List of basic discrete mathematics topics
From Wikipedia, the free encyclopedia
- For a more comprehensive list, see the List of discrete mathematics topics.
Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite mathematics are countable sets, such as integers, finite graphs, and formal languages. Discrete mathematics has become popular in recent decades because of its applications to computer science. Concepts and notations from discrete mathematics are useful to study or describe objects or problems in computer algorithms and programming languages. In some mathematics curricula, finite mathematics courses cover discrete mathematical concepts for business, while discrete mathematics courses emphasize concepts for computer science majors. For contrast, see continuum, topology, and mathematical analysis.
Included below are many of the standard terms used routinely in university-level courses and in research papers. This is not, however, intended as a complete list of mathematical terms; just a selection of typical terms of art that may be encountered.
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Contents |
[edit] Nature of discrete mathematics
- Main article: Discrete mathematics
[edit] The discrete mathematics subjects
- Logic - a study of reasoning;
- Set theory - a study of collections of elements;
- Number theory;
- Combinatorics - a study of counting;
- Graph theory;
- Digital geometry and digital topology;
- Algorithmics - a study of methods of calculation;
- Information theory;
- Computability and complexity theories - dealing with theoretical and practical limitations of algorithms;
- Elementary probability theory and Markov chains;
- Linear algebra - a study of related linear equations.
- Functions
- Partially Ordered Sets
- Probability
- Proofs
- Counting and Relations
- Collections
[edit] Discrete 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.
- Automata theory
- Combinatorics
- Combinatorial geometry
- Computational geometry
- Digital geometry
- Discrete geometry
- Graph theory
- Mathematical logic
- Combinatorial optimization
- Set theory
- Combinatorial topology
- Number theory
- Information theory
- Game theory
[edit] History of discrete mathematics
- Main article: History of discrete mathematics
[edit] Concepts in discrete mathematics
[edit] Sets
- Set
- Ordered pair
- Cartesian product
- Power set
- Simple theorems in the algebra of sets
- Naive set theory
- Multiset
[edit] 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 map
- Pigeonhole principle
- Relation composition
- Permutations
- Symmetry
[edit] Operations
[edit] Arithmetic
- Decimal
- Binary numeral system
- Divisor
- Division by zero
- Indeterminate form
- Empty product
- Euclidean algorithm
- Fundamental theorem of arithmetic
- Modular arithmetic
- Successor function
[edit] 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
- Groups
- Group isomorphism
- Subgroups
- Fermat's little theorem
- Cryptography
- Faulhaber's formula
[edit] 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
[edit] 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
- Contrapositive
- Mathematical induction
[edit] Combinatorics
- Permutations and combinations
- Permutation
- Combination
- Factorial
- Pascal's triangle
- Combinatorial proof
[edit] Probability
- Average
- Expectation
- Discrete random variable
- Sample space
- Events
- Conditional Probability
- Independence
- Random variables
- Expectation
[edit] Propositional logic
[edit] Discrete mathematicians
[edit] Discrete mathematics lists
- Main article: List of discrete mathematics topics
[edit] See also
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