Showing posts with label Michael Starbird. Show all posts
Showing posts with label Michael Starbird. Show all posts

Friday, February 28, 2014

MAA Books Beat: Collapse and Distillation

Written by Steve Kennedy, MAA Books Beat is a column written for MAA FOCUS. Collapse and Distillation appears in the February/March 2014 issue.


Collapse and Distillation


Things fall apart–but why? And how? Perhaps it is mere anarchy loosed on the world, but Charlie Hadlock has other ideas. In Six Sources of Collapse, published last year by MAA, Hadlock describes a half-dozen mechanisms that lead to collapses that seem abrupt.

He begins with the humble passenger pigeon. Two centuries ago North America was, literally, aswarm with passenger pigeons. In 1813 Aubudon observed a flock that obscured the midday sun and took three days to pass. Alexander Wilson once observed a flock that he estimated contained more than 2 billion individual birds; that is eight times the current estimate for the world’s total rock pigeon population. A single nesting ground near Sparta, Wisconsin, covered 850 square miles and housed an estimated hundred million birds. Flocks were so thick that folks hunted by swinging a stick in the air and picking up what came down.

It seems hard to credit that we hunted such abundance to complete extinction. (The last known passenger pigeon, Martha, died at the Cincinnati Zoo in 1914.) Hadlock explains the mechanism as the blank and pitiless result of evolution–the birds had evolved to live in enormous flocks. Their reproductive success depended on that, and these gigantic flocks were well adapted to a completely forested eastern United States. A flock of half a billion birds could denude and befoul a patch of forest in a few days, then move on to the next patch. Human settlement and forest clearing limited the available resources for this behavior. The combined effect of thinned forest and thinned flock (from a tide of hunting) led to dramatic population collapse.

Friday, October 25, 2013

Annie Selden Reviews Distilling Ideas

Annie Selden reviews Distilling Ideas: An Introduction to Mathematical Thinking by Brian P. Katz and Michael Starbird as part of MAA Reviews. 

The authors of this book, as they explain in their first chapter, are taking readers/students on a journey — one that will “add new, powerful inquiry skills” to a student’s repertoire: abstraction, exploration, conjecture, justification, application, and extension. The book is clearly intended for inquiry-based mathematics courses. It is replete with explorations to undertake, definitions to explore, and theorems to prove, but there are no sample proofs or answers.

The book has five chapters, with the middle three chapters on graphs, groups, and ε-δ calculus constituting the bulk of the book. To me, it is clear that any one of these middle chapters by itself has the potential to be used for an entire one-semester course. There is really enough material in the ε-δ calculus chapter for an introductory junior level real analysis course. Similarly, the group theory chapter gets to Sylow’s Theorem and has more in it than most students could cover in one-semester when doing all the work themselves.

Read the full review here


Annie Selden is Adjunct Professor of Mathematics at New Mexico State University and Professor Emerita of Mathematics from Tennessee Technological University. She regularly teaches graduate courses in mathematics and mathematics education.