Mathematics - Why Math?
Mathematics is the Queen of the Sciences, and Arithmetic the Queen of Mathematics -- C.F. Gauss
Frequently, people equate mathematics with arithmetic and other types of numerical computation. In fact, many areas of mathematics (calculus, numerical analysis) are primarily concerned with efficient computations. The development of elegant advanced tools of computation is indeed a part of our discipline.
But mathematics is much more. Modern mathematics -- that is, twentieth century mathematics -- claims a much broader part of human inquiry:
The science of Pure Mathematics, in its modern developments, may claim to be the most original creation of the human spirit. -A.N. Whitehead
Some describe mathematics as the study of functions: calculus is the study of differentiable and integral functions, algebra is the study of homomorphisms, topology is the study of continuous functions. Others describe it as a study of structures or sets. Number systems to networks -- even functions themselves -- can all be described in terms of systems of sets. Still others see mathematics as the discipline of logical problem-solving. At the basis of all of this is a way of thinking. Mathematicians are in the business of logical reasoning. In every area of mathematics, students and teachers together build entire theories from first principles, rigorously and critically testing each claim.
Progressing from basic assumptions and motivated by unsolved problems, we ascend through each theory, always insisting on rigorous proofs of each theorem and keeping our eye on the applications for guidance.
A typical course in modern mathematics begins with nothing more than a few definitions and a modest set of assumptions.
``When I use a word,'' Humpty-Dumpty said, ``it means just what I choose it to mean -- neither more nor less.'' --Lewis Carroll
From such a meager starting point, a mathematician is trained to build a system of truths, a set of tools, via the rigours of logic.
So mathematics is a way of thinking, a way of learning. A wide variety of courses can be found in the department. Some are theoretical, some are applied, some both. Some are more difficult than others, but the beginning student should beware: mathematics has a few surprises in store.
Be ready for a challenge and be ready to see some aspects of mathematics that you never knew existed!
read about the UW Math program 
Mathematics: the swiss army knife of Science