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This book chronicles Donald Burkholder's thirty-five year study of martingales and its consequences. Here are some of the highlights.

Pioneering work by Burkholder and Donald Austin on the discrete time martingale square function led to Burkholder and Richard Gundy's proof of inequalities comparing the quadratic variations and maximal functions of continuous martingales, inequalities which are now indispensable tools for stochastic analysis. Part of their proof showed how novel distributional inequalities between the maximal function and quadratic variation lead to inequalities for...

ACROSS THE WIDE MISSOURI

In the summer of 1819, Alexander Campbell and his family and their servants, along with other travelers, departed from the comparative comfort of their home in Highland County, Virginia, to set forth on a pio-neering trek to the wilderness country of the Missouri Territory. James Brown Campbell, the family's eldest son, then only twenty years of age, began keeping a diary of their journey, recounting their terrible hardships, both on the way and after arriving in the "Promised Land," plus a detailed account of his work surveying parts of Missouri Territory, and...