6.8 The Introduction

Perhaps the worst way to begin a paper is with a list of notation or definitions, such as Let G be an abelian group and H be a subgroup of G, or Let be the complex field or the real field , and let be the linear space of all m x n matrices over . If we use A* to denote the conjugate transpose of A. It can be argued that the first sentence should be the best in the paper its job is to entice the uncommitted reader into reading the whole paper. A list of notation will not achieve this aim, but a clear, crisp and imaginative statement may. King [152] gives a slightly different specification for the first sentence: "The first sentence has a dual function: it must carry some essential information, particularly the problem under consideration, and at the same time gently translate the reader into the body of the article."

Ideally, an introduction is fairly short say a few hundred words. It should define the problem, explain what the work attempts to do, and outline the plan of attack. Unless there is good reason not to do so, it is advisable to summarize the results achieved. Knowing the problem and the progress made on it, the reader can decide after reading the introduction whether to read the whole paper. You may want to leave the punch-line to the end, but in doing so you risk the...