# ADVANCED FINITE MATHEMATICS

## About the course

First of all, this course is the new version of the old “Discrete Mathematics” course. (The state standards are at the link below.)

I introduced a semester-long discrete mathematics course in the 06-07 school year. As there were no state objectives or standards for this course (even though it was on the approved list of courses), it was up to me to determine what to teach and the book to use.

As an initial guide, I turned to Georgia Perimeter College’s discrete mathematics course. This may seem an odd choice, but some magnet school students in 2004 and 2005 took the course through the Joint Enrollment program, and absolutely hated it. According to them, the class did not move fast enough and they were slowed down by the regular, non-JE college students. However, the topic structure and the textbook were good, so I adopted and adapted them.

With no published state standards, I was free to alter the topics as I wanted. Some years, I would include graph theory, some years I would not. Some years would include function theory, and some years not. Every year included logic, set theory, number theory, basic proof techniques, counting, and probability.

Eventually, the course became a semester long (paired with the semester-long History of Mathematics course). In the 2010-2011 school year, the state abolished the course. But by 2015, with feedback from alumni whoo found the course to be the most beneficial mathematics course they took in high school, I wrote a brand-new curriculum for a new version of the course, which was first taught for the 2016-2017 school year as a year-long course. I have taught this course every year since.

## The syllabus

The course syllabus is aligned with the textbook chapter and sections.

For five consecutive years I taught this course under the name “Discrete Math” (from 06-07 to 10-11), and I was happy to bring it back in its current form for the 2016-2017 school year.

## The textbook

The textbook I use is the remarkable and easy-to-understand Discrete Mathematics with Applications, fifth edition, by Susanna S. Epp. Students over the years have commented that the book is very easy to follow. They also comment that problems are generally very good and illustrate the concepts perfectly.

**Old tests from previous years**