## Friday, March 7, 2014

### 101 Careers in Mathematics

3rd Edition
Andrew Sterret, Editor

This third edition of the immensely popular 101 Careers in Mathematics contains updates on the career paths of individuals profiled in the first and second editions, along with many new profiles. No career counselor should be without this valuable resource.

The authors of the essays in this volume describe a wide variety of careers for which a background in the mathematical sciences is useful. Each of the jobs presented shows real people in real jobs. Their individual histories demonstrate how the study of mathematics was useful in landing well-paying jobs in predictable places such as IBM, AT&T, and American Airlines, and in surprising places such as FedEx Corporation, L.L. Bean, and Perdue Farms, Inc. You will also learn about job opportunities in the Federal Government as well as exciting careers in the arts, sculpture, music, and television. There are really no limits to what you can do if you are well prepared in mathematics.

The degrees earned by the authors profiled here range from bachelor’s to master’s to PhD in approximately equal numbers. Most of the writers use the mathematical sciences on a daily basis in their work. Others rely on the general problem-solving skills acquired in mathematics as they deal with complex issues.

## 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, February 21, 2014

### Suzanne Caulk Reviews Resources for Preparing Middle School Mathematics Teachers

Suzanne Caulk reviews Resources for Preparing Middle School Mathematics Teachers edited by Cheryl Beaver, Laurie Burton, Maria Fung, and Klay Kruczek as part of MAA Reviews.

Playing a role in the preparation of middle school mathematics teachers is fun and challenging. It can often be difficult, however, to find course materials aimed at this particular group of teachers. Resources for Preparing Middle School Mathematics Teachers is a treasure trove of ideas and materials designed to support educators preparing these instructors.

The first half of the book contains descriptions of programs preparing pre-service teachers and another section about programs for in-service teachers. These articles contain many details, including program requirements, course descriptions, bibliographies, comparisons to other programs, challenges in running the programs, and reflections on what has been accomplished and where these programs are heading. The descriptions often give the context of the programs, so that one has an idea not only of the characteristics of the people being served by them, but also of the size and resources of the departments providing the programs.

## Friday, February 14, 2014

### New Textbook Coming Soon

#### Ordinary Differential Equations: From Calculus to Dynamical Systems

by V. W. Noonburg
Catalog Code: FCDS

This book presents a modern treatment of material traditionally covered in the sophomore-level course in ordinary differential equations. While this course is usually required for engineering students, the material is attractive to students in any field of applied science, including those in the biological sciences.

The standard analytic methods for solving first and second-order differential equations are covered in the first three chapters. Numerical and graphical methods are considered side-by-side with the analytic methods and are then used throughout the text. An early emphasis on the graphical treatment of autonomous first-order equations leads easily onto a discussion of bifurcation of solutions with respect to parameters.

The fourth chapter begins the study of linear systems of first-order equations and includes a section containing all of the material on matrix algebra needed in the remainder of the text. Building on the linear analysis, the fifth chapter brings the student to a level where two-dimensional nonlinear systems can be analyzed graphically via the phase plane. The study of bifurcations is extended to systems of equations using several compelling examples, many of which are drawn from population biology. In this chapter, the student is gently introduced to some of the more important results in the theory of dynamical systems. A student project involving a problem recently appearing in the mathematical literature on dynamical systems is included at the end of chapter 5.

A full treatment of the Laplace transform is given in Chapter 6, with several of the examples taken from the biological sciences. An appendix contains completely worked-out solutions to all of the odd-numbered exercises.

The book is aimed at students with a good calculus background who want to learn more about how calculus is used to solve real problems in today's world. It can be used as a text for the introductory differential equations course, and is readable enough to be used even if the class is being “flipped.” The book is also accessible as a self-study text for anyone who has completed two terms of calculus, including highly motivated high school students. Graduate students preparing to take courses in dynamical systems theory will also find this text useful.

## Friday, February 7, 2014

### MAA Review of More Fallacies, Flaws and Flimflam

Fernando Q. Gouvêa reviews More Fallacies, Flaws and Flimflam by Edward J. Barbeau as part of MAA Reviews.

Some fifteen years ago, I reviewed Mathematical Fallacies, Flaws and Flimflam, the first book collecting the best of Edward J. Barbeau’s regular column in the College Mathematics Journal. Much of what I said then applies here as well: this is an entertaining book that can also be useful in the classroom.

The typical FFF item gives an example of a mathematical argument that is wrong but tricky. Sometimes the problem is that the argument, while visibly (even extravagantly) incorrect, gives the right answer. Other times, the argument contains a subtle error, or uses a method that is correct for unexpected reasons.

For example, here’s a method (section 1.4) for adding two fractions with the same single-digit denominator and single-digit numerators, such as 5/8 and 1/8. First you juxtapose the two denominators to get 88. Then you juxtapose the numerators, getting 51, but of course addition is commutative, so you should also juxtapose them in the other order, getting 15. So

58+18=51+1588=6688=68.

Neat, and perhaps an interesting one to try on students. A more advanced example is found in section 4.6, where L’Hospital’s rule is applied to

limxxsinx2x+sinx2

to prove that 1=1. In section 6.9, a long computation shows that

10x4+1x6+1dx=0.""