Friday, April 18, 2014

MAA Books Beat: Extraordinary Book on Ordinary Differential Equations

Written by Steve Kennedy, MAA Books Beat is a column written for MAA FOCUSExtraordinary Book on Ordinary Differential Equations appears in the April/May 2014 issue.

Mathematics changes slowly; the mathematics curriculum changes even more slowly. A few years ago, to celebrate the tercentenary of L'Hôpital's Calculus, some colleagues and I read it seminar-style. The most striking thing about the experience was that his table of contents looked shockingly similar to our departmental calculus syllabus. That being said, in the 30 years I've been teaching collegiate mathematics, there is one course in the undergraduate math curriculum that has changed dramatically–the course in ordinary differential equations (ODE).

These changes are rooted in the calculus reform movement of the late 1980s and early 1990s, the easy access to powerful computing and visualization, and the rise of dynamical systems theory and its accompanying qualitative point of view.

The calc reform movement taught us to explain everything from graphical, numerical, and symbolic perspectives. Computing, of course, made it possible to do this in effective ways, especially the numerical and graphical bits. Dynamical systems provided entirely new ways of thinking about the evolution and bifurcation of systems.

The New on View

All these changes are fully on view in Virginia (“Anne”) Noonburg's Ordinary Differential Equations from Calculus to Dynamical Systems, newly released by the MAA. Noonburg has a distinguished record of research in dynamical systems, especially concentrating on equations that model biological systems. You clearly see these intellectual interests in this book.

Tuesday, April 15, 2014

Undergraduate Mathematics for the Life Sciences

Check out David Bressoud's post Mathematics for the Biological Sciences in his blog Launchings where he discusses one of our latest ebooks, Undergraduate Mathematics for the Life Sciences: Models, Processes, and Directions edited by Glenn Ledder, Jenna P. Carpenter, and Timothy D. Comar.

MAA has just published a Notes volume, Undergraduate Mathematics for the Life Sciences: Models, Processes, and Directions [1] that provides examples and advice for mathematics departments that want to reach out to the growing population of biological science majors.

Biological science majors have replaced prospective engineers as the largest group of students taking regular Calculus I. From the MAA’s Calculus Survey [2], just over 28% of all students in mainstream Calculus I intend to pursue a major in the biological sciences, the largest single group of majors in this course.

Read the full post here.

Friday, April 4, 2014

Mathematics, Magic, and Mystery

The American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics have announced that the theme for Mathematics Awareness Month (MAM), April 2014, is Mathematics, Magic, and Mystery. The theme echoes the title of a 1956 book by renowned math popularizer Martin Gardner, whose extensive writings introduced the public to hexaflexagons, polyominoes, John Conway’s “Game of Life,” Penrose tiles, the Mandelbrot set, and much more. For more than half a century Gardner inspired enthusiasts of all ages to engage deeply with mathematics, and many of his readers chose to pursue it as a career. The year 2014 marks the centennial of Gardner’s birth.

This year the MAM Committee and volunteers have put together 30 theme-related activities. Each day in April one activity will be revealed that corresponds with an image on the theme poster. So stay tuned to to see some behind-the-scenes explanations and videos of Mathematics, Magic, and Mystery!

Martin Gardner in MAA Books

Gardner was perhaps best known as the author of the "Mathematical Games" column for Scientific American, which ran from 1956 to 1981. Throughout his career he wrote more than 70 books and collections of essays on topics ranging from Lewis Carroll and magic tricks to philosophy, religion, and scientific skepticism. Several of his most popular writings are available in the MAA Store.

Eight works by Gardner himself, published between 1999 and 2010, supplemented by 33 chapters written in response to Gardner's work 
Gardner's Scientific American column "Mathematical Games" on a single, searchable source

Nineteen tantalizing conundrums
Included here are chapters on Conway's surreal numbers, Mandelbrot's fractals, and Smullyan's logic puzzles

The inaugural volume in Martin Gardner's New Mathematical Library. These mathematical recreations delight and perplex while demonstrating principles of logic, probability, geometry, and other fields of mathematics.

The second volume in Gardner's New Mathematical Library, updated chapters, including new game variations, mathematical proofs, and other developments and discoveries, to challenge and fascinate a new generation of readers.

Packing spheres, Reversi, braids, polyominoes, board games, and the puzzles of Lewis Carroll

The challenging problems presented here are based on geometry, logarithms, topology, probability, weird number sequences, logic and, virtually every other aspect of mathematics as well as wordplay.

Friday, March 28, 2014

Bill Wood Reviews Exploring Advanced Euclidean Geometry with GeoGebra

Bill Woods reviews Exploring Advanced Euclidean Geometry with GeoGebra by Gerard Venema as part of MAA Reviews.

Exploring Advanced Euclidean Geometry with GeoGebra is written for an inquiry-based approach, with lots of exercises and just enough narrative and historical commentary to hold it all together. It is not the sort of book you read without some paper and probably a computer in front of you. What makes the book special is the inclusion of GeoGebra exercises (clearly identified with a *) to encourage experimentation. Exercises may ask students to construct a visualization of a theorem, verify results, and build examples and conjectures. Eventually the student gets to proving a theorem, but not before playing with the statement quite a bit.

The book focuses on “advanced” planar Euclidean geometry, which the author defines to mean anything developed after Euclid’s Elements. This makes it an excellent candidate text for a second course in Euclidean geometry using inquiry-based methods that minimize lecture and maximize student discovery. There is also much value to be mined as a supplement to other Euclidean geometry texts. The author suggests a structure in which this text is used as something of a lab manual rather than a primary text.

Even if it does not fit for course adoption, this book is worth any geometry teacher’s attention as way to reconnect with the learning experience they want for their students.

Read the full review here.

Friday, March 14, 2014

New eBook: Textbooks, Testing, Training: How We Discourage Thinking

Textbooks, Testing, Training: How We Discourage Thinking

by Stephen S. Willoughby

Willoughby's essay is a gem. It should be in the hands of every young teacher. I wish that I had read it many years ago. I have no doubt that many of his observations and the information he imparts will remain with me for a while. I certainly hope so. A collection of reminiscences from other teachers with their valuable insights and experiences (who could write with such expertise as he does) would make a fine addition to the education literature.
— James Tattersall, Providence College

Steven S. Willoughby has taught mathematics for 59 years and he has seen everything. Some of it has annoyed him, some has inspired him. This little book is something of a valedictory and he shares some parting thoughts as he contemplates the end of his teaching career. Steve has strong, cogent and mostly negative opinions about textbooks, standardized testing, and teacher training. These opinions have been forged in the cauldron of the classroom of a deeply caring teacher. They might not please you, but they ought to make you think. They should spark needed debate in our community. Ultimately this is a human tale with rough parallels to Hardy's Apology; replace "Mathematician's" with "Teacher's" perhaps. Every teacher will sympathize with Steve's frustrations and empathize with the humanity and compassion that animated his life's work and that beat at the center of this book.

Order your copy today in the MAA eBooks Store.
(PDF: $11.00,  POD: $18.00)