Symbolic Mathematics

Symbolic Mathematics in Artificial Intelligence

1. Artificial Intelligence

2. Symbolic Mathematics Solving Algebra Problems

3. SYMBOLIC MATHEMATICS: In mathematics and computerscience it is a scientific area it is refers to the study and development of algorithms and s oftware for manipulating mathematical expressions . Symbolic calculations use symbols. Symbolic computation is the sub-area of the mathematicsand computer science which solve symbolic problems o n symbolic objects representable on computer. Examples : Algebraic expressions Logical prepositions Programs

4. SYMBOLIC MATHEMATICS: Symbolic AI was the dominant technique of AI research from the mid- 1950s until the middle 1990s. One of the best-known symbolic mathematics software packages is mathematica. Other include ESP, AXIOM*, MAT-LAB.

5. H istory of AI, the research field is divided into two camps Symbolic AI Non-symbolic AI Symbolists firmly believed in developing an intelligent system based on rules and knowledge and whose actions were interpretable. Non-symbolic approach strived to build a computational system inspired by the human brain.

6. Symbolic Mathematics Finally Yields To Neural Networks By translating symbolic math into tree-like structures, neural networks can finally begin to solve more abstract problems. To allow a neural net work to process the symbols like a mathematician, charton and lample began by translating mathematical expressions into more useful forms. They ended up re - interpreting them . Mathematical operators such as addition, subtraction, multiplication and division became junctions on the tree. For almost all the problems, the program took less than 1 second to generate correct solutions.

7. Symbolic Mathematics Finally Yields To Neural Networks

8. SOLVING ALGEBRA PROBLEMS STUDENT : STUDENT was another early language understanding program, written by daniel bobrow as his Ph.D. Research project in 1964. It was designed to read and solve the kind of word problems found in high school algebra books. An example is: If the number of customers tom gets is twice the square of 20% of the number of advertisements he runs, and the number of advertisements is 45, then what is the number of customers tom gets? Student could correctly reply that the number of customers is 162.

9. STUDENT: SOLVING ALGEBRA PROBLEMS To do this, STUDENT must be far more sophisticated than ELIZA ; it must process and “understand” a great deal of the input, rather than just concentrate on a few key words. STUDENT program uses little more than the pattern- matching techniques of ELIZA to translate the input into a set of algebraic equations. From there, it must know enough algebra to solve the equations, but that is not very difficult. And it must compute a response, rather than just fill in blanks.

10. SOLVING ALGEBRA PROBLEMS The real work is done by solve, which has the following specification: (1) Find an equation with exactly one occurrence of an unknown in it. (2) Transform that equation so that the unknown is isolated on the left-hand side. This can be done if we limit the operators to +, -, *,and /. (3) Evaluate the arithmetic on the right-hand side, yielding a numeric value for the unknown. (4) Substitute the numeric value for the unknown in all the other equations, and remember the known value. Then try to solve the resulting set of equations. (5) If step (1) fails—if there is no equation with exactly one unknown—then just return the known values and don’t try to solve anything else.