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Two-dimensional plot (red curve) of the algebraic equation . Elementary algebra, also known as college algebra, [ 1 ] encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, [ 2 ] whilst algebra introduces variables (quantities without fixed values).
Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler, in 1736, [ 1 ] laid the foundations of graph theory and prefigured the idea of topology.
College algebra is offered at many community colleges as remedial courses for students who did not pass courses before Calculus. [69] It should not be confused with abstract algebra and linear algebra , taken by students who major in mathematics and allied fields (such as computer science) in four-year colleges and universities.
Often, the problem is to decompose a graph into subgraphs isomorphic to a fixed graph; for instance, decomposing a complete graph into Hamiltonian cycles. Other problems specify a family of graphs into which a given graph should be decomposed, for instance, a family of cycles, or decomposing a complete graph K n into n − 1 specified trees ...
Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms ...
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
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