[share_ebook] A.First.Course.in.Discrete.Mathematics

Description

Author: Ian Anderson
Publisher: Springer
Pages: 200
ISBN: 1-85233-236-0

 ггетасе

This addition to the SUMS series of textbooks is an introduction to various as-
pects of discrete mathematics. It is intended as a textbook which could be used
at undergraduate level, probably in the second year of an English undergradu-
ate mathematics course. Some textbooks on discrete mathematics are written
primarily for computing science students, but the present book is intended for
students following a mathematics course. The place of discrete mathematics in
the undergraduate curriculum is now fairly well established, and it is certain
that its place in the curriculum will be maintained in the third millennium.
Discrete mathematics has several aspects. One fundamental part is
enumeration, the study of counting arrangements of various types. We might
count the number of ways of choosing six lottery numbers from 1,2,... , 49, or
the number of spanning trees in a complete graph, or the number of ways of
arranging 16 teams into four groups of four. We develop methods of counting
which can deal with such problems.
Next, graph theory can be used to model a variety of situations - road
systems, chemical molecules, timetables for examinations. We introduce the
basic types of graph and give some indication of what the important properties
are that a graph might possess.
The third area of discrete mathematics to be discussed in this book is that of
configurations or arrangements. Latin squares are arrangements of symbols
in a particular way; such arrangements can be used to construct experimental
designs, magic squares and tournament designs. This leads us on to have a look
at block designs, which were discussed extensively by statisticians as well as
mathematicians due to their usefulness in the design of experiments. The book
closes with a brief introduction to the ideas behind error-correcting codes.
The reader does not require a great deal of technical knowledge to be able
to cope with the contents of the book. A knowledge of the method of proof by
induction, an acquaintance with the elements of matrix theory and of arithmetic
modulo n, a familiarity with geometric series and a certain clarity of thought

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