600 pages 49 line diagrams
Hardback | ISBN: 0-88385-538-0 | Not yet published - available
from August 2004
This biography of Gauss, by far the most comprehensive in
English, is the work of a professor of German, G. Waldo
Dunnington, who devoted most of his scholarly career to studying
the life of Germany's greatest mathematician. The author was
inspired to pursue this project at the age of twelve when he
learned from his teacher in Missouri that no full biography of
Gauss existed at the time. His teacher was Gauss痴 great
granddaughter, Minna Waldeck Gauss. Long out of print and almost
impossible to find on the used book market, this valuable piece
of scholarship is being reissued in an augmented form with
introductory remarks, an expanded and updated bibliography, and a
commentary on Gauss痴 mathematical diary, by the eminent British
mathematical historian, Jeremy Gray.
Contents
1. Introduction: family background; 2. The enchanted boyhood; 3.
Student days; 4. The young man; 5. Astronomy and matrimony; 6.
Further activity; 7. Back to Gotingen; 8. Labour and sorrow; 9.
The young professor: a decade of discovery, 1812・822; 10.
Geodesy and bereavement: the transitional decade, 1822・832; 11.
Alliance with Weber: strenuous years; 12. The electromagnetic
telegraph; 13. Magnetism: physics dominant; 14. Surface theory,
crystallography, and optics; 15. Germination: non-Euclidean
geometry; 16. Trials and triumphs: experiencing conflict; 17.
Milestones on the highways and byways; 18. Senex mirabilis; 19.
Monarch of mathematics in Europe; 20. The doyen of German
science, 1832・855; 21. Gathering up the threads: a broad
horizon; 22. Religio Scientiae: a profession of belief from the
philosopher and lover of truth; 23. Sunset and eventide:
renunciation; 24. Epilogue: 1. Apotheosis: orations of Ewald and
Sartorious; 2. Valhalla: posthumous recognition and honours;
Appendices; Index.
200 pages
Hardback | ISBN: 0-8838-5015-X | Not yet published - available
from August 2004
A classic advanced textbook, containing a cross-section of ideas,
techniques and results that give the reader an unparalleled
introductory overview of the subject. The author gives an
integrated presentation of overall theory and its applications
in, for example, the study of groups of matrices, group
representations, and in settling the problems of Burnside and
Kurosh. Readers are also informed of open questions. Definitions
are kept to a minimum and the statements of the theorems are
sharp and clear.
Contents
1. The Jacobson radical; 2. Semisimple rings; 3. Commutativity
theorems; 4. Simple algebras; 5. Representations of finite
groups; 6. Polynomial identities; 7. Goldie’s theorem; 8. The
Golob-Shafarevitch theorem.
Reviews
‘This beautiful book is the result of the author's wide and
deep knowledge of the subject matter combined with his gift for
exposition …The well selected material is offered in an
integrated presentation of the structure theory of noncommutative
(associative rings) and its applications. Besides seeing the
theory at work in the study of groups of matrices, group
representations, and in settling the problems of Burnside and
Kurosh, there are, or there are given the bases for the
construction of counterexamples, so the reader can see how a
theorem fails under weaker assumptions. Readers are also informed
of open questions and of the latest generalizations not presented
in the book … the style is lively and smooth. Definitions are
kept to a minimum and the statements of the theorems are sharp
and clear. This book will appeal to many a reader. It would be
wonderful as a textbook … those interested in studying or
reviewing its subject matter or looking for a rounded account of
it could do no better than choosing this book for this purpose.’
AMS Bulletin
391 pages 75 exercises 150 figures 50 worked examples
Paperback | ISBN: 0-521-60857-0 | Not yet published - available
from August 2004
Linear Logic is a branch of proof theory which provides refined
tools for the study of the computational aspects of proofs. These
tools include a duality-based categorical semantics, an intrinsic
graphical representation of proofs, the introduction of well-behaved
non-commutative logical connectives, and the concepts of polarity
and focalisation. These various aspects are illustrated here
through introductory tutorials as well as more specialised
contributions, with a particular emphasis on applications to
computer science: denotational semantics, lambda-calculus, logic
programming and concurrency theory. The volume is rounded-off by
two invited contributions on new topics rooted in recent
developments of linear logic. The book derives from a summer
school that was the climax of the EU Training and Mobility of
Researchers project ‘Linear Logic in Computer Science’. It is
an excellent introduction to some of the most active research
topics in the area.
