Mathematics

Mathematics is way of describing the relationships between numbers and other measurable quantities. Mathematics can also express with the help of simple equations interactions among the smallest particles as well as the farthest objects in the known Universe. Mathematics allows scientists to communicate ideas using universally accepted terminology. It is truly the language of science.

We benefit from the results of mathematical research every day. The fiber-optic network carrying out telephone conversations was designed with the help of mathematics. Our computers are the result of millions of hours of mathematical analysis. Weather prediction, the design of fuel-efficient automobiles and airplanes, traffic control and medical imaging all depend upon mathematical analysis.

For the most part mathematics remains behind the scenes. We use the final results without thinking really about complexity underlying the technology in our lives. But the phenomenal advances in technology over the last 100 years parallel the rise of mathematics as an independent discipline.

Until the 17^th century arithmetic, algebra and geometry we the only mathematical disciplines, and mathematics was virtually indistinguishing from science and philosophy. Developed by the ancient Greeks, these systems for investigating the world were preserved by Islamic scholars and passed on by Christian monks during the Middle Ages. Mathematics finally became a field in its own right with the development of calculus by English mathematician Isaac Newton and German philosopher and mathematician Gottfried Wilhelm Leibniz during the 17^th century and the creation of rigorous mathematical analysis during the 18^th century by French mathematician Augustin Louise Cauchy and his contemporaries. Until the late 19^th century, however, mathematics was used mainly by physicists, chemists and engineers.

At the end of the 1800s, scientific researchers began probing the limits of observation, investigating the parts of the atom and the nature of light. Scientists discovered the electron in 1897. They learned that light consisted of electro-magnetic waves in the 1860s, but physicist Albert Einstein showed in 1905 that light could also behave as particles. These discoveries, along with enquiries into the wavelike nature of matter, led in turn to the rise of theoretical physics and to the creation of complex mathematical models that demonstrated physical laws. Einstein mathematically demonstrated the equivalence of mass and energy, summarized by the famous equation E = mc², in his special theory of relativity in 1905.

Later, Einstein’s general theory of relativity extended special relativity to accelerated systems and showed gravity to be an effect of acceleration. These mathematical models marked the creation of modern physics. Their success in predicting new physical phenomena, such as black holes antimatter, led to the explosion of mathematical analysis. Areas in pure mathematics – that is, theory as opposed to applied, or practical, mathematics – became particularly active.

A similar explosion of activity began in applied mathematics after the invention of the electronic computer, the ENIAC (Electronic Numerical Integrator and Calculator), in 1946. Initially built to calculate the trajectory of artillery shells, ENIAC was later used for nuclear weapons research, weather prediction and wind-tunnel design. Computers aided the development of efficient numerical methods for solving complex mathematical systems.

Without mathematics to describe physical phenomena, we might be living in a world with beautiful art, literature and philosophy but no technology. Even the medical advances of the last 50 years might not have occurred. Science and technology, in their turn, have provided many of the problems that motivated progress in mathematics. Such problems include the behavior of weather systems, the motion of planets in the outer space and subatomic particles in the matter, and also the creation of speedier and smaller computers that can perform multiple tasks simultaneously.

Task 7

Give the Ukrainian for:

Numbers and other measurable quantities; equations as well as interactions; to communicate ideas; universally accepted terminology; to benefit from the results; to depend upon analysis; weather prediction; traffic control; to remain behind the scenes; weather prediction; traffic control; to remain behind the scenes; complexity underlying the technology; phenomenal advances in technology; virtually indistinguishable; systems for investigating the world; the Middle Ages; to become a field in its own right, the creation of rigorous mathematical analysis, contemporary; light consists of electronic waves; light can also behave as particles; to lead; in turn; theory of relativity; efficient numerical methods; to provide; to prove.

