Math History on the Net

arXiv.org was originally designed to be a repository for pre-prints of physics articles, but it has since been expanded to other disciplines. I recently discovered that even though most of the math pre-prints are out of my league, there is one category of math articles that I have a good chance of understand: math history.

So if you want to explore mathematicians writing the history of mathematics, go here. (I found an interesting article on the solution of the Poincare conjecture in this haystack.)

The former historian in me has to point out, however, that for the most part, mathematicians writing history (of mathematics) is fascinating for the general “we are interested in math” audience. But historians will cringe at the teleology and absence of any culture in these narratives; they tend to be self-contained, internalist, and lack nearly everything that historians value in their craft.

There are really good historical works on mathematics written by mathematicians, I’m sure. But I guess I want to say that there are really good historical works on mathematics written by historians too. I would argue — from what little I’ve read in both realms — that these works by historians are often better, more considered, and more interesting. And the really good ones don’t skimp on the mathematics either, but delve deep into the mathematics, and relate the mathematics to culture.

A few from the top of my head:

Karl Pearson: The Scientific Life in the Statistical Age (Ted Porter)
Masters of Theory: Cambridge and the Rise of Mathematical Physics (Andrew Warwick)
Mechanizing Proof: Computing, Risk, and Trust (Donald MacKenzie)*
*Actually, this is a sociology of mathematics book.

Help? Multivariable Calculus!

I need help! GACK!

So I’ve decided that my one week of lazing about and reading (finished Middlesex and the teen novel It’s Kind of A Funny Story, and started Heat) is officially over [1]. It’s time to get to work!

A mere two hours ago, I hoisted the Multivariable Calc book that I’ll be teaching from next year from the pile on the floor to my desk and gave it my first run through. It looks okay [2].

I’m designing this course from scratch, and I wanted to ask for some advice for anyone who has taught it, or has ever designed a course from scratch…

  1. Anything — print or web resources, jokes, songs, videos, pictures? Also, it doesn’t have to be about multivariable calculus; any advice on how to design a really awesome course from scratch would be much appreciated! How long did it take you, what resources did you draw upon, did you make a general outline of topics or a specific day-by-day schedule, did you write your assessments beforehand or during the school year once you’ve gauged the students’ abilities, and the other million questions that I’m thinking of.
  2. Does you know of any good software for graphing in 3-D that is open source (read: free) and works on a PC? I know of SAGE, and OCTAVE, and the like, but I’m wondering if those programs are a bit overkill for this course. Is there something less bulky out there? Maybe even a really powerful 3-D graphing calculator that people like? 

    UPDATE: I just remembered that SAGE came out with the online SAGE notebook, which is what I think I’ll probably implement! It’s like MAPLE in terms of the command line, and it seems extraordinarily powerful. 
     

  3. How do you teach your students to graph in 3-D by hand? How do you do it on the board? SmartBoard?
     
  4. Have you ever taught a class with 3-5 students before? Do you treat it like a regular class — with lecturing but with more individualized attention? Or did you teach it seminar style? What would a seminar style math class look like?
     
  5. Do you have any good investigative activities or projects for multivariable calc? Or that you do in calc that can be extended?
  6. Have you ever just thrown out teaching from a textbook and used an online textbook? Or mixed and matched textbooks? Or taught without any book?
My big idea at the moment is to make a course with no exams. These are kids who are accelerated enough to have taken AP Calculus before their senior year. I want to expose them to the idea that math can be a big series of puzzles. That math can be investigative instead of regurgitative. That math can be collaborative. That math can be hard and challenging and rewarding if they persevere. And since we have a tiny class (maybe 3-5 students), this is definitely possible. So as I said, no exams. Instead, we’ll have nightly homework assignments with the more fundamental and basic questions, and then “problem sets” with investigative problems due at the end of each chapter. The problem sets can be worked on alone or with others, but the write-ups need to be done alone, and they will be graded on correctness and clarity. Who knows, maybe I’ll even teach them to use LaTeX (well, MiKTeX) to write up their solutions.

