In the mood for a good brain workout? Well search no farther! The fourth installment of the Carnival of Mathematics has arrived! Just look beneath the fold for some first rate math blogging:

Over at Universe of Discourse, Mark Dominus gets us started with some wise words about Bernoulli Processes. Also have a look at this post, in which continued fractions are employed in the service of the age old question: How old are you, *really*.

Then move over to Fightin’ the Resistance of Matter for a heavy-duty post on homological algebra, from sirix. Brought back some bad memories from my topology qualification exam in graduate school, but well worth a look anyway.

Dave Marain of MathNotations has a fascinating post on the evolution of a difficult standardized test math problem. Math and evolution? My kind of post! See also his post on Geometry and Reasoning. Much food for thought.

Matthew Paulson of Getting Green runs the numbers on whether it pays to become an IBO (Individual Business Operator), of Quixtar. His conclusion: probably not.

Praveen has some advice for evaluating roots larger than the square with the Unix Basic Calculator.

Laurie Bluedorn offers some advice about teaching mathematics to young children, over at Trivium Pursuit.

The Geomblog discusses order polytopes, a beautiful connection between combinatorics and geometry.

Having trouble keeping clear on all of the separation axioms in point-set topology? Juan M. Bello Rivas comes to the rescue with this nifty diagram.

Brent Diggs of The Ominous Comma points to some fascinating, math-inspired artwork. Worth having a look just for the amusing graphic at the top of the blog!

Michael Tang weighs in with this fascinating post on the problem of finding the last two digits of 3^{1000}. Lot’s of good number theory in this one. He also offers this post about the axiomatic method, and this one attempting to lay out the axioms for Christianity. I’m not quite sure if that last one really counts as math blogging, but it makes for interesting reading nevertheless.

David Eppstein of Livejournal discusses how to visualize the space of linear threshold functions. Very cool pictures in this one.

Michi’s Blog poses some questions in algebraic topology. Also have a look at his elegant introduction to representation theory.

Charles Daney of Science and Reason introduces some basic ideas from abstract algebra. You might want to read this one before tackling Michi’s post on representation theory.

The Unapologetic Mathematician, aka John Armstrong, discusses the mathematics behind the Rubik’s cube. Fascinating stuff.

After all of the hard work of those last few posts, Denise of Let’s Play Math offers up some lighter fare in the form of some amusing math quotes.

Finally, FoxMaths reports on the results of some numerical invesitgations.

Thanks to every one who contributed! I have not received word yet on who will be hosting the fifth installment of the carnival, but I will post that information as soon as I have it.