Comments on MATH 206
JB (Buck) Stephen
based on Dosey/Spence 5th Ed.
MATH 206 is now required in various emphases in the CSCI program, and the majority of the
students taking MATH 206 are computer science majors: however, a typical class may also contain
majors in the various social sciences.
The underlying mathematical theme of the of the course delivery should address the following
goals - which also include the general education goals of the course:
1. Develop a basic understanding and ability to apply combinatorial models for structure (equiv-
alence relations, partial orders, graphical representation).
2. Develop an appreciation of proceduralism and an ability to structure an approach to various
types of problems. In particular, a distinction should be made between ad hoc methodology
and approaches applicable only to special cases, and generalizable techniques.
For example, when discussing the Euclidean algorithm for finding the greatest common divisor,
one should point out
(a) IF we can factor the two integers involved, then the gcd can be easily obtained, BUT
facoring is difficult.
(b) The Euclidean algorithm is applicable whether or not we have the factors of the integers,
and is less complex than finding the factors.
3. Develop a basic understanding of computational complexity. This should be reinforced through-
out the course and efficiency should be discussed.
For example: in section 1.4 various techniques for evaluating polynomials are discussed. At this
time discuss that computers perform addition much faster than multiplication and compare the
number of multiplications involved in evaluating the polinomials on both sides of an equation
such as the one preceding Horner’s method on pg 27.
4. An understanding of the halting problem - that is, how do we know a process ends. For instance,
the Euclidean algorithm ends eventually because the remainders decrease at every step and
are bounded below by 0. Contrast the with long division, which may never end.
With reference to the Euclidean algorithm, I note that this is another chance to discuss com-
plexity, in particular, given integers aand bwe do not have an effective way to predict the
actual number of steps we have to take to get the gcd, even though it is bounded by the largest
integer.
5. Develop the basic counting skills needed to further investigate combinatorial problems and
complexity.
6. Develop an understanding of the basics of formal logic.
7. Provide an introduction to matrices, their uses as data structures, and their use in representing
graphs and enumerating paths.
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