Introduction and Small Talk
What is discrete mathematics?... Anyone know? "Not yet" right? If you've studied math in elementary, middle, high school, or even up to college in your second semester, you've likely only encountered general mathematics, such as the basics of arithmetic. In academic terms, though, mathematics itself is divided into around 12 courses, like linear algebra, logic, and so on. Each topic usually has a link between the first chapter and the last. For example, in linear algebra, chapter one is about matrices, chapter two about determinants (which also uses matrices), chapter three about inverses (also involving matrices), and systems of linear equations (also with matrices). However, discrete mathematics is a bit different. Discrete mathematics, as the name suggests, is still mathematics (of course, as you have studied before), but "discrete" itself means unconnected, fragmented, or discontinuous. So, in discrete mathematics, you will study topics that don’t necessarily link from chapter one to the last chapter. Surprising, right? &%$#
Topics of Discussion
For the night class, the topics we’ll cover are:
- Introduction
- Logic
- Sets
- Relations and Functions
- Mathematical Induction
- Combinatorics
- Graphs
- Trees
For topics 1-5, you have studied some of these, right? Topic 6 connects to permutations and combinations (which you may have learned in high school). Remember?
Then, graphs are core to discrete mathematics, and we’ll explore this topic extensively because it underpins many other courses, like Operating Systems. Have you studied operating systems yet? If so, then you may know about Congruence. What does Congruence include? Or, let’s put it this way—what are the consequences of Congruence? Any guesses? &^%$##@#$ (suddenly I’m at a deadlock). Exclusion, Starvation—what else? Hehehehe.
Alright, we’ll save that for another time. Graph concepts are also widely applied in real life, like in electrical installation models (series or parallel), traffic light installation schemes, route and road direction modeling, and much more. Okay, we’ll cover this in more detail later, as I have 125 slides to go through on this topic!
Trees
No, these are not plants, but rather trees in the context of graphs, which are also applied in real life for data structures, like in-order, pre-order traversals. Familiar with these terms? Okay, we’ll save that for later.
As for references, feel free to use any as long as all the material is covered. Or, you could simply use my material, which is quite comprehensive. Once I’ve uploaded it, I’ll let you know. We’ll set the grading criteria later based on the results of the first test, so I’ll follow up on the range.
September 15, 2014
