This text aims to give an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math majors, especially those who intend to teach middle and high school mathematics. A difference between this text and most other discrete math books is that this book is intended to be used in a class taught using problem oriented or inquiry based methods.
- 3: Symbolic Logic and Proofs
- Logic is the study of consequence. Given a few mathematical statements or facts, we want to be able to draw some conclusions. Whenever we find an “answer” in math, we really have a (perhaps hidden) argument. Mathematics is really about proving general statements (like the Intermediate Value Theorem), and this too is done via an argument, usually called a proof. We start with some given conditions, the premises of our argument, and from these we find a consequence of interest, our conclusion.
- 4: Graph Theory
- Graph Theory is a relatively new area of mathematics, first studied by the super famous mathematician Leonhard Euler in 1735. Since then it has blossomed in to a powerful tool used in nearly every branch of science and is currently an active area of mathematics research.
Thumbnail: A Venn diagram illustrating the intersection of two sets. (Public Domain; Cepheus via Wikipedia).