- •(Наименование кафедры)
- •6М051000 «Математика» 6м050800 «Механика» 6м50900 «мкм» (шифр и название специальности)
- •2. Название дисциплины: Иностранный язык
- •4.Пререквизиты учебной дисциплины: -
- •5. Характеристика учебной дисциплины:
- •5.3 Задачи изучения дисциплины:
- •5.4 Содержание учебной дисциплины.
- •5.5. План изучения учебной дисциплины
- •6. Список основной и дополнительной литературы.
- •6.2 Дополнительная литература.
- •7. Контроль и оценка результатов обучения.
- •3. План практических занятий Unit 1 Theme: Political system of Kazakhstan
- •Political System of Kazakhstan
- •Grammar: Linking clauses. Time and Reason.
- •Foreign Policy
- •Grammar: Linking clauses. Result and Purpose.
- •Political System of Great Britain
- •Grammar: Linking clauses. Contrast and Reduced.
- •What are some social problems in the usa
- •Grammar: The uses of Conditionals.
- •Mathematics as a science
- •See the Unit 6 from the Oxford Practice Grammar by George Yule and follow the instructions.
- •Theme: Computer models
- •See the Unit 10 from the Oxford Practice Grammar by George Yule and follow the instructions.
- •Unit 7 Theme: Development of Internet
- •Development of Internet
- •Supercomputer and Mainframe
- •Unit 8 Theme: Geometry as a science Grammar: Complex Modals
- •Geometry as a science
- •Gottfried Wilhelm von Leibniz (1646-1716) Germany
- •See the Unit 3 from the Oxford Practice Grammar by George Yule and follow the instructions.
- •Unit 9 Theme: Computer programs Grammar: Simple Infinitives and Gerunds
- •Computer programs
- •See the Unit 11 from the Oxford Practice Grammar by George Yule and follow the instructions.
- •Unit 10 Theme: Information systems
- •Information systems
- •See the Unit 13 from the Oxford Practice Grammar by George Yule and follow the instructions.
- •Unit 11 Theme: The role of computers in modern life Grammar: Prepositions and prepositional phrases
- •The role of computers in modern life
- •See the Unit 13 from the Oxford Practice Grammar by George Yule and follow the instructions.
- •Unit 12 Theme: Interactive board. How does it work?
- •Interactive board. How does it work?
- •See the Unit 11 from the Oxford Practice Grammar by George Yule and follow the instructions.
- •Unit 13 Theme: New technology Grammar: Complex Infinitives and Gerunds
- •New technology
- •See the Unit 11 from the Oxford Practice Grammar by George Yule and follow the instructions.
- •Unit 14 Theme: Computer types Grammar: Verbs and Infinitives and Gerunds
- •Computer types
- •See the Unit 11 from the Oxford Practice Grammar by George Yule and follow the instructions.
- •Theme: Computer-addicted Grammar Review
- •Computer-addicted
- •The Signs of Problematic Computer Use
- •How to Help Computer Obsessed Friends
- •Grammar Review.
- •4. Список основной и дополнительной литературы
- •4.2 Дополнительная литература.
- •5. План проведения практических занятий
- •6. Задания для самостоятельной работы обучающихся в неаудиторных занятиях
- •7. Материалы для текущего и рубежного контроля, а также материалы для итогового контроля по завершению дисциплины Текущий контроль
- •Final test
- •2. Глоссарий
- •Intel – compatible –
- •Материалы для итогового контроля
- •6М060900 «Математика», 6м060100 «Механика»,
Unit 8 Theme: Geometry as a science Grammar: Complex Modals
Objectives: By the end of this unit, students should be able to use active vocabulary of this theme in different forms of speech exercises.
Methodical instructions: This theme must be worked out during two lessons a week according to timetable.
Lexical material: Introduce and fix new vocabulary on theme “Geometry as a science”. Define the basic peculiarities of its functions and its role in our life. Grammar: Introduce and practice the Complex Modals.
Ex.1 Read and translate the text
Geometry as a science
Geometry (Ancient Greek: geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of a formal mathematical science emerging in the West as early as Thales (6th Century BC). By the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.[1] Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially mapping the positions of the stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. Both geometry and astronomy were considered in the classical world to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.
In Euclid's time there was no clear distinction between physical space and geometrical space. Since the 19th-century discovery of non-Euclidean geometry, the concept of space has undergone a radical transformation, and the question arose: which geometrical space best fits physical space? With the rise of formal mathematics in the 20th century, also 'space' (and 'point', 'line', 'plane') lost its intuitive contents, so today we have to distinguish between physical space, geometrical spaces (in which 'space', 'point' etc. still have their intuitive meaning) and abstract spaces. Contemporary geometry considers manifolds, spaces that are considerably more abstract than the familiar Euclidean space, which they only approximately resemble at small scales. These spaces may be endowed with additional structure, allowing one to speak about length. Modern geometry has multiple strong bonds with physics, exemplified by the ties between pseudo-Riemannian geometry and general relativity. One of the youngest physical theories, string theory, is also very geometric in flavour.
Gottfried Wilhelm von Leibniz (1646-1716) Germany
Leibniz was one of the most brilliant and prolific intellectuals ever; and his influence in mathematics (especially his co-invention of the infinitesimal calculus) was immense. His childhood IQ has been estimated as second-highest in all of history, behind only Goethe. Descriptions which have been applied to Leibniz include "one of the two greatest universal geniuses" (da Vinci was the other); "the most important logician between Aristotle and Boole;" and the "Father of Applied Science." Leibniz described himself as "the most teachable of mortals."
Mathematics was just a self-taught sideline for Leibniz, who was a philosopher, lawyer, historian, diplomat and renowned inventor. Because he "wasted his youth" before learning mathematics, he probably ranked behind the Bernoullis as well as Newton in pure mathematical talent, and thus he may be the only mathematician among the Top Ten who was never the greatest living algorist or theorem prover. We won't try to summarize Leibniz' contributions to philosophy and diverse other fields including biology; as just three examples: he predicted the Earth's molten core, introduced the notion of subconscious mind, and built the first calculator that could do multiplication. Leibniz also had
political influence: he consulted to both the Holy Roman and Russian Emperors; another of his patrons was Sophia Wittelsbach, who was only distantly in line for the British throne, but was made Heir Presumptive. (Sophia died before Queen Anne, but her son was crowned King George I of England.)
Ex.2 Mark true and false sentences:
1 Geometry (Ancient Greek: geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures
2 Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes
3 By the 2nd century BC geometry was put into an axiomatic form by Euclid
4 Newton developed ingenious techniques for calculating areas and volumes
5 Since the 17th-century discovery of non-Euclidean geometry, the concept of space has undergone a radical transformation
6 Both geometry and astronomy were considered in the classical world to be part of the Quadrivium
7 So today we have to distinguish between physical space, geometrical spaces (in which 'space', 'point' etc. still have their intuitive meaning
8 Modern geometry has not multiple strong bonds with physics, exemplified by the ties between pseudo-Riemannian geometry and general relativity
Ex 3 Answer the questions:
1 What is the meaning of the word “Geometry” ?
2 When was geometry put into an axiomatic form by Euclid?
3 What do you know about Wilhelm von Leibniz?
Grammar: Complex Modals.