What is the word problem group theory?

In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G is the algorithmic problem of deciding whether two words in the generators represent the same element.

How do I solve this word problem?

Problem-Solving Strategy

1. Read the word problem. Make sure you understand all the words and ideas.
2. Identify what you are looking for.
3. Name what you are looking for.
4. Translate into an equation.
5. Solve the equation using good algebra techniques.
6. Check the answer in the problem.
7. Answer the question with a complete sentence.

What is a word problem with examples?

Word problems commonly include mathematical modelling questions, where data and information about a certain system is given and a student is required to develop a model. For example: Jane had $5.00, then spent $2.00. How much does she have now?

What are four problem solving steps?

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:

1. Step 1: Understand the problem.
2. Step 2: Devise a plan (translate).
3. Step 3: Carry out the plan (solve).
4. Step 4: Look back (check and interpret).

What is the importance of group theory in physics?

Group theory. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography . One of the most important mathematical achievements of the 20th century was the collaborative effort,…

What are the three main sources of group theory?

Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic strand was begun by Leonhard Euler, and developed by Gauss’s work on modular arithmetic and additive and multiplicative groups related to quadratic fields.

What is the history of group theory in geometry?

In geometry, groups first became important in projective geometry and, later, non-Euclidean geometry. Felix Klein’s Erlangen program proclaimed group theory to be the organizing principle of geometry. Galois, in the 1830s, was the first to employ groups to determine the solvability of polynomial equations.

What is combinatorial and geometric group theory?

Combinatorial and geometric group theory. Combinatorial group theory studies groups from the perspective of generators and relations. It is particularly useful where finiteness assumptions are satisfied, for example finitely generated groups, or finitely presented groups (i.e. in addition the relations are finite).