The course required to satisfy this requirement is M325K: Discrete Mathematics.

This course can be thought of as an introduction to the language and culture of mathematics. As such, it is a useful course for a mathematics teacher, and for multiple reasons.

Much difficulty with mathematics arises because arguments and usages that are fine in everyday language, are ``wrong'' in mathematical language. On the other hand, throughout its history, the power of mathematics has been entwined with precisely this difficulty. Its precision as a language, and the absoluteness of its statements are often what make mathematics seem hard. All of this comes under the heading of rigor, and rigor is a key concern of this course.

A central part of the rigor of modern mathematics involves its insistence on proofs. To a large extent, this course is an introduction to proofs and the writing of proofs. Some of the time the student learns about the need and art of proving simple things that may seem obvious. Through its discussion of the paradoxes, the course tries to address the need for proofs for simple things. Other times the proofs should concern deeper and even surprising results. Both sorts of proofs will be found in the number theory component of this course. Besides convincing one of the truth of a statement, proofs can explain and focus on what's vital. Also, despite their formal nature, finding proofs will be seen by the student as a combination of logic and intuition. This combination of formal rigor and intuition is a key component of mathematics.

This course also is an introduction to the power and difficulties of abstract mathematics. Through formal logic, and graph theory, the student will see how mathematics extracts essentials and finds patterns. This abstraction process is related to the process of modeling, where ``real world'' phenomenon are described, necessarily inexactly, via models which pick out essential attributes and their interaction. Once again, the graph theory portion of this class can serve as an example.

Sometimes rigor and proof are employed to deal with abstraction, and sometimes they are employed to make exact something very concrete liking counting. The mathematics of counting is called ``combinatorics'', and this course often has an introduction to this subject. Counting is usually the first mathematics anyone learns, but in combinatorics one quickly learns that counting can have surprising depth and subtlety just as in number theory. For example, here one often utilizes a common trick in mathematics, that of understanding or proving something by looking at it in two ways. Once again the goal here is to make rigorous something commonplace but deep.

All of this rigor, and all of the abstraction and modeling, would be of no use unless mathematics used these tools to give answers. For example, a formula (say the quadratic formula) will give an answer ``mechanically'', without cleverness or intuition. This is a common occurrence in high school mathematics. In the wider mathematical world, there are mechanical processes for finding certain answers that are not formulas and these are called algorithms. This course considers specific important algorithms, and considers where algorithms are lacking and intuition takes over. For example, the Euclidean algorithm is often treated in the number theory part. This is a very efficient process that is a key part of algorithmic mathematics. More abstractly, this course covers an algorithm, or more precisely a decision procedure, for formal propositional logic. On the other hand, when the course turns to predicate (quantifier including) logic the student will not have a mechanical algorithm to employ and will have to turn to more intuitive approaches.

The best mathematics teachers put their particular material in the framework and context of the wider mathematical world, and this course is an introduction to the mathematics that lies beyond, and seems quite different from, the traditional high school subjects. By taking a closer look a simple things like numbers, by abstracting essentials and modeling via graphs, and by treating formal logic, the course hopes to broaden the mathematical perspective of its students, so they can in turn do the same for their students.

Although most high school curricula do not include a course specifically in discrete mathematics, some do. Discrete Mathematics Through Applications is one example of a textbook for a high school course in discrete mathematics. It has recently been ordered for the UTeach Resource Center. The 1989 Curriculum and Evaluation Standards for School Mathematics discusses the role of Discrete Mathematics in the 9-12 curriculum