I am writing about our new book "Mathematical Masterpieces: Further Chronicles by the Explorers", which is a sibling to our earlier book "Mathematical Expeditions: Chronicles by the Explorers". While "Expeditions" was aimed primarily at a lower division undergraduate audience, "Masterpieces" aims to the upper division.
We are expecting to have a book signing with Springer at the January 2008 Joint Mathematics Meetings in San Diego, and we hope we might see you there.
The new book is based on original sources from our course Great Theorems: The Art of Mathematics, presented as a capstone for the undergraduate curriculum. Annotated historical texts tell the stories of four great mathematical adventures through the millenia, in the words of the discoverers, for which we provide context, explanation, and a unifying view.
Here are four independent chapters telling the stories of the Bernoulli numbers as the passage between discrete and continuous phenomena, the search for numerical solutions to equations throughout time, the discovery of curvature and geometric space, and the quest for patterns in prime numbers. Each story is told through the words of the pioneers of mathematical thought. Particular advantages of the historical approach include providing context to mathematical inquiry, perspective to proposed conceptual solutions, and a glimpse into the direction research has taken.
The text is ideal for an undergraduate seminar, independent reading, an upper division history of mathematics course, a capstone course for majors, or upper division enrichment for majors in secondary mathematics education, engineering, or the sciences. It offers a wealth of student exercises with a prerequisite of at most multivariable calculus, and has many portraits, artwork, facsimiles of original works, and figures.
You may see and read many sections from Mathematical Masterpieces at our web pages http://www.math.nmsu.edu/~history, as well as much related information on teaching with primary sources.
Our chapters are
* The Bridge Between Continuous and Discrete * Solving Equations Numerically: Finding Our Roots * Curvature and the Notion of Space * Patterns in Prime Numbers: The Quadratic Reciprocity Law,
and the authors of some of the original sources around which the chapter stories are respectively crafted are Archimedes, Fermat, Pascal, Jakob Bernoulli, Euler; Khayyam, Qin, Cardano, Newton, Simpson, Smale; Huygens, Newton, Euler, Gauss, Riemann; Euler, Lagrange, Legendre, Gauss, Eisenstein.
We hope that you or your students may enjoy the book and find it rewarding.
Best wishes, David Pengelley (and coauthors Arthur Knoebel, Reinhard Laubenbacher, Jerry Lodder)