Discrete Mathematics

3 units

Topics include sets, relations, functions, lo logic, numerical proof, graphs, binary, octal and hexadecimal number systems, combinatorics, induction and recursion, permutations, and voting theory. Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying smoothly, the objects studied in discrete mathematics - such as integers, graphs, and statements in logic do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics excludes topics in continuous mathematics such as calculus and analysis. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the integers, including rational numbers but not real numbers). However, there is no exact, universally agreed, definition of the term discrete mathematics. Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.