Mathematics Concept
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A Mathematics Concept is a concept that forms part of the foundational knowledge and theoretical framework of mathematics.
- AKA: Mathematical Concept, Math Concept, Mathematical Idea, Mathematical Notion.
- Context:
- It can typically involve numbers and their mathematical operations, mathematical relations, mathematical combinations, and mathematical abstractions.
- It can typically involve mathematical spaces and their mathematical structures, mathematical measurements, mathematical transformations, and mathematical generalizations.
- It can typically be expressed through mathematical language using mathematical terms, mathematical symbols, and mathematical notations.
- It can typically be formalized through mathematical definitions that specify its mathematical properties and mathematical relationships.
- It can typically be studied through mathematical theories that explore its implications and applications.
- It can typically be demonstrated through mathematical proofs that establish its validity and connections.
- It can typically be taught through mathematics education using mathematical examples and mathematical problems.
- It can typically be applied to solve real-world problems through mathematical modeling and mathematical analysis.
- It can often build upon simpler mathematics concepts to form more complex mathematical structures.
- It can often connect to other mathematics concepts through mathematical relationships and mathematical equivalences.
- It can often be visualized through mathematical diagrams, mathematical graphs, and mathematical representations.
- It can often evolve through mathematical research leading to new mathematical discoveries.
- It can often be implemented in computational systems through mathematical algorithms and mathematical software.
- It can often bridge different mathematical domains through mathematical unifications.
- It can often inspire mathematical conjectures and open mathematical problems.
- It can range from being a Simple Mathematics Concept to being a Complex Mathematics Concept, depending on its conceptual depth.
- It can range from being a Concrete Mathematics Concept to being an Abstract Mathematics Concept, depending on its abstraction level.
- It can range from being an Elementary Mathematics Concept to being an Advanced Mathematics Concept, depending on its mathematical sophistication.
- It can range from being a Pure Mathematics Concept to being an Applied Mathematics Concept, depending on its application focus.
- It can range from being a Classical Mathematics Concept to being a Modern Mathematics Concept, depending on its historical period.
- It can be referenced by mathematical terms in mathematical literature and mathematical discourse.
- It can be organized into mathematical taxonomies and mathematical hierarchies.
- It can be assessed through mathematical problem solving and mathematical reasoning.
- ...
- Example(s):
- Number Concepts, such as:
- Natural Number: counting numbers 1, 2, 3, ...
- Prime Number: numbers divisible only by 1 and themselves.
- Infinity: concept of unboundedness.
- Zero: additive identity and placeholder.
- Irrational Number: numbers like π and e.
- Algebraic Concepts, such as:
- Variable: symbol representing unknown quantity.
- Equation: mathematical statement of equality.
- Function: mapping between sets.
- Group Theory Concept: symmetry and transformation.
- Ring Theory Concept: algebraic structure with operations.
- Geometric Concepts, such as:
- Point: location with no dimension.
- Line: one-dimensional extent.
- Circle: points equidistant from center.
- Euclidean Geometry Concept: flat space geometry.
- Non-Euclidean Geometry Concept: curved space geometry.
- Calculus Concepts, such as:
- Limit: value approached by function.
- Derivative: rate of change.
- Integral: area under curve.
- Continuity: unbroken function behavior.
- Differential Equation: relating functions and derivatives.
- Statistical Concepts, such as:
- Mean: average value.
- Standard Deviation: measure of spread.
- Probability Distribution: likelihood patterns.
- Hypothesis Testing: statistical inference.
- Correlation: relationship between variables.
- Discrete Mathematics Concepts, such as:
- Set: collection of distinct objects.
- Graph Theory Concept: networks and connections.
- Combinatorics Concept: counting and arrangement.
- Logic Concept: formal reasoning.
- Algorithm: computational procedure.
- Linear Algebra Concepts, such as:
- Vector: directed magnitude.
- Matrix: rectangular array of numbers.
- Eigenvalue: scaling factor.
- Vector Space: algebraic structure.
- Linear Transformation: structure-preserving map.
- Topology Concepts, such as:
- Open Set: neighborhood concept.
- Continuity: preserved under mapping.
- Compactness: finite subcover property.
- Connectedness: single piece property.
- Number Theory Concepts, such as:
- Divisibility: factor relationship.
- Modular Arithmetic: remainder systems.
- Diophantine Equation: integer solutions.
- Category Theory Concepts, such as:
- Morphism: structure-preserving map.
- Functor: mapping between categories.
- Natural Transformation: systematic construction.
- ...
- Number Concepts, such as:
- Counter-Example(s):
- Physics Concept, such as force, energy, molecule (natural science rather than pure mathematics).
- Computer Science Concept, such as space complexity, Quicksort algorithm (computational rather than mathematical).
- Engineering Concept, such as circuit design, structural analysis (applied technology rather than mathematics).
- Chemistry Concept, such as chemical bond, reaction rate (empirical science rather than mathematics).
- Biology Concept, such as evolution, cell division (life science rather than mathematics).
- Philosophy Concept (except philosophy of mathematics), which uses different reasoning methods.
- Artistic Concept, which involves aesthetic rather than mathematical principles.
- See: Mathematics, Mathematical Object, Mathematical Structure, Mathematical Term, Theoretical Mathematics, Applied Mathematics, Mathematics Education, Mathematical Theory, Mathematical Proof, Mathematics Textbook, Mathematical Word Problem, Statistical Concept, Discrete Mathematics Concept, Linear Algebra Concept, Geometry Concept, Mathematical Beauty, Mathematical Knowledge, Mathematical Reasoning, Quantitative Reasoning Task.
References
2007
- http://www.merriam-webster.com/dictionary/mathematics
- QUOTE: the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations