Contrast to other math degrees
The obvious alternatives to an ACMS degree are the BS
degrees in mathematics, computer science, and computer engineering. The
following few paragraphs are intended to help you make the choice that
is right for you.
Note first of all the term "mathematical sciences" is a misnomer.
According to the Oxford English Dictionary, In modern use, ("Science"
is ) often treated as synonymous with "Natural and Physical Science",
and thus restricted to those branches of study that relate to the
phenomena of the material universe and their laws, sometimes with
implied exclusion of pure mathematics. This is now the dominant sense
in ordinary use.
Applied mathematics, computer science and engineering, and statistics
are not sciences but rather engineering disciplines, while pure
mathematics is in a category by itself. The goal of engineering
disciplines is to provide tools - for computing the lift of an airplane
wing, for encrypting information transmitted over the Internet, for
providing ubiquitous high speed wireless Internet access, for
summarizing and displaying click data from an E-Commerce site. The
primary criterion for evaluating the work of an engineer is
utilitarian: is the tool useful? The primary criterion for evaluating
the work of a mathematician is aesthetic: are the definitions,
theorems, proofs beautiful and do they contribute to internal structure
of mathematical knowledge? This by no means implies that mathematics is
not useful; nothing could be further from the truth. Highly abstract
areas of mathematics seemingly far removed from the "real world" (like
number theory) have turned out to be fundamental to the solution of
engineering problems (like encrypting information). It is just that
usefulness is not, and should not be, the criterion.
Beauty is not only evident in mathematical research. You can encounter
and enjoy it even in undergraduate courses like Abstract Algebra, where
the definitions, the theorems, and the proofs have been polished to a
high gloss by generations of mathematicians. For more information on
the various degrees offered by the Mathematics Department, follow the
link to degree programs in "Undergraduate Program in Mathematics"
(http://www.math.washington.edu/Undergrad).
If you are the kind of person who enjoys collaborating with others in
solving concrete problems, then you might choose the ACMS major or one
of the CSE majors. An important difference is that the ACMS major has a
much broader mathematics content than the CSE degrees. You will have to
learn what constitutes a proof, as well as some basic techniques for
proving theorems. Definitions and methods will be primarily expressed
in the language of mathematics, rather than in the form of data
structures and algorithms.
A fundamental concept at the core of the ACMS program is modeling -
casting a real world problem in a way that makes it amenable to
mathematical, statistical, or computational analysis. Modeling is a
creative activity and often a crucial step in understanding problems. A
prototypical example of modeling is kinetic gas theory. Kinetic gas
theory models the atoms or molecules in a gas as elastic balls moving
with a certain distribution of speeds. From this simple model many of
the properties of gases, like the connection between pressure and
temperature, can be derived using mathematical arguments. Somewhat
simplified, models come in two varieties, discrete - thinking of a DNA
molecule as a string over a four letter alphabet , or continuous -
thinking of the pressure over an airplane wing as a real-valued
function on a two-dimensional surface. Many models, like kinetic gas
theory or Mendel's famous model of inheritance, have a statistical
component. Continuous modeling, while central to many applications, is
not part of the CSE undergraduate curriculum, and statistical modeling
is only a small component.