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  2. Modular arithmetic - Wikipedia

    en.wikipedia.org/wiki/Modular_arithmetic

    Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...

  3. Order of operations - Wikipedia

    en.wikipedia.org/wiki/Order_of_operations

    Order of operations. In mathematicsand computer programming, the order of operationsis a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and an ...

  4. Module (mathematics) - Wikipedia

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

    In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module also generalizes the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers . Like a vector space, a module is an additive abelian group, and scalar ...

  5. Mathematical logic - Wikipedia

    en.wikipedia.org/wiki/Mathematical_logic

    v. t. e. Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.

  6. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

  7. American Mathematics Competitions - Wikipedia

    en.wikipedia.org/wiki/American_Mathematics...

    The American Mathematics Competitions ( AMC s) are the first of a series of competitions in secondary school mathematics sponsored by the Mathematical Association of America that determine the United States of America's team for the International Mathematical Olympiad (IMO). The selection process takes place over the course of roughly five stages.

  8. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures ...

  9. Set (mathematics) - Wikipedia

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

    Set (mathematics) A set of polygons in an Euler diagram. This set equals the one depicted above since both have the very same elements. In mathematics, a set is a collection of different [ 1] things; [ 2][ 3][ 4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points ...