Analysis and synthesis in solving math problems. Analysis and synthesis are widely used in solving mathematical problems. Recall that the analysis is a method of reasoning from the desired data. Synthesis method of reasoning, leading from the desired data. Both of these methods are usually applied in the relationship.
Analysis and synthesis are used practically every kind of decision of tasks, each task:
1) analysis and synthesis in solving problems of proof.
2) analysis and synthesis when solving the task text. Text tasks here named mathematical tasks where input information contains not only the mathematical data, but some plot (plot).
When solving the task of text using the apparatus of arithmetic role analysis comes down to planning decision task is solved more often synthetic method.
3) analysis and synthesis to solving problems on construction in geometry.
Analysis and synthesis are applied and in meeting the challenges of building in geometry, otherwise, constructive geometry tasks. As you know, these tasks are updated according to the following pattern: analysis, build, proof of study. The title of the first part of the analysis speaks for itself: it's really a method of analysis, leading from the search ("suppose that desired shape built") to the data, more precisely, to their use in the build. When analyzing the build plan is planned, which is synthetic means. In proving it is possible to use both analysis and synthesis, but more often is applied last. Study suggests preferential application of the method of analysis.
Other common methods of problem solving.
Discussed in the preceding paragraphs of analysis and synthesis are the most common methods of problem solving. The following are common methods for solving tasks, which have a more limited application.
One of them is the comprehensive method of sampling, which is based on the identification of all the logical possibilities and selection of them that satisfy such tasks. If the logical possibilities of matching tasks, finite number, it may be possible to go through all of them and during this iteration completely match highlight. By using this technique are being addressed through, inter alia, some rudimentary tasks of theoretical-numerical content. Comprehensive sampling math problem solver method with great success and can be used for solving many logical problems. The development of specified reception serve some methods of solution in integers or rational numbers indeterminate equations, in particular well. known method of dispersion.
The second method is a method of information. The gist of it is that the data were subjected to successive tasks.. The end of the resulting thus transform chain can be State, simple which gives the desired ' results. For example, if you want the equation solver, usually make such final sequence of equations equivalent to this, the latest of which is the equation of ' an obvious solution. Similarly, comes when solving systems of equations, inequalities, systems of equations and inequalities.
Problem solving on proof very often represents a chain of identical transformations, stretching from left side of demonstrable right identities, or vice versa, or from the left and right parts of the same expression. Of course, the specified mixing must be understood and as diversion, as the ultimate sequence leading from the desired data. This method is most often used in cases where a specified ratio has the property of transitivity.
These are equivalence relations (equality, equations, identities, logical, parallelism) m (severe and non-severe inequality, inclusion sets the logical following). Reception "information" lies at the core of solving geometric build tasks. In every task of this kind requires: on the basis of shape data (or data items), using the specified structural elements to build a shape that satisfies certain conditions.
This means that the desired build must be reduced to the so-called basic builds performed by real instruments.
Method information finds permanent use when solving the task text the arithmetic means. The crux of the matter here is that this problem is reduced to simple tasks.
Problem solving on theorem proving in its basis is also mixing: allegation is previously proven theorems and axioms and definitions introduced earlier in this scientific field. Prove-it means bring a new theorem (task) would ultimately lead to the axioms.
The third method of solving tasks have their basis simulation (mathematical and substantive). To model different mathematical objects are involved: numerical formulas, numeric, alphabetic, table formulas, functions, algebraic or differential equations and their systems of inequalities, systems of inequalities (as well as inequalities and equations), ranks, geometric shapes.