Defining combinatorics is a little tricky. In the broadest terms, it's about looking at a finite set of objects and asking questions about them. For example, "How many possible hands are there in poker?" or "What pattern exists in this set of numbers?" From a more theoretical perspective, combinatorics can be defined in terms of what it isn't: It doesn't have a unique theoretical basis like other mathematical fields, e.g. algebra and calculus, do. Instead, its methods are based on taking techniques from other fields and applying them in new and creative ways.
Each section in the course is made up of text explanations, examples, video lectures and exercises. While the text and video content aren't identical, we've worked to make sure that the text and video both constitute a complete explanation of the material so, for example, if you're a video person, you can ignore the text, watch the videos and get all the content. Similarly, you could just read through the text and get all of the course content.
If you would like a physical copy of the material, you can purchase the text through our on demand publisher. The text in the paper version corresponds to the text content in the classroom.
Level of Difficulty
The introductory combinatorics classroom is part of our algebra two curriculum. While the material is presented at a technical level, it should be accessible to anyone with an understanding of high school level algebra. The first chapter requires no special mathematical background beyond arithmetic. This chapter is a great example of what I discussed in the opening paragraph - it's all about creative applications of some relatively basic concepts. Chapters two and three, on the other hand, both make use of polynomials so students should be familiar with their basic methods, specifically evaluating polynomials for specific values and multipyling two polynomials together.