MAA Review of Beyond the Quadratic Formula

Mark Hunacek reviews Beyond the Quadratic Formula by Ron Irving as part of MAA Reviews.

"Combining mathematics and history, this text tells, in a way accessible to beginning students, the interesting story of how formulas came to be discovered for the roots of third and fourth degree polynomials, and why nobody will discover corresponding formulas for fifth (or higher) degree polynomials.

Specifically, the book begins with an introductory chapter on polynomials (treated informally as formal expressions rather than rigorously defined), and is followed by a chapter on quadratic equations, in which the familiar quadratic formula is derived from several different points of view. The study of cubic equations begins in the next chapter, which discusses Cardano’s formula. One of the more amusing aspects of Cardano’s formula is that even nice, simple numbers can wind up being represented by horrendous sums of cube roots of expressions involving square roots; lots of examples are provided in the book. "

Read the full review here.

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Two New CRM Books

The MAA has two new Classroom Resource Materials books! Paradoxes and Sophisms in Calculus By Sergiy Klymchuk and Susan Staples Paradoxes and Sophisms in Calculus offers a delightful supplementary resource to enhance the study of single variable calculus. By the word paradox the authors mean a surprising, unexpected, counter-intuitive statement that looks invalid, but in fact is true. The word sophism describes intentionally invalid reasoning that looks formally correct, but in fact contains a subtle mistake or flaw. In other words, a sophism is a false proof of an incorrect statement. A collection of over fifty paradoxes and sophisms showcases the subtleties of this subject and leads students to contemplate the underlying concepts. A number of the examples treat historically significant issues that arose in the development of calculus, while others more naturally challenge readers to understand common misconceptions. Sophisms and paradoxes from the areas of functions, limits, derivatives, integrals, sequences, and series are explored. The book could be useful for high school teachers and university faculty as a teaching resource; high school and college students as a learning resource; and a professional development resource for calculus instructors.

Exploring Advanced Euclidean Geometry  with GeoGebra By Gerard Venema This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in the subject. Topics covered include triangle centers, inscribed, circumscribed, and escribed circles, medial and orthic triangles, the nine-point circle, duality, and the theorems of Ceva and Menelaus, as well as numerous applications of those theorems. The final chapter explores constructions in the Poincaré disk model for hyperbolic geometry. The book can be used either as a computer laboratory manual to supplement an undergraduate course in geometry or as a stand-alone introduction to advanced topics in Euclidean geometry.  Both books are currently available in the MAA eBooks Store. Print copies will be available in the MAA Store shortly.

William Satzer reviews Explorations in Complex Analysis

The following review of Explorations in Complex Analysis by William Satzer was published as an MAA Review in December 2012. "This new offering from the MAA is a collection of six inducements or invitations to further research for undergraduates with some background in complex analysis. The book is flexible enough to be a source of enrichment material, a basis for research projects, the kernel of a capstone course, or just a tool to ignite the interest of the mathematically curious..." Read the full review here.
William Satzer is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.
Buy your copy of Explorations in Complex Analysis today at the MAA Store or MAA eBooks Store.
Last week to receive 10% off your entire purchase in the MAA eBooks Store. Use the coupon code 1507664649.    Offer expires February 28, 2013