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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]
On the other hand, the fact that a particular algorithm does not solve the word problem for a particular group does not show that the group has an unsolvable word problem. For instance Dehn's algorithm does not solve the word problem for the fundamental group of the torus. However this group is the direct product of two infinite cyclic groups ...
Word problem may refer to: Word problem (mathematics education) , a type of textbook exercise or exam question to have students apply abstract mathematical concepts to real-world situations Word problem (mathematics) , a decision problem for algebraic identities in mathematics and computer science
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.
In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z −1 xzz and y −1 zxx −1 yz −1 are words in the set {x, y, z}. Two different words may evaluate to the same value in G, [1] or even in every group. [2]
In all participating countries the challenge is a multiple-choice test. Collecting results, marking, and awarding prizes are regulated and organized nationally. In most countries, the challenge runs for 50 up to 75 minutes. [13] It consists of 24 up to 30 problems. The sections for 3 point-, 4 point-, and 5 point-problems are equally divided.
Group of Two (G2): hypothetical and informal grouping between the United States and China, representing the countries with the two largest economies in the world EU's G6 - France, Germany, Italy, Poland, Spain, and the United Kingdom - countries with largest populations and thus the majority of votes in the Council of the European Union
NWEA assessments are used by over 50,000 schools and districts in 149 countries. [3] There are over 16.2 million students using NWEA. [ 4 ] Its primary assessment product is the MAP Suite, a collection of formative and interim assessments that help teachers identify unique student learning needs, track skill mastery, and measure academic growth ...