List of basic discrete mathematics topics
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This is a list of basic discrete mathematics topics, by Wikipedia page. Included here is much of the standard mathematical language, used in university-level courses and routinely in research papers. This is not, however, intended as a complete glossary of mathematical terms; just a selection of typical terms of art that may be encountered.
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Sets
- Set
- Ordered pair
- Cartesian product
- Power set
- Simple theorems in the algebra of sets
- Naive set theory
- Multiset
Functions
- Function
- How to specify a function
- Domain of a function
- Codomain
- Range of a function
- Image (mathematics)
- Injective function
- Surjection
- Bijection
- Function composition
- Partial function
- Multivalued function
- Binary function
- Floor function
- Sign function
- Inclusion (mathematics)
Operations
Arithmetic
- Decimal
- Binary numeral system
- Divisor
- Division by zero
- Indeterminate form
- Empty product
- Euclidean algorithm
- Fundamental theorem of arithmetic
- Modular arithmetic
- Successor function
Elementary algebra
- Left-hand side and right-hand side of an equation
- Linear equation
- Quadratic equation
- Solution point
- Arithmetic progression
- Recurrence relation
- Finite difference
- Difference operator
Mathematical relations
- Binary relation
- Mathematical relation
- Reflexive relation
- Reflexive property of equality
- Symmetric relation
- Symmetric property of equality
- Antisymmetric relation
- Transitivity (mathematics)
- Equivalence and identity
Mathematical phraseology
- If and only if (iff)
- Necessary and sufficient
- Distinct
- Difference
- Absolute value
- Up to
- Modulo
- Characterization (mathematics)
- Normal form
- Canonical form
- Without loss of generality
- Vacuous truth
- Contradiction, Reductio ad absurdum
- Counterexample
- Sufficiently large
- Pons Asinorum
- Table of mathematical symbols
Combinatorics
Probability
Propositional logic
Mathematical disciplines
For further reading in discrete mathematics, beyond a basic level, see these pages. Many of these disciplines are closely related to computer science.