Task 8

Give the English for:

Спосіб вираження відношень; оптоволоконна мережа; бути сконструйованим; у більшості випадків; незалежна науков дисципліна; бути збереженим; стародавні греки; ісламські вчені; християнські монахи; межі результатів наукових спостережень; хвильова природа матерії; створення складних математичних моделей; рівнозначність маси та енергії; позначили створення сучасної фізики; успіх у передбаченні; фізичні явища; чорні діри та антиматерія; подібний сплеск активності; дослідження ядерної зброї; розвиток ефективних числових методів; успіх медицини; стати причиною поступу в математиці.

Task 9

Read the text again and find the answers to the questions:

1. What is mathematics?

2. What can mathematics express?

3. How can mathematics help scientists?

4. What do we benefit from the results of mathematical research every day?

5. When did mathematics become a field on its own right?

6. Who first developed mathematical knowledge?

7. What branches of mathematics were the only mathematical disciplines until the 17^th century?

8. What do you know about scientific research in the end of 18^th and beginning of the 19^th centuries?

9. Name several well-known mathematicians and say what they are famous for?

10. What role does the invention of computer play in science?

11. Science, technology and mathematics. What can you say about their interplay in modern life?

Task 10

Give the derivatives of the words completing the table below, translate them:

noun	verb	adjective	adverb
mathematics
		phenomenal
	compute
science
	symbolize
equivalence
			relatively
universe
	investigate
nature
		observable

Task 11

Give the English equivalents for the following words and phrases:

Математик, фізик, філософ, хімік, інженер, вчитель, вчений, теоретик; математика, фізика, хімія, наука, філософія, теорія, аналіз; математичний, фізичний, хімічний, науковий, філософський, теоретичний; видатний математик, відомий вчений, нова наука, теорія відносності.

Task 12

Arrange the following in pairs of

1. synonyms: numbers, area, creation, investigating, measurable quantities, practical, communicate, advance, calculate, scholars, invention, applied, probing, scientific researchers, progress, field, pass on, compute;

2. antonyms: special, unknown, applied mathematics, initially, ancient, general, multiple, complex, modern, the only, simple, famous, pure mathematics.

Task 13

Translate into English using active vocabulary on the topic:

1. Сучасні електронні пристрої дозволяють обмінюватися знімками, відео та зображеннями на відстані. 2. Математика так само як фізика є прикладними науками. 3. Вчені виражають нові теорії та описують винаходи за допомогою загальноприйнятих термінів. 4. Людство отримує користь від прогрессу науки та техніки. 5. Наше майбутнє залежить від результатів нашої роботи сьогодні. Математика як незалежна галузь науки довго лишалася в тіні. 6. Прогноз погоди грунтується на спостереженнях за природними явищами та змінами кліматичних умов. 7. Будь-яке рівняння складається з двох частин. 8. Сучасні дослідження доводять електро-магнітну природу світла. 9. Спостереження покажуть як поводитиме себе тварина в нових умовах. 10. Енштейн – автор теорії відносності.

Task 14

Fill in the gaps:

1. Until the 17^th … arithmetic, algebra and … we the only … disciplines, and mathematics was virtually indistinguishing from … and philosophy. Developed by the … Greeks, these systems for … the world were … by Islamic scholars and passed on by Christian … during the Middle Ages. Mathematics finally became a field in its own … with the development of calculus by English … Isaac Newton and German philosopher and mathematician Gottfried Wilhelm Leibniz during the 17^th century and the … of rigorous mathematical analysis during the 18^th century by French mathematician Augustin Louise Cauchy and his …. Until the late 19^th century, however, mathematics was used … by physicists, chemists and engineers.

2. Mathematics is way of describing the … between numbers and other … quantities. Mathematics can also … with the help of simple … interactions among the smallest … as well as the farthest objects in the known …. Mathematics allows scientists to … ideas using universally accepted … . It is truly the … of science.

3. Without mathematics to describe physical …, we might be living in a world with … art, literature and philosophy but no …. Even the medical … of the last 50 years might not have occurred. Science and technology, in their turn, have provided many of the problems that … progress in mathematics. Such problems include the … of weather systems, the … of planets in the outer … and subatomic particles in the matter, and also the … of speedier and smaller computers that can perform multiple tasks … .

