The book has seen its first full semester of use. I thank my Fall 2020 students, especially Chris Grigsby and Robert Dwyer, for their diligent search for mistakes. Before the Spring 2021 semester, some of the problems in the combinatorics section will see revision (both for wording and content). If you have comments, please send them to wweathers at coastal dot edu.
It is my tentative plan to convert this book into the PreTeXt format in the summer of 2021. Its current organization is horrible, but it was made in haste after the COVID-19 outbreak.
The table of contents is reproduced here for mobile readers. Scroll beyond for an introduction to the materials for students and instructors.
If you are reading this, one of these five statements are true:
For 1-3, read on; for 4, skip to the next section; good luck to 5.
There are three components to this book Elementary discrete mathematics: the text, the problems, and the videos. All three parts have the goal of making discrete math accessible to anyone, at all levels of mathematical and physical ability. Note that accessibility was a guiding principle in the construction of the resources: the web format for the book was chosen purposefully and the videos all have full subtitles. This is all currently a work in progress so if you find that a particular item is not fully accessible to you send an e-mail to wweathers at coastal dot edu and I will make it a priority.
If you are viewing the book on a desktop or laptop computer or a suitably large tablet, you will find a table of contents on the left-hand side that contains links to each of the book’s eighteen chapters, the four video playlists, and the problem page. Furthermore the end of each chapter contains a link to its corresponding problem set.
Though a tablet or computer is preferred, you may read the book on your phone as well. Since the side navigation does not display on mobile browsers, there is a table of contents at the very top of the text as well. Finally, be warned that you may have to reorient your device for some items (e.g. the truth tables in Chapter 2) to display correctly. If even after reorientation the mobile version of the book is difficult to read, let me know at wweathers at coastal dot edu.
Your workflow should be text-videos-problems or videos-text-problems. It is not obvious to me whether you should watch the videos or read the text first; I expect everyone will have their own preference. The videos are organized into four “units” (these are exams in my course): Sets and Logic, Proof and Recursion, Combinatorics, and Relations. It should be clear from the title and description of each video what the relevant chapter is. Then, you should work the problems. They more or less ramp from straightforward checks on the material to more interesting explanations. If you struggle with the problems, ask your instructor; if you are an independent learner and I am not busy sending me an e-mail may prove fruitful.
Finally, focus on communication and understanding. There is a lot to learn here, and some of it is difficult; but if you focus on trying to understand the concepts and communicating them with a classmate or peer, you should do well.
So you want to use these materials for your own course? Fantastic. These resources are for the free use of any instructor who is dedicated to building an inclusive and supportive classroom environment. You are free to modify the resources however you want and use whichever ones you like.
To that end, let’s discuss dependencies. Chapters 1-8, which comprise the first and second parts of my course, are fundamental. With a little rewriting you could transpose chapters 1 and 2/3 (doing logic before sets), and for students who are not going on to computer science courses you may choose to skip the discussions on binary numbers (Chapter 5 – though, bit strings will be important for combinatorics later) and asymptotics (Chapter 7). Chapters 9-13 (on combinatorics) and Chapters 14-18 (on relations) are basically interchangeable, though there are problems in sets 14-18 that assume the reader knows how to count. Of course, these can be reordered.
If you would like the source files for the book and problems, send an e-mail to wweathers at coastal dot edu. While the videos can’t be easily edited to suit your purposes, you are welcome to use them in your classes as well.
If you find this book useful enough that you would like to pay something for it, please instead donate to Mathematically Gifted and Black, an organization that highlights mathematicians of the African Diaspora and supports predoctoral mathematicians.