Preface; 1. Foundations of computation; 2. Sets and mappings; 3. Evaluation of functions; 4. Groups, rings and fields; 5. Vector spaces; 6. Linear mappings I; 7. Linear functionals; 8. Inner products and norms; 9. Linear mappings II; 10. Convergence in normed vector spaces; 11. Group representations; 12. Special functions; Appendices.
A mathematical and computational education for students, researchers, and practising engineers.
'The emphasis on computation sets Cantrell's book apart … it would
provide an excellent introduction to some of the computational
issues in applying numerics to non-linear dynamical problems.'
David Jefferies, The Times Higher Education Supplement
'Precisely because one can dip in, this book has a very real value
as a reference for science graduates with some mathematical
background who find themselves seriously in need of some more.'
Derek Raine, The Observatory
'… unique in the sense that it sails across the ocean of
contemporary advanced mathematics by an impressive tour de force
…'. Thomas Z. Fahidy, Measurement Science & Technology
'… an excellent job of surveying selected topics of modern
mathematics that graduate students of physics and engineering are
likely to encounter.' Any Magid, Computer Applications
'It is not the contents of the book that is really original -
albeit one could already prize the good selection of materials by
the author - but it is the way they are presented, the choice of
examples and exercises, the way to solve the exercises, and the
successful equilibrium between the basic classical concepts and
issues that no student can skip, and the computational tools
nowadays available, that are remarkable … a book to be recommended,
from beginning to end.' E. Elizalde, Zentralblatt für Mathematik
und ihre Grenzgebiete Mathematics Abstracts
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