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2. Mathematical object - Wikipedia

   en.wikipedia.org/wiki/Mathematical_object

   Mathematical constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order to prove that an example exists. Contrastingly, in classical mathematics, one can prove the existence of a mathematical object without "finding" that object explicitly, by assuming its non-existence and then ...

3. Lists of mathematics topics - Wikipedia

   en.wikipedia.org/wiki/Lists_of_mathematics_topics

   Many mathematics journals ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The subject codes so listed are used by the two major reviewing databases, Mathematical Reviews and Zentralblatt MATH.

4. Glossary of areas of mathematics - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_areas_of...

   Mathematics is a broad subject that is commonly divided in many areas or branches that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers. This glossary is alphabetically sorted.

5. Abstraction (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Abstraction_(mathematics)

   Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

6. Class (set theory) - Wikipedia

   en.wikipedia.org/wiki/Class_(set_theory)

   Examples include the class of all groups, the class of all vector spaces, and many others. In category theory, a category whose collection of objects forms a proper class (or whose collection of morphisms forms a proper class) is called a large category. The surreal numbers are a proper class of objects that have the properties of a field.

7. Mathematical diagram - Wikipedia

   en.wikipedia.org/wiki/Mathematical_diagram

   In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.

8. Characterization (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Characterization_(mathematics)

   In mathematics, a characterization of an object is a set of conditions that, while possibly different from the definition of the object, is logically equivalent to it. [1] To say that "Property P characterizes object X" is to say that not only does X have property P, but that X is the only thing that has property P (i.e., P is a defining ...

9. Category of rings - Wikipedia

   en.wikipedia.org/wiki/Category_of_rings

   The category of commutative rings, denoted CRing, is the full subcategory of Ring whose objects are all commutative rings. This category is one of the central objects of study in the subject of commutative algebra. Any ring can be made commutative by taking the quotient by the ideal generated by all elements of the form (xy − yx).