Date: Sat, 1 Feb 1997 15:10:07 -0500
From: Alex Bogomolny
You mention that you are new to the net. From this I surmise you are looking for the Internet resources. Several sites stand out but each requires your active envolvement in the selection process:
You can all also start from my collection page where all of the above are listed: https://www.cut-the-knot.com/collection.shtml
If I may suggest this, let your students do the work. Organize a seminar where the fellows present topics and have discussions. To prepare for a 25-30 min talk should not take more than a couple of hours if you choose topics and material judiciously.
Now, how to select topics. With the present state of affairs, I would attempt to create a small library of good math books and use Internet as a supplemental source. The books I am going to recommend can be bought through my Bookstore (https://www.cut-the-knot.com/books/index.shtml) but this is not why I recommend them (I am getting 8% commission on books which are not a special order for which the commission is 0.) Books are more systematic and some of them became classic which is too early to say of any of the Internet resources.
I have several favorites:
- S.Barr, Experiments in Topology. A lot of hands-on activities with many different kinds of the Moebius strip and Klein bottle.
- R.Courant and H.Robbins, What is Mathematics? A huge part of math is touched upon. Fascinating experiments with soap films.
- H.Rademacher and O.Toeplitz, Enjoyment of Mathematics. 28 Essays on finest math topics.
- R.Honsberger, Ingenuity in Mathematics. Kind of a follow up to the previous one.
- H.Dorrie, 100 Great Problems of Elementary Mathematics, Indeed 100 problems with history and proofs.
These five will keep your kids busy for a good while. Try to find out which topics they liked more for a future follow-up. See if they like programming or have any penchant for it. Remind them I.Newton self taught himself by reading what he could find.
The main thing is that during discussions they should pose questions and, if anything was unclear, indicate what it was and why. This may serve as a suggestion what to look into next.
Let me know how it goes.