Conversational Practice1. Disagree with the following negative statements and keep the conversation going where possible. Begin your answer with the opening phrases: It’s not correct… It’s not right, I am afraid… It’s wrong,… On the contrary… Quite the reverse… 1. Scientists do not think and reason in terms of abstractions. 2. Maths is not a free creation of the human mind and reasoning. 3. Pure maths cannot be applied to the physical world. 4. Mathematicians do not seek useful applications of their theories. 5. Pure maths theories do not find any practical applications. 6. Pure maths theories are often not significant and they are entirely forgotten in say, 50 years.
2. Agree or disagree with the statements. Use the introductory phrases: That’s right… Exactly. Certainly… I fully agree to it… I don’t think so. This is not the case… It’s wrong, I am afraid. Quite the reverse… The definition is inappropriate…
1. A math formula has a direct real physical counterpart. 2. Mathematicians do not rely on their intuitive judgement – they seek to give a rigorous proof. 3. If you want to know what a math theorem states, see what its proofs prove. 4. Maths is both intelligible and enjoyable. 5. Mathematicians do not deal with applications of maths. 6. An idea expressed in symbols is more scientific than the same thought presented in words. 7. Most mathematicians are not incentive to art and beauty. 3. Compose questions and a) answer them in writing at home according to the model; b) practice them orally in class:
Should you ask me what a “set” is, I’d say that unless otherwise specified “set” is an undefined concept in modern maths. 1. … що таке «математика», … 2. … що таке «постулат», … 3. … що таке «прикладна математика», … 4. … яка різниця між «чистою математикою» і «прикладною математикою», … 5. … де і коли виникла перша математична школа, … 6. … що означає поняття «a variable», … 7. … які найбільш фундаментальні поняття сучасної математики, … 4. Practise problem questions and answers. Work in pairs. Change over! 1. What do you feel looking at a book page sprinkled with 2. Does the mathematician write in the language of maths to hide his knowledge from the world at large? 3. Do new symbols often appear in maths? 4. When do mathematicians introduce new symbols and signs into the language of maths? 5. To whom is language of maths “foreign”?
5. What is implied in the following assertion? There is no national prejudice in maths. 6. Discuss the statements given below. Use the following phrases: Mathematicians reject… The statement does not imply… Scientists do not claim… That’s right... Exactly. Certainly… I fully agree to it… I don’t think so. This is not the case… It’s wrong, I am afraid. Quite the reverse… The definition is inappropriate… 1. Most mathematicians object to the separation of pure and applied aspects of maths. Why? Do pure and applied maths have common language, methods, applications?
2. Mathematicians – what are they? When (why) does a person make up his mind to become a mathematician? What motivates and directs the activities of mathematicians? What mathematician(s) to your mind, is (are) the most distinguished and why? 3. Wherein is the beauty of maths? Beautiful maths is the greatest contribution of the man’s mind to all the civilization. Prove it.
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’s and 
’s, = ‘s and other math symbols and signs?