Hopefully I’ll use this blog to post about the evolution of the course design as the summer progresses… so don’t change that RSS reader!

[1] Other books that are lined up to be read this summer are Fight Club, The Kite Runner, and The Adventures of Huckleberry Finn (all for school); if I have time, I also want to read Lazarus’ Closed Chambers, Tartt’s The Little Friend, Dewey’s The School and Society and The Child and the Curriculum, Pais’ The Science and the Life of Albert Einstein, and finish up the second half of Gogol’s Dead Souls. 

[2] I’m using Anton’s Calculus, Early Transcendentals, 8th Edition. My school uses the first half of the book in calc classes and I don’t want to make my students buy a second book. My initial opinion: the book is okay but seems to be unnecessarily dense in places, and could have left a number of sections out. The exercises at the end of each section are quite good.

Delicious Linky Links

I’ve been doing a lot of “internetsing” in the past few weeks. Some things of note:

  1. Math Teacher Mambo’s “volumes of revolutions” project [here]
  2. A superduper awesome puzzle to give to your students when learning trigonometry: “explain this crop circle” [here]. If I gave extra credit, I would probably give it to the student who could explain the math encoded within it.
  3. Wordle [here] creates clouds from texts — text frequency. I love the idea for using this to create images for a English class website (different word clouds, different books), or for the cover of a dissertation or a book. I created the images below. Guess which books they are for? (I got them from Project Gutenberg.) An interesting English discussion could spring out of this type of word counting…
  4. SensibleUnits.com [here] converts standard distances and sizes to things we non computers understand.Example: 500 gigabytes is 17 dual layer HD DVDs, 160 Human Genomes, 62 Window Vistas Installation, 190 English Wikipedias (without images)
  5. For an English or History class, have students design a facebook page for famous authors, poets, scientists, political figures, etc. Look at this one for Einstein on DaleBasler.com [here].
More to come. Later.

Summer… yawn.

Ho hum. I don’t know what to do with my days, and I’m only really on day two. I tried watching TV this morning… Tyra Banks and Divorce Court just don’t capture my interest.

I can’t seem to read more than 10 pages of a book before I get tired of it. I’m in the middle of three different books now.

I suppose I should shower, now that it’s 1 o’clock. I think I’m going to go to my school campus to spend some time before I meet up with some friends at our local watering hole. Let’s hope that won’t be how I pass most of my time in the next few months.

Note: I do have a whole list of school related and non-school related things to do this summer. But it’s hard to take that first step… or in my case, scooch out of bed.

Boom de yada

Come on a digital journey with me

Stop 1: Watch this

Stop 2: Read this

Stop 3: Listen to this: click

Stop 4: Get the idea to make a derivative video and song about myself! Because I’m a narcissist! And it sounds like hella fun! Yeah! And heck, maybe I could show it to my class on the first day of school as an introduction.

Stop 5: Watch this

Take the truism about playing around with technology to heart: yeah, it’s fun, but if you’re going to use it in the classroom, make sure it’s for the students and not (only) for your own narcissistic pleasure… schools tend not to discriminate between good and bad uses of technology in the classroom… “you’re good if you use it, whether it results in student understanding or not”… don’t get sucked into that praise.

Stop 6: Seriously decide to learn how to deal with sound, images, and video. I want to go from having learned to do this…

…to get to someplace better, and to turn that into something teaching-&-learning related. Pictures and sound and videos are powerful resources. Not only do they have the power to make something more interesting, but they have the power to make something more memorable and understandable. Or at least get you to ask questions. Case in point, make the next stop.

Stop 7: Watch this.

Can’t get a better opening hook than that. (And you don’t even need to say anything.) You know how I know? Because I thought, as you probably thought, “Awesome,” followed by a “What the heck?!” and “How’d that happen?!”

Now all I need is a lot of spare time to fiddle around with my computer. And a video camera. And to get over my fear of seeing and hearing myself electronically.