A Mathematician's Scrapbook by Dunham, William;

Long description:

In studying mathematics, one can encounter surprises, whether in results that seem astonishing or in proofs that lead down unexpected paths. Over his career, the author came across many such gems. This book includes his favorites and invites readers to experience the same sense of wonder they inspired in him.

Here are results about number theory, Euclidean geometry, trigonometry, algebra, and infinite series, with stories from the history of mathematics added to the mix. There are theorems from such masters as Euler, Newton, and Ramanujan, while some lesser known mathematicians get their moments in the spotlight. Although the author does not avoid technical details, his narrative style makes the book accessible to anyone with an interest in mathematics.

“[This book] is irresistibly fun. It has everything you’d expect from Dunham: delightful math and charming stories, all delivered with his trademark clarity, wit, and enthusiasm.”

- Steven Strogatz, Cornell University, and author of Infinite Powers

“This is a great read, tremendously entertaining (and informative). Dunham is truly the master of us all with regards to writing about fascinating mathematics.”

- Clifford Taubes, Harvard University

“As always, Dunham’s unique gift for mathematical storytelling shines through. [His] enthusiasm for mathematics jumps off the page and sweeps his reader along on a joyous intellectual ride.”

- Linda McGuire, Muhlenberg College

“As the book’s title promises, unexpected results abound. I encourage you to let Dunham be your guide to some of the wonders of mathematics – you are in for an intellectual treat.

- Howard Stone, Princeton University

Table of Contents:

Preface.- Simple Things.- The Infinitude of Primes: Euclid, Ersatz, and Erdos.- On the Twin Prime Conjecture.- On the Twin Composite Conjecture.- A Prime Family Resemblance.- Once More, Into the Primes.- Your Humble Servant Is, Newton.- Newton's (Original) Method.- The First Great Max/Min Problem.- The Roots of All Evil.- What's Your Sign.- The Square Root of Two and a Shaggy-Log Story.- A Ramanujan Morsel. The Biblical Value of Pi, or Not.- The Power of the Powers of Three.- The Demonic Harmonic Series.- Euler Sums a Series.- The Math Matriarchs of Bryn Mawr.- The Triangle Inequality in Euclid.- Isosceleast Triangles.- My Favorite Proof of Morely's Theorem (as of this morning).- Euclid, Euler, and the Regular Solids.- The Magic of Commutativity.- Wondrous Formulae.- Proving is Believing.- Mathematics and the Humanities.- References.