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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.
The mathematics reference desk is useful if you have a question and don't know where to look up the answer. Explore the category system. The mathematics portal is a good "way in" to mathematics articles on Wikipedia. If you are in doubt, ask at the mathematics reference desk.
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers. It is typically taught to secondary school students and at introductory college level in the United States, [5] and builds on their understanding of arithmetic. The use of variables to denote quantities allows ...
[1] If the C*-algebra acts topologically irreducibly on the Hilbert space , {,,} is a set of vectors and {,,} is a linearly independent set of vectors in , there is an in such that =. If B x j = y j {\displaystyle Bx_{j}=y_{j}} for some self-adjoint operator B {\displaystyle B} , then A {\displaystyle A} can be chosen to be self-adjoint.
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