I (ref) solicited comments from top computer scientists and summarized some of 
what I received:

   Why Numerical Methods Is Important For Undergrad Computer Science Majors

(NA below stands for "numerical methods/numerical analysis/numerical software/
scientific computing")

- NA is the key bridge between non-computer scientists (engineers, economists,
  medical researchers, mathematicians, scientists of all flavors, and engineers
  of all flavors) and computer science. It is crucial that computer scientists
  understand one of the most common styles, languages, and class of problems 
  for which non-computer scientists use computers. Scientific computing remains
  one of the strongest stimulants for developing scalable parallel computing. 
  Indeed NA has always been the leader in computer science. Virtually all the 
  Turing Award winners have had a strong NA background. It could be argued that
  all of computer science has its roots in NA.
 
- NA extends, reviews, and applies in a wonderful way much crucial mathematics 
  related to modeling of all kinds: multivariate calculus, linear algebra, and
  floating point arithmetic. This review and discussion is extremely valuable 
  for computer science students who often end up with weak backgrounds in 
  continuum mathematics, as opposed to discrete mathematics. Our graduates need
  to understand why supercomputers are built. Our graduates should have a sense
  of computer graphics' potential and limitations and this requires some idea 
  of splines and the algorithms that are the core of graphics software. Our 
  graduates can not call themselves scientists if they are ignorant of the 
  basic contexts of calculus. NA puts the calculus in a useful and reasonable 
  context. 

- A NA course is ultimately the most valuable CS course in opening up FUTURE 
  job opportunities in that it provides specific skills that can be used in so 
  many ways. Knowing how to program and knowing NA is enough to be useful on 
  many simulation projects. A very high percentage of our undergrads will 
  encounter quantitative computing of some kind when they graduate. Compared to
  other kinds of computing, numerical computing has more depth. Whereas other 
  types of computing like data base computing can be picked up on your own, any
  student not having exposure to numerical methods in school curriculum will be
  blocked from any kind of meaningful and useful contribution to a project 
  where quantitative computing is needed. Examples where bad work is done by 
  computer scientists ignorant of numerical issues abound. Incidentally as at 
  other preeminent departments, e.g., U. Illinois "ALL our good students do 
  well in the Numerical Methods course." In my opinion this should also hold 
  elsewhere.

- At an intellectual level, it is quite important to know something about NA 
  since there are definite limits to what can be simulated on a computer (just
  as there are definite limits to what problems are computable). E.g., chaos 
  theory implies that certain kinds of long-range forecasting are impossible no
  matter what algorithm or computer is used. Similarly, complexity and 
  algorithmic issues currently prevent the direct simulation of complex 
  problems.
 
- It should be realized that NA is pervasive in ALL of computer science and 
  this is precisely the type of course that needs to be a cornerstone of our 
  curriculum.  A colleague at a Canadian university points out at the beginning
  of each semester that with only a "cursory search through just the current 
  editions of journals in our library, I am able to quote numerical articles 
  from journals in Data Base, Graphics, Networking, Parallel Computing, 
  Software Methodology, and Artificial Intelligence." He continues that they 
  have "courses in Information Retrieval where they are discussing algorithms 
  for latent semantic indexing which are based on the singular value 
  decomposition, which all the students in the class did last year in Numerical
  Linear Algebra. In Software Engineering the students are writing a system to 
  simulate the generation of large scale software packages - and this has them 
  wondering about numerical integration, and finding zeros of functions given 
  implicitly by other functions. In the Network course they have frequent 
  numerical modelling problems. And, finally, in the Graphics class 
  computational geometry problems, mainly linear algebraic, keep cropping up."
 
  Comments from industry and national labs, e.g.
- "A CS major needs to know and understand the types of numerical methods that 
  are used on computers by scientists, engineers, and in business. The ones 
  that will work in engineering companies or do basic science will obviously 
  need to know these methods. If they write compilers or translators they 
  benefit from an understanding of what some of the users will need for their
  work.  Operating system writers also need to know these numerical methods for
  a variety of tasks including scheduling (new schedulers developed here at 
  LANL (Los Alamos National Labs) do a fair amount of calculations do determine
  the optimal scheduling on our advanced computers that have several hundred 
  users competing for resources). If applicants don't have numerical background
  it could limit their employment possibilities. In any area you care to 
  mention people use the computers to do mathematics for them, and if you are 
  the one who writes and maintains applications and tools you will need to 
  understand computational mathematics and numerical methods." Similar comments
  could be included from a computer scientist from Kodak in NY and the manager 
  of the computer science department in information services research at 
  Boeing.
 
Issue of Responsibility
- The GAO (General Accounting Office) report on roundoff error and the Patriot 
  missile is an example where lack of the most basic understanding of errors
  (namely correlated errors can cancel) led to an erroneous conclusion. (The 
  technical person responsible for the report had the title of computer 
  scientist; too bad he did not take Numerical Methods.)