4. At the end of the 1800s, scientific … began probing the limits of observation, investigating the parts of the atom and the nature of … . Scientists discovered the … in 1897. They learned that light consisted of electro-magnetic … in the 1860s, but … Albert Einstein showed in 1905 that light could also behave as …. These …, along with enquiries into the wavelike nature of matter, led in turn to the rise of theoretical … and to the … of complex mathematical models that demonstrated physical … . Einstein mathematically demonstrated the … of mass and energy, summarized by the famous … E= mc, in his special theory of … relativity in 1905.

5. We … from the results of mathematical … every day. The fiber-optic network carrying out telephone … was designed with the help of mathematics. Our computers are the result of millions of hours of … analysis. Weather …, the design of … automobiles and airplanes, … control and medical imaging – all … upon mathematical analysis. For the most part mathematics … behind the scenes. We use the final results without thinking really about … underlying the technology in our lives. But the phenomenal … in technology over the last 100 years parallel the rise of mathematics as an … discipline.

Task 15

Render the text in English:

Математика – це спосіб опису відношень між числами та іншими величинами. Математика може виражати за допомогою простих рівнянь взаємодію найменших часток, а також далеких об’єктів у Всесвіті. Ми щодня отримуємо користь від математичних досліджень. Передбачення погоди, телефоний зв'язок, робота комп'ютерних мереж, розробка нового та економічного транспорту, розвиток медицини залежать від математичного аналізу.

Математика стала незалежною наукою лише близько 100 років тому. Вона була започаткована древніми греками, збережена ісламськими вченими та передана християнським монахам у Середньовіччі. Однак аж до кінця 19-го століття математика використовувалась в основному фізиками, хіміками та інженерами.

Наприкінці 19-го століття вчені відкрили електрон, довели хвилеподібну природу матерії, встановили, що світло складається з електоро-магнітних хвиль. Ці відкриття призвели до створення складних математичних моделей, що демонстрували фізичні закони. Успіх у передбаченні та поясненні нових фізичних відкриттів призвів до розвитку сучасної фізики, математичного аналізу та винайдення комп'ютера.

Математика дає змогу вченим обмінюватися ідеями, використовуючи загальноприйняту термінологію та методи обчислення явищ у різних галузях. Математика – це мова науки.

Task 16

Tell about the way mathematics became an independent science. Use the following as a plan.

1. Mathematics, the way of describing the relationships between numbers and other measurable quantities, express, simple equations, interactions, particles, objects in the known Universe, scientists, to communicate ideas, terminology, the language of science.

2. Benefit from, network, conversations, computers, mathematical analysis, weather prediction, fuel-efficient, traffic control and medical imaging, depend upon.

3. Remains behind the scenes, the final results, complexity, technology, phenomenal advances, parallel the rise of mathematics.

4. Arithmetic, algebra and geometry, indistinguishing, the ancient Greeks, Islamic scholars, Christian monks, Middle Ages, a field in its own right, contemporaries, mainly by physicists, chemists and engineers.

5. Scientific researchers, limits of observation, investigating the parts of the atom and the nature of light, discovered, the electron, light, electro-magnetic waves light, particles, these discoveries, theoretical physics, creation of complex mathematical models, physical laws, the equivalence of mass and energy, equation, special theory of relativity.

6. General theory of relativity, gravity, effect of acceleration, models, creation of modern physics, success in predicting, explosion of mathematical analysis, pure mathematics, particularly active.

7. Explosion of activity, applied mathematics, invention, computer, trajectory of artillery shells, nuclear weapons research, weather prediction, wind-tunnel design, development, numerical methods, solving complex mathematical systems.

8. Mathematics, physical phenomena, beautiful art, literature, philosophy, no technology, medical advances, science and technology, motivated progress in mathematics,behavior of weather systems, the motion of planets in the outer space, subatomic particles in the matter, creation of speedier and smaller computers, simultaneously.