Friday, March 27, 2015

MAA Books Store: Buy 1 Get One 1/2 Off

Buy I, Mathematician and get 50% off* A Mathematician Comes of Age.

Hurry! This deal ends Tuesday, March 31.

I, Mathematician
Peter Casazza, Steven G. Krantz and Randi D. Ruden, Editors
List: $50.00 MAA Member: $40.00

Mathematicians have pondered the psychology of the members of our tribe probably since mathematics was invented, but for certain since Hadamard's The Psychology of Invention in the Mathematical Field. The editors asked two dozen prominent mathematicians (and one spouse thereof) to ruminate on what makes us different. The answers they got are thoughtful, interesting and thought-provoking.

A Mathematician Comes of Age
Steven G. Krantz
List: $60.00 MAA Member: $48.00

The book provides background, data, and analysis for understanding the concept of mathematical maturity. It turns the idea of mathematical maturity from a topic for coffee-room conversation to a topic for analysis and serious consideration.

*Discount is off the list price. No code needed. To receive the discount, both items must be placed in your cart. Offer expires March 31, 2015 at midnight.

Friday, March 13, 2015

New MAA Textbook: Modeling Approach in Biology

by Steve Kennedy

When biology was primarily a descriptive science, biologists had little need of mathematical services (and our science). But a revolution has occurred—more precisely, is occurring—in biology, and the discipline is becoming increasingly mathematical and computational. In 2003, a report (Bio2010) from the National Academy of Sciences (NAS) set a goal of having biology undergraduates be quantitatively literate by 2010:

It is essential that biology undergraduates become quantitatively literate, studying the mathematical concepts of change, modeling, equilibria and stability, structure of a system, interactions among components, data and measurement, visualization, and algorithms. Every student should acquire the ability to analyze issues in these contexts in some depth, using analytical methods (e.g., pencil and paper) and appropriate computational tools. An appropriate course of study would include aspects of probability, statistics, discrete models, linear algebra, calculus and differential equations, modeling and programming.

Five years past 2010, the goal hasn't been met fully. The current state of affairs is well described in the draft CUPM Curriculum Guide. That report, besides enumerating biological and mathematical core competencies for biomathematics study, strongly urges foundational courses in modeling and data analysis as the beginning steps of such study.

And that brings me, finally, to my point. MAA Books has just released a book perfectly suited for that foundational modeling course, Jim Cornette and Ralph Ackerman’s Calculus for the life Sciences: A Modeling Approach. If you teach a life sciences calculus course, you may already be aware of the existence of this book, as draft versions have been on the Internet for several years. Reading this terrific and innovative book, you realize that it could have been written in reaction to the first sentence of the NAS report—it addresses, in a deep and significant way, every single mathematical concept listed in the quote above.

Chapter 1 is a primer on modeling in the biological realm, and biological modeling is the theme and frame for the entire book. The authors build models of bacterial growth, light penetration through a column of water, and dynamics of a colony of mold in the first few pages. In each case there is actual data that needs fitting. In the case of the mold colony, that data is a set of photographs of the colony growing on a ruled sheet of graph paper, and the students need to make their own approximations. Fundamental questions about the nature of mathematical modeling—trying to approximate a real-world phenomenon with an equation—are all laid out for the students to wrestle with.

Students intending to major in the life sciences now outnumber engineering and physical science majors in college and university Calculus I courses. Cornette and Ackerman’s textbook takes into account the needs of that plurality. And it does so not just by including examples and problems with a biological flavor—the authors have reimagined the entire year-long calculus course with the needs of biology students as the organizing principle. Thus, to mention just one example among many, your students using this book could get a substantial dose of discrete and continuous dynamical systems theory in their year of calculus study.

Cornette and Ackerman have produced a beautifully written introduction to the uses of mathematics in the life sciences. The exposition is crystalline, the problems are overwhelmingly from biology and interesting and rich, and the emphasis on modeling is invigorating. This book should become the standard text for this course. Please take special note of the student-friendly price—$35 for an ebook.

This article was written for MAA FOCUS as part of MAA Books Beat. It appears in the February/March 2015 issue.

Friday, February 27, 2015

Joel Haack Reviews How Euler Did Even More

Joel Haack reviewed How Euler Did Even More by C. Edward Sandifer as part of MAA Reviews.

