'Et moi, ... , so j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point al!e.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non­ The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell 0. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlinearities 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 computer science .. .'; 'One service category theory has rendered mathematics ... '. All armably true. And all statements obtainable this way form part of the raison d'etre of this series.

1. Introduction.- 2. Linear Programming.- 3. Unimodularity and Network Flows. Cutting-Plane Methods.- 4. Branch-and-Bound Methods.- 5. The Knapsack Problem.- 6. Equivalent Formulations for Integer Programs.- 7. Relaxations of Integer Problems. Duality.- 8. Some Particular Integer Programming Problems.- 9. Near-Optimal Methods.- 10. Conclusions.