Basics of Mathematics, Мотина О.П., 2014

Basics of Mathematics, Мотина О.П., 2014.

  Цель пособия - развитие навыков перевода и понимания научной литературы по основным разделам математической науки. Обучение по данному пособию ориентировано также на развитие навыков устной речи в сфере профессиональной коммуникации и углубление знаний лексико-грамматического материала профориентационного характера.
Учебное пособие предназначено для студентов факультета математики и информационных технологий.

Basics of Mathematics, Мотина О.П., 2014


Definitions of Mathematics.
Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science. A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. Some just say, "Mathematics is what mathematicians do."

Three leading types of definition of mathematics are called logicist, intuitionist, and formalist, each reflecting a different philosophical school of thought. All have severe problems, none has widespread acceptance, and no reconciliation seems possible.

ОГЛАВЛЕНИЕ.
PART I: DEFINITIONS AND HISTORY OF MATHEMATICS.
UNIT 1: WHAT IS MATHEMATICS?.
Grammar (Part I: Articles).
Grammar (Part II: Pronouns).
UNIT 2: DEFINITIONS OF MATHEMATICS.
Grammar (Present Forms).
UNIT 3: HISTORY OF MATHEMATICS.
Grammar (Past Forms).
UNIT 4: NOTATION, LANGUAGE AND RIGOR MATHEMATICS.
Grammar (Future Forms).
PART II: FIELDS OF MATHEMATICS.
UNIT 5: PURE MATHEMATICS.
Grammar (Passive Voice).
UNIT 6: ARITHMETIC.
Grammar (Conditionals).
UNIT 7: ALGEBRA.
Grammar (Modal verbs).
UNIT 8: GEOMETRY.
Grammar (The Infinitive).
UNIT 9: MATHEMATICAL ANALYSIS.
Grammar (The Gerund).
UNIT 10: APPLIED MATHEMATICS.
Grammar (The Participle).
SUPPLEMENTARY READING.
PART III: NOTABLE MATHEMATICIANS.
Top 10 Greatest Mathematicians.
Pythagoras of Samos.
Andrew Wiles.
Isaac Newton and Wilhelm Leibniz.
Leonardo Pisano Bigollo.
Alan Turing.
Rene Descartes.
Euclid.
G. F. Bernhard Riemann.
Carl Friedrich Gauss.
Leonhard Euler.
Literature.



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