C. Edward Sandifer’s How Euler Did Even More is the second collection of his monthly columns from MAA Online, “How Euler Did It.” The first collection, also titled How Euler Did It, appeared in 2007 as part of the five-volume set published by the MAA in recognition of the tercentenary of Euler’s birth. It contained Sandifer’s columns from November 2003 through February 2007. This second collection contains his columns from March 2007 through February 2010, with the addition of two guest columns by Rob Bradley and one by Dominic Klyve. (Bradley assisted Sandifer with the details of the publication of this collection.)

There are several ways to read this book. First, one may choose simply to open it at random to read Sandifer’s discussion of how Euler attacked and thought about certain problems. Sandifer places Euler’s work into context of the mathematics of his time, then describes what Euler did and how he did it and why it mattered, keeping in mind the advice of John Fauvel that Sandifer references in How Euler Did It: “Content, Context and Significance.” An alternative would be to read the columns for particular topics that Euler considered; the columns are organized into sections on geometry, number theory, combinatorics, analysis, applied mathematics, and Euleriana. This last section includes two columns reflecting on Euler as teacher, two on light-hearted topics (Euler and the hollow earth and Euler and pirates), and one discussing of Euler’s fallibility.

Read the full review here.

Joel Haack is Professor of Mathematics at the University of Northern Iowa.

Friday, February 13, 2015

2015 Beckenbach Book Prize Winner

The Beckenbach Book Prize, established in 1986, is the successor to the MAA Book Prize established in 1982. It is named for the late Edwin Beckenbach, a long-time leader in the publications program of the Association and a well-known professor of mathematics at the University of California at Los Angeles. The Prize of $2,500 is intended to recognize the author(s) of a distinguished, innovative book published by the MAA and to encourage the writing of such books. The award is not given on a regularly scheduled basis. To be considered for the Beckenbach Prize a book must have been published during the five years preceding the Award.

The 2015 Beckenbach Book Prize winner is:

By Seth Braver

PDF Price: $28.00
Print-on-Demand Price: $47.50

Mathematicians of all stripes know that the non-Euclidean revolution was a game-changer in 19th  century mathematics. But relatively few mathematicians are acquainted with the little book that heralded this revolution: Nikolai Lobachevski’s Theory of Parallels (in German, 1840).

Seth Braver has come to our rescue. In Lobachevski Illuminated, he gives us a translation of the text, accompanies each of its 37 propositions with an extensive commentary, and places these ideas in their proper historical context. As a result, Braver has done nothing less than give new life to an old masterpiece.

The reader of Lobachevski Illuminated will encounter a host of provocative questions, will delve deeply into the history of geometry, and will gain a thorough appreciation of the genius of Nikolai Lobachevski.

Friday, January 23, 2015

New Calculus Textbooks from the MAA

Looking for a new calculus textbook? Check out these two just published by the MAA.

Calculus for the Life Sciences: A Modeling Approach
James L. Cornette and Ralph A. Ackerman

Available only as an ebook. PDF price: $35.00

Freshman and sophomore life sciences students respond well to the modeling approach to calculus, difference equations, and differential equations presented in this book. Examples of population dynamics, pharmacokinetics, and biologically relevant physical processes are introduced in Chapter 1, and these and other life sciences topics are developed throughout the text.

The ultimate goal of calculus for many life sciences students primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral is crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance.

Students should have studied algebra, geometry and trigonometry, but may be life sciences students because they have not enjoyed their previous mathematics courses. This text can help them understand the relevance and importance of mathematics to their world. It is not a simplistic approach, however, and indeed is written with the belief that the mathematical depth of a course in calculus for the life sciences should be comparable to that of the traditional course for physics and engineering students.

College Calculus: A One-Term Course for Students with Previous Calculus Experience
Michael E. Boardman and Roger B. Nelsen

List price: $60.00 | MAA Member: $48.00

This textbook is for students who have successfully experienced an introductory calculus course in high school. College Calculus begins with a brief review of some of the content of the high school calculus course, and proceeds to give students a thorough grounding in the remaining topics in single variable calculus, including integration techniques, applications of the definite integral, separable and linear differential equations, hyperbolic functions, parametric equations and polar coordinates, L’Hôpital’s rule and improper integrals, continuous probability models, and infinite series. Each chapter concludes with several “Explorations,” extended discovery investigations to supplement that chapter’s material.

The text is ideal as the basis of a course focused on the needs of prospective majors in the STEM disciplines (science, technology, engineering, and mathematics). A one-term course based on this text provides students with a solid foundation in single variable calculus and prepares them for the next course in college level mathematics, be it multivariable calculus, linear algebra, a course in discrete mathematics, statistics, etc.