We all have heard about how important is qualitative analysis of, e.g., differential equations, lest the numerical solution leads us astray. But have we heard any lecture on situations which defy calculus, and yet can be tackled by a modern computer? Of course, the Monte Carlo method. Anything else? If you can’t come up with anything else, read the book by Paul Nahin for a lot more.


The Symmetries of Things

This week’s book will take understanding of spaces to a whole new level. John Conway, Heidi Burgiel and Chaim Goodman-Strauss are bringing to the layperson (OK, I concede, to laypeople with some math under their belt) an amazingly beautiful topic: the relationship between topology and simmetry. Presenting the discrete groups with the orbifold approach is not only incredibly elegant, but also fruitful, the subject is thus richly connected with other math subjects. As usual I don’t want to clutter with my words and prefer readers to see the book. Only one final comment: most of the book does not really have math prerequisites in the technical sense, but it does require effort and concentration. It is certainly possible for a high-school student or even a younger child to study it, but it has to be someone who enjoys learning. On the other hand, this is the perfect book for those who love to study, but they truly love math because it’s beautiful.

The Shape of Space

I think the “book of the week” column has to start with a book by Jeff Weeks 🙂

We are going to talk here about an awesome book, The Shape of Space, and a dull book, Exploring the shape of space, a dumbed version for schools. Why schools have to be stupid places, it beats me, but anyway. In any case, get the dumb book and grab the included CD (not sold separately) for a great video interview, including Macs before OS X, and for some applets on multiconnected spaces. You can also, since you are at it, try out the nicest “activity”: design 2D living beings. Then, it’s time to study the real book.

The Shape of Space is by far the best resource for multiconnected spaces at elementary level. Nothing is taken for granted, the book even explains what a Klein bottle is. Including exercises of all sorts. Quit wasting time reading this review, and open the book. Super-recommended for anyone who can read: illitterate friends, get someone to read this to you.