise, I found myself to be the best math student in my Swarthmore class ('67). Well, someone who was just as able chose economics instead, and in the year ahead was someone much better; he still is much better, at least as a research mathematician; Robert MacPherson became a professor at MIT, and now is a permanent member of the Institute for Advanced Study, and has won international math prizes.
I went straight to grad school in math -- at Princeton! But I went on Leave after two years. First, it was the Vietnam War period, and grad school deferments had been eliminated. Second, for various reasons I was an unhappy outsider at grad school. I ended up getting a job teaching math (and being a dorm master and coach) at the Phillips Exeter Academy in New Hampshire. This was a wonderful experience for me. I learned a great deal about teaching, had mostly exciting classes, and was happily busy with many activities.
After two years I returned to Princeton, switched from analysis- topology into the emerging math area of "discrete mathematics". This area includes some very old material, like counting arguments (permutations and combinations) and the Towers of Hanoi game I played as a kid, but it had only recently become a coherent field. I was fortunate to finish a Ph.D. in one year with an advisor who cared a lot that his students finish up and who shared his considerable perspective on the mathematics profession. (Albert W Tucker, one of the founders of linear programming and game theory, died in January 1995; I miss him.) Then I returned to Exeter for a year, next spent 15 months as a post-doc at the University of Waterloo in Canada (75 miles west of Toronto), and then came back to Princeton as an instructor and later assistant professor. Then in 1979 I was hired as an associate professor at Swarthmore.
For the first 6 years at Swarthmore I was also in charge of all high school competitions run by the MAA (Mathematical Association of America) In high school some of you may have taken or heard about these exams: the AMC10 and AMC12 (previously called the AHSME), the AIME, and the USA Math Olympiad. I've always liked both solving and writing problems, and I think one of my strengths as a teacher is choosing and creating instructive problems. (I hope it's a strength, because I spend an unusual amount of time on it.)
Another thing I did for two years was take a Leave and work as a program officer for the Sloan Foundation in New York. I solicited grant proposals for academic innovation and helped decide funding. In particular, I was involved with a Sloan program called The New Liberal Arts, where we encouraged institutions to promote the use of quantitative and mathematical methods throughout the school's curriculum.
I've always been very interested in teaching and general educational issues, and in recent years I've emphasized these interests much more than research - not a typical priority among professors, but more acceptable and less uncommon at liberal arts colleges than at universities.
My activities of the last few years fit this outlook well. During 2000-03 I had two jobs. 2/5 time I was a professor of mathematics, and 3/5 time I was the APIT - Associate Provost for Information Technology. As APIT, I helped coordinate the use of technology at Swarthmore and plan for its future. Technology is expensive, all of it is trendy, and some of it is good. At Swarthmore we want to find the technology that works best with our up close and personal approach to education and then commit the resources needed to buy it and use it well. To give a small example, I was involved with the introduction of the Blackboard Course Management Software that a great many faculty now use (though few as much as me!).
Then I had a year of Leave, and next I became Chair of Math/Stat. So now I teach 3/5 time and administer 2/5 time. Even being chair fits in with my interest in general educational issues (and seems to fit in with my penchant to be organized about things and generate lots of emails). Yes, a chair has to deal with (and save others from) a lot of nitty gritty administration, like budgets and overseeing the progress of all the majors. But a chair also gets to try to lead a department, and in my first year as chair I helped the department reach consensus on various curricular changes.
Anyway, I polished that handle so carefully that now I have been reappointed for another 4 years - with the first of them (07-08) a year's leave.
In my professor role, for several years leading up to 2004 my main goal, after teaching one or two courses each semester, was producing the 3rd edition of my Discrete Algorithmic Mathematics book; this was pretty much a full-time job during my 2003-04 Leave. For my coming leave I may get to turn to other projects that have been on the backburner. A general project of mine (following from my APIT days) is to help figure out how a college like Swarthmore can best make use of electronic resources like Blackboard. One theory is that online resources will make face to face education obsolete. But I think they can make the education at places like Swarthmore even more valuable, but allowing us to offload from the classroom everything except those things that a classroom does best. That sounds great, but what exactly does it mean, and does it work?
I also have other writing projects I can take off the backburner. I am the writer of a linear algebra chapter for the algebra 2 book of a new high school series (yes, a linear algebra chapter - well, more like vector and matrix algebra). That has to come off the backburner because there are deadlines. Other writing projects are a guide to writing mathematics for undergraduates and a "transition to higher math" book (getting students used to writing proofs and thinking like mathematicians). The former already exists (see the link on my website) but needs substantial revisions, and the latter exists only as problem sets. For research, intriguing problems sometimes come along that I can work on with students. I did some research several years ago on the game FlipSide (a "lights out" type game) with two students whom I was able to hire for the summer; this involved a nice use of linear algebra. But currently my ideas for writing and for curricular development interest me more than research projects with students (sorry).
