Numerical Algorithmic Science and Engineering (NAS&E) or more compactly Numerical
Algorithmics is the theoretical and empirical study and the practical implementation and
application of algorithms for solving finite-dimensional problems of a numeric nature. The
variables of such problems are either discrete-valued or continuous over the reals or and as
is often the case a combination of the two and they may or may not have an underlying network
graph structure. This re-emerging discipline of numerical algorithmics within computer science
is the counterpart of the now well-established discipline of numerical analysis within
mathematics where the latter's emphasis is on infinite-dimensional continuous numerical
problems and their finite-dimensional continuous approximates. A discussion of the underlying
rationale for numerical algorithmics its foundational models of computation its
organizational details and its role in conjunction with numerical analysis in support of the
modern modus operandi of scientific computing or computational science & engineering is the
primary focus of this short monograph. It comprises six chapters each with its own
bibliography. Chapters 2 3 and 6 present the book's primary content. Chapters 1 4 and 5 are
briefer and they provide contextual material for the three primary chapters and smooth the
transition between them. Mathematical formalism has been kept to a minimum and whenever
possible visual and verbal forms of presentation are employed and the discussion enlivened
through the use of motivating quotations and illustrative examples. The reader is expected to
have a working knowledge of the basics of computer science an exposure to basic linear algebra
and calculus (and perhaps some real analysis) and an understanding of elementary mathematical
concepts such as convexity of sets and functions networks and graphs and so on. Although this
book is not suitable for use as the principal textbook for a course on numerical algorithmics
(NAS&E) it will be of value as a supplementary reference for a variety of courses. It can also
serve as the primary text for a research seminar. And it can be recommended for self-study of
the foundations and organization of NAS&E to graduate and advanced undergraduate students with
sufficient mathematical maturity and a background in computing. When departments of computer
science were first created within universities worldwide during the middle of the twentieth
century numerical analysis was an important part of the curriculum. Its role within the
discipline of computer science has greatly diminished over time if not vanished altogether
and specialists in that area are now to be found mainly within other fields in particular
mathematics and the physical sciences. A central concern of this monograph is the regrettable
downward trajectory of numerical analysis within computer science and how it can be arrested
and suitably reconstituted. Resorting to a biblical metaphor numerical algorithmics (NAS&E) as
envisioned herein is neither old wine in new bottles nor new wine in old bottles but rather
this re-emerging discipline is a decantation of an age-old vintage that can hopefully find its
proper place within the larger arena of computer science and at what appears now to be an
opportune time.
