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Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
A trivial example. In mathematics, the mountain climbing problem is a mathematical problem that considers a two-dimensional mountain range (represented as a continuous function), and asks whether it is possible for two mountain climbers starting at sea level on the left and right sides of the mountain to meet at the summit, while maintaining equal altitudes at all times.
For functions in certain classes, the problem of determining: whether two functions are equal, known as the zero-equivalence problem (see Richardson's theorem); [4] the zeroes of a function; whether the indefinite integral of a function is also in the class. [5] Of course, some subclasses of these problems are decidable.
Linear function: First degree polynomial, graph is a straight line. Quadratic function: Second degree polynomial, graph is a parabola. Cubic function: Third degree polynomial. Quartic function: Fourth degree polynomial. Quintic function: Fifth degree polynomial. Rational functions: A ratio of two polynomials. nth root
Integral Calculus. Theory of Functions.; and (II) Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry. The volumes are highly regarded for the quality of their problems and their method of organisation, not by topic but by method of solution, with a focus on cultivating the student's problem-solving skills. Each ...
For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; and they are used in calculus and ...
13. Impossibility of the solution of the general equation of 7th degree by means of functions of only two arguments. 14. Proof of the finiteness of certain complete systems of functions. 15. Rigorous foundation of Schubert's enumerative calculus. 16. Problem of the topology of algebraic curves and surfaces. 17. Expression of definite forms by ...
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