What is discrete mathematics?
Q: What is discrete mathematics?
A: Discrete mathematics is the study of mathematical structures that are discrete rather than continuous. It involves objects such as integers, graphs, and statements in logic which have distinct, separated values and do not vary smoothly like real numbers.
Q: What topics does it exclude?
A: Discrete mathematics excludes topics in "continuous mathematics" such as calculus and analysis.
Q: How can discrete objects be counted?
A: Discrete objects can often be counted using integers.
Q: What is the definition of discrete mathematics?
A: Mathematicians say that this is the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the natural numbers, including rational numbers but not real numbers). However, there is no exact, universally agreed upon definition of the term "discrete mathematics." Many times, it is described less by what is included than by what is excluded - continuously varying quantities and related notions.
Q: Are all objects studied in discrete mathematics finite or infinite?
A: The set of objects studied in discrete mathematics can be either finite or infinite. The term finite mathematics sometimes applies to parts of the field which deals with finite sets particularly those areas relevant to business.
Q: How did research in discrete math increase during the 20th century?
A: Research in discrete math increased during the latter half of the twentieth century partly due to developments in digital computers which operate in discrete steps and store data in discrete bits.
Q: How are concepts from discrete math used outside its field?
A: Concepts and notations from discrete math are useful for studying and describing problems and objects within computer science such as algorithms, programming languages, cryptography etc., while computer implementations help apply ideas from this field to real-world problems like operations research.
