Preface About This Resource
The word discrete in the title of our course means separate; something that is not smooth.
In the study of discrete mathematics we will typically concern ourselves with discrete objects such as the integers, graphs, finite and countable sets. (In contrast, excluded from this are objects that may vary continuously, such as those ones covered in trigonometry, calculus, and Euclidean geometry.)
In these notes we take a tour through a variety of topics including counting techniques, the pigeonhole principle, number theory, and graph theory. Material is presented in a manner that encourages the reader to actively engage with the material, via inline exercises (called ‘checkpoints’) scattered throughout each section. A number of historical explorations and asides give context to some of these topics, and hopefully allow for a critical reflection on the historical and political underpinnings of the field and of mathematics as a whole.
These notes are being developed specifically for the Fall/Winter 2020-2024 offerings of MAT202: Introduction to Discrete Mathematics course at the University of Toronto Mississauga. For the online offering of this course a number of short videos will be produced and uploaded into the HTML version of these notes, to be inline with the text and in close proximity to the topic being discussed. These videos will be created and uploaded throughout the term.
A PDF (with no solutions or videos) will also be posted for offline access to the notes. The goal is to provide students with as many means of accessing and learning the material as possible (video, audio, text) but also for these notes to represent a logical flow for the course that supports student self-study.
Notable changes from the Fall/Winter 2019-2020 PDF notes include:
- Section 1.4 removed and expanded to a new appendix on mathematical communication;
- A number of historical explorations added throughout the text (there are plans for more in the future);
- Sections 5.2 and 5.5 each split into two smaller sections; paths and connectedness defined earlier in chapter;
- A small number of exercises (both inline and end-of-chapter) now have solutions in the HTML version (a few are added every year);
- New appendices added that index the introduction of new notation (Appendix B), list results (Appendix C), and compile examples and exercises (Appendix D).
- Selected questions from tests and exams up to 2023 have been included as well.