Contents
Part I. Tutorials: 1. Category theory for linear logicians R.
Blute and Ph. Scott; 2. Proof nets and the x-calculus S.
Guerrini; 3. An overview of linear logic programming D. Miller; 4.
Linearity and nonlinearity in distributed computation G. Winskel;
5. An axiomatic approach to structural rules for locative linear
logic J. M. Andreoli; 6. An introduction to uniformity in ludics
C. Faggian, M. R. Fleury-Donnadieu and M. Quatrini; 7. Slicing
polarized addictive normalization O. Laurent and L. Toratora De
Falco; 8. A topological correctness criterion for muliplicative
noncommutative logic P.A. Mellies; 9. Bicategories in algebra and
linguistics J. Lambek; 10. Between logic and quantic: a tract J.
Y. Girard.
519 pages 126 line diagrams 6 half-tones 6 tables
Hardback | ISBN: 0521834929 | Not yet published - available from
August 2004
Mathematical methods are essential tools for all physical
scientists. This second edition provides a comprehensive tour of
the mathematical knowledge and techniques that are needed by
students in this area. In contrast to more traditional textbooks,
all the material is presented in the form of problems. Within
these problems the basic mathematical theory and its physical
applications are well integrated. The mathematical insights that
the student acquires are therefore driven by their physical
insight. Topics that are covered include vector calculus, linear
algebra, Fourier analysis, scale analysis, complex integration,
Green’s functions, normal modes, tensor calculus, and
perturbation theory. The second edition contains new chapters on
dimensional analysis, variational calculus, and the asymptotic
evaluation of integrals. This book can be used by undergraduates,
and lower-level graduate students in the physical sciences. It
can serve as a stand-alone text, or as a source of problems and
examples to complement other textbooks.
Contents
1. Introduction; 2. Dimensional analysis; 3. Power series; 4.
Spherical and cylindrical coordinates; 5. The gradient; 6. The
divergence of a vector field; 7. The curl of a vector field; 8.
The theorem of Gauss; 9. The theorem of Stokes; 10. The
Laplacian; 11. Conservation laws; 12. Scale analysis; 13. Linear
algebra; 14. The Dirac delta function; 15. Fourier analysis; 16.
Analytic functions; 17. Complex integration; 18. Green’s
functions: principles; 19. Green’s functions: examples; 20.
Normal modes; 21. Potential theory; 22. Cartesian tensors; 23.
Perturbation theory; 24. Asymptotic evaluation of integrals; 25.
Variational calculus; 26. Epilogue, on power and knowledge;
References.
488 pages 126 line diagrams 1 table 190 exercises
Hardback | ISBN: 0-521-47018-8 | Not yet published - available from January
2005
Series: NEW MATHEMATICAL MONOGRAPHS
During the last two decades several remarkable new results were
discovered about harmonic measure in the complex plane. This book
provides a careful survey of these results and an introduction to
the branch of analysis which contains them. Many of these
results, due to Bishop, Carleson, Jones, Makarov, Wolff and
others, appear here in book form for the first time. The book is
accessible to students who have completed standard graduate
courses in real and complex analysis. The first four chapters
provide the needed background material on univalent functions,
potential theory, and extremal length, and each chapter has many
exercises to further inform and teach the readers.
Contents
1. Jordan domains; 2. Finitely connected domains; 3. Potential
theory; 4. Extremal distance; 5. Applications and reverse
inequalities; 6. Simply connected domains, part one; 7. Bloch
functions and quasicircles; 8. Simply connected domains, part
two; 9. Infinitely connected domains; 10. Rectifiability and
quadratic expressions; Appendices.