After reading other Carnivals of Math and hosting this one, I'm wondering if anyone feels there might be a need to have two Carnivals of Mathematics:
A Carnival of Mathematics for middle and secondary grades and
A Carnival of Advanced Math for undergraduate and graduate level as well as for the research mathematicians out there.
Another approach might be to have both a Carnival of Math Education (a category into which my blog might naturally fall) and A Carnival of Mathematics.
I may be way off here and outvoted by the vast majority of readers who may simply prefer to pick and choose the posts that interest them, but there does seem to be a clear demarcation between these categories (in the non-algebraic sense of course!). The Carnival may need to reach a critical mass before this would be practical but I'd be interested in your comments here.
With the above in mind, I will begin with math blogs that focus on middle and secondary grades...
jd2718 has a wonderful variation on the Four Fours Puzzle. He has an uncanny knack for taking a good problem and adding enough complexity to it to boggle the mind! This problem is still open-ended and waiting for more ideas...
Alane over at Math Notes demonstrates divisibility tests for 7 and 11 and provides easily understood explanations for why these rules work. Her other post introduces students to perhaps their first mathematical proof, the classic "irrationality of √2" by contradiction. To assess their understanding of indirect proof one might modify the problem to "Show that √3 is irrational."
In Patty Paper Trisection, Denise, at Let's Play Math, challenges her readers to prove that Math Trek's origami trisection referred to in Carnival #9 really works. Denise has an engaging writing style that invites her readers to challenge themselves. She sees math problems as puzzles, a view shared by many who have a passion for our subject. This post is designed for students and teachers in grades 7-12 as well as homeschoolers.
Murray Bourne over at squarecirclez offers us a practical application of semi-log graph paper in plotting the dramatic increase in the ranking of You Tube in just a year and a half. The vertical scale is equally spaced, marked in powers of 10 -- logs base 10 to the rescue! Students will eat this up! He also is promoting a fascinating change in standard math notation (thanks, Murray, for promoting the name of my blog!)
Mark D from the Universe of Discourse shares a recurrence form for binomial coefficients that is far more efficient than the traditional factorial definition. He suggests that this ancient relation (published nearly 1300 years ago) has not gotten the recognition it deserves. Since the last student project in my BC Calculus class focused on efficient formulas for approximating pi (Ramanujan's formula in particular), your post fit right into the discussion.
Vlorbik on Math Ed has a fascinating post on Textbooks and Notations.
He contends, and I concur, that current texts over-stress natural language (as in spelling out the meanings of symbols in English) for set-theoretic formulas, conditional probability in particular. My philosophy has always been to introduce concepts and formulas in colloquial language to which students can relate, then move on to the formal symbolism of mathematics as early as possible. Students need to appreciate the efficiency of symbolic notation and how it provides a universal language for mathematical discourse, not subject to interpretation! Once again, great justification for the name of my blog! I knew there was a method to my madness (aka, dumb luck!).
On the technical research side of mathematics we have a couple for you to digest...
The Unapologetic Mathematician writes about the importance of category theory for undergrad math majors. Categories have become significant in contemporary mathematics. For background, read the Wikipedia article on category theory.
Michi at Michi's Blog presents a technical piece in the area of homological algebra (If only I could recall anything Professor Dyer was trying to teach me in algebraic topology 40 years ago!). The posting deals with combinatorics and coding of a very important tool for his current research - looking at extended algebraic structures in group cohomology.
Michi also recommended Terry Tao's blog. I particularly enjoyed his Advice on Mathematical Careers.
And now for something completely different...
A monthly feature, Who's Counting?, on ABC News.com is authored by the internationally recognized mathematician and author John Allen Paulos. His specialties are statistics and logic but he is also well-known for the popularizations of mathematics he has written (Innumeracy, etc.). He is a Professor of Math at Temple University and he knows how to make math interesting and meaningful. Read through some of his articles from the past 2 years. There's considerable food for thought in these articles and enough material there for projects for Statistics/AP Stat classes for every month of the school year! Not to mention that it makes for fascinating reading. He is a gifted writer who weaves a beautiful web.
I want to personally thank all of our contributors who were considerate about replying by June 13th! Further, those who responded to my gmail account provided some fascinating insights about their passion for mathematics. I felt right at home...
There are so many outstanding math bloggers out there. I can never do justice to all of them. This Carnival is just the tip of the iceberg. One that I've recently discovered is Mathematics Weblog. The author has concisely summarized all of the Carnivals to date and his discussion of math humor is worth the read (he reviews books like Comic Sections and Mathematics Made Difficult). If the books are as humorous as their titles, they're worth looking at!
I haven't yet mentioned any of my recent postings on this Carnival as I wanted to celebrate others' blogs, not mine. However, I'm working on a way to introduce and develop recursive functions and linear recurrence relations for grades 7-12. It will be entitled --
"Take any number, Add Three, Divide the Result by -1. Now Repeat this!" I hope you will look for it and share your comments as we approach our summer break (for me, a more permanent break!). Also, all of those 'beautiful' mortgage formulas I've been alluding to in the series of posts on applications of exponential functions are now displayed as screenshots from the TI-84. Those posts have received many visits and I'm not sure if it's more for the math or more for mortgage advice (believe me, you don't want advice from me on that!).
Update: Submitted late but I decided to add it on 6-15:
An interesting brain teaser for the frontal lobes on SharpBrains. To solve it you need to analyze balance-scale relationships among 3 quantities (spades, clubs and diamonds). Some might try this mentally using logic, others may want to set up algebraic equations. Have fun!
Would you believe, another couple of late additions that I discovered in my web travels--
Best of the Web - Math Blogs
(Of course my blog didn't make the cut!!)
Not Even Wrong - A Random Collection of Stuff (a nice summary of some technical math blogs from a Columbia math professor I believe)
There's no end to this so I had better stop...
Stay tuned for our next Carnival on June 29th over at Grey Matters.