This course will cover fundamentals of geometrically convergent numerical algorithms in the following contexts, among others:

• quadrature
• interpolation
• differentiation
• Taylor, Laurent, Chebyshev, and Pade
• expansion methods for Laplace equation and other PDEs

The complex plane is used throughout, and students in the course should arrive reasonably comfortable with complex variables. For those who are, I hope this will be an exciting adventure, deepening both their understanding of numerical algorithms and their ability to use them. The title reflects a fascinating historical side of this subject: many of the ideas come from the 1950s and 1960s or earlier, but were largely lost since they could not flourish on the computers of that time. In each case I do my best to pin down who really discovered a technique and to list some of the best-known rediscoverers -- and to give the right theorems.

This course will be assessed by Special Topics consisting of solving exercises from the book.

The draft preface of the book gives further information about the subject.