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Topic: Mathematical Masterpieces: a sibling for Mathematical Expeditions
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David Pengelley

Posts: 61
Registered: 12/3/04
Mathematical Masterpieces: a sibling for Mathematical Expeditions
Posted: Dec 14, 2007 6:57 PM
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Dear colleagues,

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

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, 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,

We hope that you or your students may enjoy the book and find it

Best wishes,
David Pengelley (and coauthors Arthur Knoebel, Reinhard Laubenbacher,
Jerry Lodder)

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