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  2. 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.

  3. AP Calculus - Wikipedia

    en.wikipedia.org/wiki/AP_Calculus

    According to the College Board: An AP course in calculus consists of a full high school academic year of work that is comparable to calculus courses in colleges and universities. It is expected that students who take an AP course in calculus will seek college credit, college placement, or both, from institutions of higher learning.

  4. AP European History - Wikipedia

    en.wikipedia.org/wiki/AP_European_History

    Advanced Placement (AP) European History (also known as AP Euro, APEH, or EHAP), is a course and examination offered by the College Board through the Advanced Placement Program. This course is for high school students who are interested in a first year university level course in European history .

  5. Jensen's inequality - Wikipedia

    en.wikipedia.org/wiki/Jensen's_inequality

    Jensen's inequality generalizes the statement that a secant line of a convex function lies above its graph. Visualizing convexity and Jensen's inequality. In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.

  6. Hilbert's fifth problem - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_fifth_problem

    The theory of Lie groups describes continuous symmetry in mathematics; its importance there and in theoretical physics (for example quark theory) grew steadily in the twentieth century. In rough terms, Lie group theory is the common ground of group theory and the theory of topological manifolds .

  7. Infimum and supremum - Wikipedia

    en.wikipedia.org/wiki/Infimum_and_supremum

    supremum = least upper bound. A lower bound of a subset of a partially ordered set (,) is an element of such that . for all .; A lower bound of is called an infimum (or greatest lower bound, or meet) of if

  8. Lambda calculus - Wikipedia

    en.wikipedia.org/wiki/Lambda_calculus

    LEQ := λm.λn.ISZERO (SUB m n), and since m = n, if LEQ m n and LEQ n m, it is straightforward to build a predicate for numerical equality. The availability of predicates and the above definition of TRUE and FALSE make it convenient to write "if-then-else" expressions in lambda calculus. For example, the predecessor function can be defined as:

  9. List of set identities and relations - Wikipedia

    en.wikipedia.org/wiki/List_of_set_identities_and...

    In constructive mathematics, "not empty" and "inhabited" are not equivalent: every inhabited set is not empty but the converse is not always guaranteed; that is, in constructive mathematics, a set that is not empty (where by definition, "is empty" means that the statement () is true) might not have an inhabitant (which is an such that ).