Two educators from UC San Diego joined forces to write this free combinatorics textbook. Includes exercises with answer key. Download PDFs of each chapter.
Free Discrete Mathematics Textbooks
In attempting to find a somewhat simple definition of discrete mathematics with you, I came to realize that it is a topic not easily defined. A few definitions even seemed to proclaim that it was not truly a field of study under the broader topic of mathematics. Discrete mathematics study objects which have distinct values.
Discrete mathematics discusses combinatorics, number theory and vertex-edge graphs. One university website indicated a course in single variable calculus is a required prerequisite.
As defined by Wikipedia, “discrete has been characterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the natural numbers, including rations numbers but not real numbers). For the most part, mathematicians don’t agree on a definition for discrete mathematics. They often describe it in terms of what it isn’t rather than what it is. It excludes topics in “continuous mathematics” like calculus and analysis.
The field of discrete mathematics has really grown due to advanced in computer technology. Discrete mathematics can be used to solve real-world problems in operations research.
Computational geometry, theoretical computer science, graph theory and combinatorics are branches of discrete mathematics. And discrete mathematics was part of the advances in crytography, telecommunications and software development of safety-critical systems.