Text 1. Mathematics

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.

Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.

There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematicians called mathematics «the science that draws necessary conclusions» or stated that «as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality». Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered.

Task 3. Make the word combinations

A B

1) necessary a) new conjectures

2) mathematical b) of abstraction reasoning

3) logical c) conclusions

4) applied d) discovery

5) practical e) axioms and definitions

6) choose f) mathematics

7) seek out g) mathematics

8) formulate h) mathematics

9) the use i) application

10) pure j) patterns

Task 4. Match the suitable parts of the sentences

1) The word «mathematics» means... 2) Mathematics is the study of... 3) The mathematicians called mathematics... 4) Mathematics evolved from...

5) Applied mathematics concerned with... 6) Mathematicians also engage in... 7) Mathematicians seek out... 8) Mathematical innovations led to...

a) «the science that draws necessary conclusions».

b) quantity, structure, space, and change.

c) a rapid increase in the rate of mathematical discovery that continues to the present day.

d) counting, measurement, and the systematic study of the shapes and motions of physical objects.

i) pure mathematics, or mathematics for its own sake, without having any application in mind.

f) application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory .

g) learning, study, science.

h) patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions .

Task 5. Fill in the gaps with the suitable words below

1. The current introductions of new concepts in any field __(1)__ mathematics to grow rapidly.

2) Axioms __(2)__ the second major component of any branch of mathematics.

3) The objective of mathematical activity __(3)__ the theorems deduced from a set of axioms.

4) The amount of information that can be __(4)__ from the some sets of axioms is almost incredible.

5) Mathematical theorems must be deductive __(5)__ and __(6)__.

6) Man __(7)__ objects in the physical world and __(8)__ numbers names to represent one aspect of experience.

7) Mathematicians __(9)__ that pure mathematics is the most original creation of the human mind.

enables constitute consists of distinguishes deduced proved established invents claim