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About Mathematics

What Is Mathematics?

"The interplay between generality and individuality, deduction and construction, logic and imagination." — Courant

Mathematics is a collection of carefully developed tools that provide ways of solving problems in a huge variety of fields. Mathematics underlies problem solving in just about any scientific field that comes to mind. For example, consider medical imaging techniques: CAT scans, PET scans and MRIs. In all of these the problem is to transform raw data obtained from scans into a useable image of what is inside the human body; in all of them the key to solving this problem lies in mathematical algorithms. (Nobel prize winners in Medicine in both 1979 (for CAT scans) and 2003 (for MRIs) achieved precisely the development of the mathematics needed to interpret the data from scans.)

A 3D image of the equation equation equation z equals sin of square root of x squared plus y squaredAs another example, cosmologists try to determine the shape of the universe. The task is to find a model that fits the experimental data. The discussion is centered in topology, a field of mathematics.

As a final example, many people do not realize the extent to which business relies on mathematics. For example, large companies (such as airline companies) rely on experts in mathematics to solve practical problems such as scheduling and resource allocation. This field, called operations research or management science, involves applying a wide variety of mathematical techniques to the practical problems of business. The importance of mathematics in fields such as engineering, physics and chemistry is clear. In a sense, mathematics is a universal tool kit for problem solving. Plattsburgh State can provide you with the foundation you need to explore applied mathematics of this type.

But there is another face of mathematics that lures many people: the sheer fascination of the problems that it addresses. It is the field in which we try to find rational ways to deal with the idea of the infinite, in which we find ways to talk about spaces with more than three dimensions, and in which we find ways to conceive of space that is not flat, but curved. Even in the familiar whole number system (1,2,3...) there are deep unsolved mysteries. For example, twin primes are pairs of prime numbers that differ from each other by two (such as 3 and 5, 5 and 7, 11 and 13). It is conjectured that there are infinitely many twin primes, but this remains an unsolved problem. There is also stunning visual beauty in mathematics, as in the study of fractals.

What Does Mathematics Mean to You?

A fractal image is made from ever smaller repetitions of the same patternMathematics is truly different things to different people. Our Math Club recently asked our faculty what mathematics was. Here is a sampling of the responses they obtained:

"It is the discovery of universal laws that govern numbers, shapes and sets. Beyond discovery, it is the formulation of these laws into axioms, theorems and methodologies. On a more poetic level, mathematics is to the universe as current is to a stream."

"It is a body of knowledge containing generic tools for modeling aspects of the world that are considered in all sciences."

"It is a human endeavor combining the best characteristics of science and of art: the precision of thought and devotion to detail and to 'the real' as in science, and the creativity and freedom of expression as in art."

Come and find out more about mathematics at Plattsburgh State!

Questions, Comments, Suggestions?

If you would like more information about the mathematics program at SUNY Plattsburgh, please contact

Robert Keever, Chairperson
Office: Hawkins Hall 244
Phone: (518) 564-4133
Fax: (518) 564-4124