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The Trachtenberg Speed System of Basic Mathematics by Jakow Trachtenberg

By Jakow Trachtenberg

The Trachtenberg velocity approach of easy arithmetic is a innovative approach for calculating and educating simple math. little ones, who had many times failed in mathematics until eventually their mom and dad despatched them to benefit this system, have been capable of practice impressive calculations inside seconds.

In one demonstration, a 10 yr previous baby, while requested to multiply 5132437201 instances 452736502785, easily wrote at the blackboard the reply, 2323641669144374104785, in seventy seconds. He by no means organize the elemental and standard line by way of line chart, multiplying and including each one row of numbers. as an alternative, he simply wrote down the reply with none of the intermediate steps.

To reveal his technique, Trachtenberg selected childrens who have been doing poorly of their institution paintings. those have been teenagers used to failure, shy and withdrawn; or on the different severe, rebellious and unmanageable. The children's responses to the recent, effortless approach of doing mathematics used to be speedy. they discovered it delightfully like a online game. the sensation of achievement quickly made them lose their unpleasant features. both vital have been the by-products the scholars attained whereas studying this new process. As those kids turned knowledgeable in dealing with numbers, they started to spurt forward in all their experiences. Their IQs went up in addition! not just did the kid learn how to compute, yet his IQ additionally went up. when you consider that all difficulties have been labored out in his head, he built an outstanding reminiscence and his skill to pay attention was once elevated. The Trachtenberg approach, as soon as discovered, can take the drudgery out of the mathematics that's a part of everyone's day-by-day stint. specialists think that the Trachtenberg procedure can have far-reaching results on schooling and technology.

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Nevertheless, these and other approaches mentioned in this section possess a number of important shortcomings as concerns applying formal methods to the design of NLPSs and to developing the theory of NLPSs. The demands of diverse application domains to the formal means for describing natural language may differ. That is why we distinguish for further analysis the following groups of application domains: • Natural-language interfaces to databases, knowledge bases, autonomous robots. , in particular, intelligent text summarization systems.

In particular, there are no adequate formal means to describe on semantic level the operations with the sets. It appears that the collection of restrictions stated above provides a useful reference-point for enriching the stock of the means and models for the mathematical study of NL-communication. 7 The Significance of Highly Expressive Formal Systems of Semantic Representations The collection of the tasks faced by the theory of semantics-oriented linguistic processors (LPs) in the beginning of the 1980s proved to be extremely complicated.

A broadly applicable mathematical model of a linguistic database, that is, a model of a collection of semantic-syntactic data associated with primary lexical units and used by the algorithms of semantic-syntactic analysis for building semantic representations of natural language texts (see Chap. 7 of this book). 8. A new method of transforming an NL-text (a statement, a command, or a question) into its semantic representation (see Chap. 8 of this book). 9. Two complex, strongly structured algorithms of semantic-syntactic analysis of NL-texts (they possess numerous common features).

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