Introduction

# Discrete Math

Discrete Math is a catch all term that includes a variety of very different topics. What unifies these subjects is their common focus on objects that can only have a distinct, separate set of values.

Many schools also use discrete math as an opportunity to give students a first introduction to mathematical proofs. We're going to take that approach here as well.

1. Propositional Logic Mathematical or formal logic takes the idea of an argument and generalizes it so that we can make decisions about what kinds of arguments are valid and which ones aren't.
1. Predicate Logic Propositinal logic is a good start but there are limites to what we can do with it. It's limited to making statements about individual objects. Predicate logic extends propositional logic to allow for statements about groups of objects and their properties.
1. Number Theory Number theory is the study or the integers and their properties. The integers are a discrete set so they fit or definition of discrete math. They also provide a good start pointing for our discussion of mathematical proofs.
1. Set Theory Sets are just collections of objects but, since many mathematical objects fit that description, set theory applies to a lot of different scenarios.
1. Sequences and Recursion A sequence is just an ordered list of numbers which you can think of as a function whose domain is the natural numbers, i.e. a discrete set.
1. Counting and Probability Combinatorics is a branch of math that studies methods of counting the ways that finite sets of objects can be arranged.
1. Finite State Automata Finite state automata give us a way to model computations by thinking of all the possible states a machine can be in.

## Our Approach to Teaching and Learning

Math is a little unusual in the academic world. Unlike a lot of subjects, you're expected to actually be able to do the math by the time the class is done. You can't get there by watching other people do math or reading it about it in a book. You have to get out a pencil and paper and do it for yourself. The video lectures are a good starting point for your study but you should also spend time working on the exercises and the "explorations" material. Important concepts are discussed in the Explorations material and the associated videos as well as in the main lectures. Problems in the Practice sections marked with a star are particularly important. You should try to solve those on your own based on the lecture material but it's also worth checking out the posted solutions for additional important techniques and concepts.

### Prior Knowledge

Discrete Math is very different from the math that most students have experience with. From the practical side we aren't going to use more than basic algebra. However, you do need a level of mathematical experience or sophistication that comes from making it through first semester calculus.

### Time to Completion

This course is modeled after a three or four credit, one semester college class. That means it can be done in roughly four months but that's going to require a relatively substantial time commitment and a steady pace. Five or six months is more realistic if you want to take a more relaxed approach.

### Technologies Used

We try to keep it simple but there are some things that we need to provide the interactive content that makes our classes special. Fortunately everything you need, including JavaScript and HTML5 compatability, is available in every modern browser.