Family. My wife of 25 years, Fran Stier, is an anthropologist turned actuary (insurance mathematician). Currently she works for AIG International, in Wilmington DE, overseeing their companies in Brazil. Earlier she dealt with Japan, and then with other parts of South America.
We have two sons, Leon age 20 and Aaron age 17. I am curious about how kids learn math (and other things) and I get to learn something about this through my family. When my kids were in elementary school (SRS, at College and N Princeton Aves, which is around the corner from our house), I helped out as a Math Dad, working on a weekly basis with kids from my sons' classes. In fact, during 1995-96 I was Chair of DIM ("Dimensions in Math") at SRS, and for several years I ran all their computers, bought and managed the math software, and taught kids and parents how to use it; DIM was fortunate to have a room for itself and a decent budget.
By nature I am a workaholic, but it was hard to be a workaholic when I had young kids and a spouse with a "real job" with long hours. Eventually our kids got old enough to take care of themselves for the most part, but then I had to drive them all over to various activities. Now one is a junior at Dartmouth, and if we are lucky, the other one will get into at least one college and we can push him out the door too. I've been able to get back to being a workaholic! Next year I can be an workaholic and travel too.
Somehow, as our kids were growing up, I found time, first, to be on the board for several years of the nursery school our kids attended (and many faculty kids attend), Trinity, and then to be president of the board for a year; and then for several years to be on the board of the local Swarthmore Swim Club, and be its president for 2 years.
Hobbies. I like hiking and racket sports -- I was the faculty squash champ one year in the early 80s -- but time constraints and a bad back kept me off the squash courts for several years. Just in the last few years I've ventured out on squash courts occasionally again, and played racquetball too (both at the Healthplex about 2 miles north of campus, where a lot of the faculty now work out), but with nowhere near the dedication (or skill) I once had. Mostly I swim when I can (lots in the summer), or ride my bike or exercycle, but not as much as I should.
I like writing essays -- maybe that's why I like email so much. (By choice, a fair amount of my professional writing is exposition and reporting as well, not research.)
I spend a lot of time on my computers. I like programming, including in TeX, a mathematical text formatting language, which allows me to get mathematics to look exactly the way I want. I like organizing things; getting first-year students into the right courses is largely a matter of careful organization and communication of information, which is perhaps why I volunteered to be "placement czar" before I became chair. I love the accessibility of all sorts of obscure information over the internet. E.g., I'm a train fan, and I've planned complicated rail trips in Europe with multiple transfers accessing schedules from my desk at home.
When I ask students for autobiographies, they write mostly about math in high school, since this is what is recent history for them. So perhaps it is appropriate for me to say a bit more about my high school days. I did do a fair amount of reading and thinking about math on my own. For instance, I bought the first book of problems from the AHSME and did all the problems. As early as 7th grade I got interested in the problem "How many ways can you win tic-tac-toe in n dimensions", which I believe I posed to myself. (In the regular 2-D game, there are 8: 3 horizontal rows, 3 vertical columns, and 2 diagonals.) I was very proud of myself for finding a general formula in terms of n. Some other reading I did was: Apostol's calculus (I heard it was used in honors calculus at Princeton; turned out it was used at Swarthmore too and I placed out of the first honors course - an honors version of Math 5-6 that no longer exists because students inclined to do honors work are almost all ready for 16); Allendorfer & Oakley "Principles of Mathematics" (still a fine book about mathematical thinking); and a book just then done by the editors of Fortune on the nature of modern mathematics. When I read a book, I tried to do most of the problems and, after the statement of every theorem, I closed the book and tried to prove it myself. This is still an excellent way to read a math book. It's slow, but in fact, in terms of understanding obtained per minute spent, it's probably the best way to read them.
On the other hand, I didn't go to any summer math programs. There are many more of them now, but there were some then. My 11th grade math teacher tried to interest me, but somehow I didn't see the point of it then.
I have prepared this autobiography because a student once asked for it in response to my asking you for yours. I was very pleased by this request. The more you learn about the adults around you, the more experiences you can draw upon in choosing your own future. I am usually pretty open if people ask. I'm also delighted to learn about you -- you bring a fascinating range of experiences to this College -- and I am therefore delighted to speak to you in person if you feel that writing your own autobiography is not enough.