'Et moi, ... , si j'avait su comment en :revenir, One scrvice mathematics has rendered the je n'y scrais point alle.' human race. lt has put common sense back Jules Veme where it bdongs, on the topmost shelf next to the dusty canister labclled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Erle T. Bc1l 0. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'.All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

1 Introduction.- 2 Polynomials: A Review.- 3 Entire Functions and Signal Recovery.- 4 Homometric Distributions.- 5 Analytic Signals and Signal Recovery from Zero Crossings.- 6 Signal Representation by Fourier Phase and Magnitude in One Dimension.- 7 Recovery of Distorted Band-Limited Signals.- 8 Compact Operators, Singular Value Analysis and Reproducing Kernel Hilbert Spaces.- 9 Kaczmarz Method, Landweber Iteration, Gerchberg-Papoulis and Regularization.- 10 Two Dimensional Signal Recovery Problems.- 11 Reconstruction Algorithms in Two Dimensions.- 12 Nonexpansive Maps and Signal Recovery.- 13 Projections on Convex Sets in Signal Recovery.- 14 Method of Generalized Projections and Steepest Descent.- 15 Closed Form Reconstruction of the Support and the Object.- 16 Fienup's Input-Output Algorithms and Variations on this Theme.- 17 Topics and Applications of Signal Recovery.- A The Geometry of Projections on Convex Sets.- B Reference Summary.- C References.