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SUMS03 Introductory Mathematics -- Applications and Methods
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Springer Undergraduate Mathematics Series(SUMS)
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Springer Undergraduate Mathematics Series
Springer-Verlag London Ltd.

Advisory
Board
P.J.
Cameron
Queen
Mary
and
Westfield
College
M.A.J.
Chaplain
University
ofDundee
K.
Erdmann
Oxford
University
L.C.G.
Rogers
University
of
Cambridge
E.
SOli
Oxford
University
J.F.
Toland
University
ofBath
Other
books in this series
A First Course
in
Discrete Mathematics
1.
Anderson
Analytic Methods for Partial Differential Equations
G.
Evans,
].
Blackledge,
P.
Yardley
Applied Geometry for Computer Graphics
and
CAD
D.
Marsh
Basic Linear Algebra
T.S.
Blyth and
E.F.
Robertson
Basic Stochastic Processes
Z.
Brzefniak and
T.
Zastawniak
Elementary Differential Geometry
A.
Pressley
Elementary
Number
Theory
G.A.
]ones
and
].M.
]ones
Elements
of
Abstract Analysis
M.
6
Searc6id
Elements
of
Logic via Numbers
and
Sets
D.L.
]ohnson
Further Linear Algebra
T.S.
Blyth and
E.F.
Robertson
Geometry
R.
Fenn
Groups, Rings
and
Fields
D.A.R.
Wallace
Hyperbolic Geometry ].
W.
Anderson
Information
and
Coding Theory
G.A.
]ones
and ]M.
]ones
Introduction to Laplace Transforms
and
Fourier Series
P.P.G.
Dyke
Introduction to Ring Theory
P.M.
Cohn
Introductory Mathematics: Algebra
and
Analysis
G.
Smith
Linear Functional Analysis
B.P.
Rynne and
M.A.
Youngson
Matrix Groups: An Introduction to
Lie
Group Theory
A.
Baker
Measure, Integral
and
Probability
M.
Capiliksi and
E.
Kopp
Multivariate Calculus
and
Geometry
S.
Dineen
Numerical Methods for Partial Differential Equations
G.
Evans,
J.
Blackledge,
P.
Yardley
Probability Models
J.
Haigh
Real Analysis JM.
Howie
Sets, Logic
and
Categories
P.
Cameron
Special Relativity
N.M.J.
Woodhouse
Symmetries
D.L.
]ohnson
Topics
in
Group Theory
G.
Smith and
O.
Tabachnikova
Topologies
and
Uniformities
I.M.
James
Vector Calculus
P.C.
Matthews

GeoffSmith
Introductory
Mathematics:
Algebra
and
Analysis
With
19
Figures
, Springer

Geoff
Smith, MA, MSc, PhD
Department
of
Mathematical Sciences, University
of
Bath, Claverton Down,
Bath
BAl
7AY, UK
Cover
illustration
elements
reproduced
by
kind
permission
of
Aptech Systems,
Inc.,
Publishers ofthe
GAUSS
Mathematica!
and
Statistica!
System,
23804
S.E.
Keot-Kangley
Road,
Maple
Va!ley,
WA
98038,
USA
Tel:
(206)
432 -7855 Fax
(206)
432
-7832
email: info@aptech.comURL:www.aptech.com
American
Statistica1
Association: Chance
Voi
8 No
1,1995
article by
KS
and
KW
Heiner 'Tree
Rings
ofthe Northern Shawangunks' page
32
fig
2
Springer-
Verlag:
Mathematica
in
Education and Research
Voi
4 Issue 3
1995
article by Roman E
Maeder,
Beatrice Amrhein
and
Oliver Gloor
'llinstrated
Mathematica:
Visualization ofMathematical Objects' page 9
fig
Il,
originally pnblished
as
a
CD
ROM
'llinstrated Mathernatics' by
TELOS:
ISBN 0-387-14222-3, German edition by
Birkhanser:
ISBN
3-7643-5100-4.
Mathematica
in
Education
and
Research
VoI
4 Issue 3
1995
article by Richard J Gaylord and
Kazume
Nishidate 'Traffic Engineering with
CeUular
Automata' page
35
fig
2.
Mathernatica in Education and Research
VoI
5 Issue 2
1996
article
by
Michael Trott 'The Implicitization
of
a Trefoil
Knot' page
14.
Mathematica
in
Education and Research
VoI
5
Issue
2
1996
article by l.ee de Cola 'Coins, Trees,
Bars
and
BeUs:
Simu1ation
of
the
Binontia1
Pro-
cess' page
19
fig
3.
Mathematica in Education and Research
VoI
5
Issue
2
1996
article by Richard Gaylord and
Kazume
Nishidate 'Contagions
Spreading' page
33
fig
1.
Mathematicain Education andResearch
Voi
5
Issue
21996 article by Joe Buhler and
Stan
Wagon
'Secrets ofthe
Madelung Constant' page
50
fig
1.
British Library Cataloguing in Publication Data
Smith, Geoffrey Charles
Introductory mathematics: algebra and analysis. - (Springer
undergraduate mathematics series)
1.
Mathematics
2.
Algebra 3. Mathematical analysis
1.
Title
510
ISBN 978-3-540-76178-5 ISBN 978-1-4471-0619-7 (eBook)
DOI 10.1007/978-1-4471-0619-7
Library
of
Congress Cataloging-in-Publication Data
Smith, Geoff, 1953-
Introductory mathematics: algebra and analysis /
Geoff
Smith
p. cm. -- (Springer undergraduate mathematics series)
Includes index.
1.
Algebra
2.
Mathematical analysis
1.
Title. II. Series.
QAI54.2.S546 1998 97-41196
510-dc21 CIP
Apart from any fair dealing for the purposes
of
research or private study,
or
criticism or review, as permitted
under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or
transmitted, in any form or
by
any means, with the prior permission in writing
of
the publishers, or in the case
of
reprographic reproduction in accordance with the terms
of
licences issued
by
the Copyright Licensing Agency.
Enquiries conceming reproduction outside those terms should
be
sent to the publishers.
Springer Undergraduate Mathematics Series ISSN 1615-2085
© Springer-Verlag London 1998
Originally published by Springer-Verlag London Limited in 1998
The use
of
registered names, trademarks etc. in this publication does not imply, even
in
the absence
of
a specific
statement, that such names are exempt from the relevant laws and regulations and therefore free for general use.
The publisher makes no representation, express or implied, with regard to the accuracy
of
the information
contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may
be made.
Typesetting: Camera ready
by
author
12/3830-54 Printed on acid-free paper SPIN 11012368

To
my
current wife
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