Англійська мова для математиків, English for mathematicians, Румянцева О.А., 2015

Англійська мова для математиків, English for mathematicians, Румянцева О.А., 2015.

   Навчальний посібник є сучасним, розробленим з урахуванням досвіду роботи, варіантом інтенсивного курсу англійської мови для студентів і аспірантів, що продовжують вивчення професійної англійської мови в магістратурі або аспірантурі університету. Робота з навчальним посібником дозволяє опанувати англійську мову на рівні, достатньому для практичного використання в професійній діяльності.

Англійська мова для математиків, English for mathematicians, Румянцева О.А., 2015


History.
Archimedes used the method of exhaustion to compute the area inside a circle by finding the area of regular polygons with more and more sides. This was an early but informal example of a limit, one of the most basic concepts in mathematical analysis.

Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, an infinite geometric sum is implicit in Zeno’s paradox of the dichotomy.

Later, Greek mathematicians such as Eudoxus and Archimedes made more explicit, but informal, use of the concepts of limits and convergence when they used the method of exhaustion to compute the area and volume of regions and solids. The explicit use of infinitesimals appears in Archimedes' The Method of Mechanical Theorems, a work rediscovered in the 20th century. In Asia, the Chinese mathematician Liu Hui used the method of exhaustion in the 3rd century AD to find the area of a circle. Zu Chongzhi established a method that would later be called Cavalieri's principle to find the volume of a sphere in the 5th century. The Indian mathematician Bhaskara II gave examples of the derivative and used what is now known as Rolle's theorem in the 12th century.

CONTENTS.
PREFACE.
UNIT l. Text 1. Introduction to Mathematical analysis.
Mathematical terminology.
Grammar. Lexical. Translation and Speaking Exercises.
UNIT 2. Text 2. Main branches of Mathematical Analysis.
Mathematical terminology.
Grammar. Lexical. Translation and Speaking Exercises.
UNIT 3. Text 3. Real numbers (Part I).
Mathematical terminology.
Grammar. Lexical. Translation and Speaking Exercises.
UNIT 4. Text 4. Real numbers (Part П).
Mathematical terminology.
Grammar. Lexical. Translation and Speaking Exercises.
UNIT 5. Text 5. Integer.
Математическая терминология.
Grammar. Lexical. Translation and Speaking Exercises.
UNIT 6. Text 6. Archimedean property.
Mathematical terminology.
Grammar. Lexical. Translation and Speaking Exercises.
UNIT 7. Text 7. Series.
Mathematical terminology.
Grammar. Lexical. Translation and Speaking Exercises.
UNIT 8. Text 8. Functions.
Mathematical terminology.
Grammar. Lexical. Translation and Speaking Exercises.
UNIT 9. Text 9. Continuous function.
Mathematical terminology.
Grammar. Lexical. Translation and Speaking Exercises.
UNIT 10. Text 10. Differential of a function.
Mathematical terminology.
Grammar. Lexical. Translation and Speaking Exercises.
UNIT 11. Text 11. Specifying a function.
Mathematical terminology.
Grammar, Lexical, Translation and Speaking Exercises.
UNIT 12. Text 12. Fermat's Last Theorem.
Mathematical terminology.
Grammar, Lexical. Translation and Speaking Exercises.
UNIT 13. Text 13. Integral.
Mathematical terminology.
Grammar, Lexical. Translation and Speaking Exercises.
UNIT 14. Text 14. Improper integrals.
Mathematical terminology.
Grammar, Lexical. Translation and Speaking Exercises.
UNIT 15. Text 15. Vector calculus.
Mathematical terminology.
Grammar, Lexical. Translation and Speaking Exercises.
UNIT 16. Text 16. Vector field.
Mathematical terminology.
Grammar, Lexical. Translation and Speaking Exercises.
REFERENCE SITES.



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