7.3 Движение декабристов (стр. 1 )

Міністерство освіти і науки, молоді та спорту України

Сумський державний університет

3958 Збірник англомовних тематичних текстів та вправ до них для студентів-магістрантів спец. 0802002 «Прикладна математика» денної форми навчання факультету ЕЛІТ

Суми

Сумський державний університет

2015

Збірник англомовних тематичних текстів та вправ до них для студентів-магістрантів спец. 0802002 «Прикладна математика» / укладач . – Суми: Сумський державний університет, 2015. – 38 с.

Кафедра іноземних мов

Unit 1

1 Name 10 famous mathematicians and describe their personal contribution to the world science.

2 Make sure that you know the words and word combinations

below. Try to memorize them.

DNA to give rise

calculus to decompose

prolific to lay out the tenets

infamous to underlie

persecution to appease

vital factor to unravel

seminal work to flee

game theory Manhattan Project

3 Read the text.

Brilliant Mathematicians And Their Impact On The Modern World

Math is one of those things that most people either love or hate.  But even if you don't count yourself a fan of mathematics, it's hard to argue that it hasn't been a vital factor in our rapid evolution as a society. We reached the moon because of math. Math allowed us to disclose the secrets of DNA, create and transmit electricity over hundreds of miles to power our homes and offices, and gave rise to computers and all that they do for the world.

 Our history is rich with mathematicians whose thoughts and discoveries continue to echo through the ages. We picked five of the most brilliant mathematicians whose work continues to help shape our modern world, sometimes hundreds of years after their death.

Isaac Newton (1642-1727) Sir Isaac Newton is considered by many to be the greatest scientist of all time. There aren't many subjects that Newton didn't influence — he was one of the inventors of calculus, built the first reflecting telescope and helped establish the field of classical mechanics with his seminal work, "Philosophiæ Naturalis Principia Mathematica." He was the first to decompose white light into its component colors and gave us the three laws of motion, now known as Newton's laws.

 Carl Gauss (1777 - 1855)If Newton is considered the greatest scientist of all time, Gauss could easily be called the greatest mathematician ever. and quickly showed himself to be a brilliant mathematician. He published "Arithmetical Investigations," a foundational textbook that laid out the tenets of number puters operate, on a the most basic level, using just two digits — 1 and 0, and many of the advancements that we've made in using computers to solve problems are solved using number theory. Gauss was prolific, and his work on number theory was just a small part of his contribution to math; you can find his influence throughout algebra, statistics, geometry, optics, astronomy and many other subjects that underlie our modern world.

 John von Neumann (1903-1957) John von Neumann was born in Budapest a few years after the start of the 20th century. He went on to design the architecture underlying nearly every single computer built on the planet today.

Von Neumann received his Ph. D in mathematics at the age of 22 while also earning a degree in chemical engineering to appease his father, who was keen on his son having a good marketable skill. In 1930, he went to work at Princeton University with Albert Einstein at the Institute of Advanced Study. Before his death in 1957, von Neumann made important discoveries in set theory, geometry, quantum mechanics, game theory, statistics, computer science and was a vital member of the Manhattan Project.

Alan Turing (1912 - 1954) Alan Turing, a British mathematician who has been called the father of computer science. During World War II, Turing bent his brain to the problem of breaking Nazi crypto-code and was the one to finally unravel messages protected by the infamous Enigma machine. Besides helping to stop Nazi Germany from achieving world domination, Alan Turing was instrumental in the development of the modern day computer. His design for a so-called "Turing machine" remains central to how computers operate today. The "Turing test" is an exercise in artificial intelligence that tests how well an AI program operates.

Benoit Mandelbrot (1924-2010)Benoit Mandelbrot is put on the list thanks to his discovery of fractal geometry. Without fractals we would be decades behind where we are now in the field of computer-generated images. Fractal formulas are also used to design cellphone antennas and computer chips, which takes advantage of the fractal's natural ability to minimize wasted space.

 Мandelbrot was born in Poland in 1924 and had to flee to France with his family in 1936 to avoid Nazi persecution. After studying in Paris, he moved to the U. S. where he found a home as an IBM Fellow. Working at IBM meant that he had access to cutting-edge technology, which allowed him to apply numerous abilities of electrical computer to his projects and problems. In 1979, Mandelbrot discovered a set of numbers, now called and described by science-fiction writer Arthur C. Clarke as Mandelbrot set, that was "one of the most beautiful and astonishing discoveries in the entire history of mathematics."   Benoit Mandelbrot died of cancer in 2010.

1 Answer the questions:

1 What achievements of human civilization did math make possible?

2 In what areas did Isaac Newton work?

3 What was personal contribution of Carl Gauss to math?

4 What inventions and discoveries was John von Neumann famous for?

5 What was the function of the Enigma machine?

6 Why are fractals so important?

2 Guess the words from the text by their definitions:

Any one of the ten Arabic numerals.

A branch of mathematics that deals with variable quantities, used to solve many mathematical problems.

Producing much/many.

A tube-like instrument with lenses for making distant objects appear nearer and larger.

To run or hurry away.

A principle, belief, doctrine.

( tenet, digit, to flee, prolific, calculus, telescope)

3 Find in the text the words that are synonyms of the words

below:

supreme, fast, form, talented, volume, to discover

4 Derive nouns from the following verbs:

to design to generate to describe

to contribute to protect to operate

to establish to discover to move

5 Add prefixes, suffixes or both to the words below to form

their derivatives from the text.

to cut, able, chemist, advance, center, infamous, cover,

to dominate, to compose

6 Translate into Ukrainian/Russian.

1 But even if you don't count yourself a fan of mathematics, it's hard to argue that it hasn't been a vital factor in our rapid evolution as a society.

2 Our history is rich with mathematicians whose thoughts and discoveries continue to echo through the ages.

3 During World War II, Turing bent his brain to the problem of breaking Nazi crypto-code and was the one to finally unravel messages protected by the infamous Enigma machine.

7 Fill in the blanks with the appropriate prepositions:

1Math allowed us to disclose the secrets ____ DNA, create and transmit electricity _____ hundreds _______ miles.

2 Sir Isaac Newton is considered ______ many to be the greatest scientist ____ all time.

3 Carl Friedrich Gauss was born to a poor family in Germany in 1777.

4 Von Neumann received his Ph. D ____ mathematics ____ the age of 22 _____ also earning a degree _____ chemical engineering.

5 Benoit Mandelbrot died _____ cancer in 2010.

Unit 2

1 What knowledge needed for your future speciality are you

expected to gain at SSU?

2 What do you know about the history of applied mathematics?

Try to remember facts, dates and names.

3 What fields does applied mathematics include today? Which of

them have you studied? Share your learning experience.

4 Make sure that you can read and understand the words

and word combinations below. Point out the terms related

directly to applied mathematics study. Memorize them.

giant fuzzy boundary

inequality pure mathematics

simplification analytical treatment

applicability black hole model

asymptotics common sense

layout differential/integral equations

reinforcement elasticity theory

stress linear algebra

deflection approximation theory

5 Read the text

What is Applied Mathematics?

Applied math is a group of methods aimed for solution of problems in sciences, engineering, economics, or medicine. These methods are originated by Newton, Euler, Lagrange, Gauss and other giants. Modern areas of applied math include Mathematical physics, Mathematical biology, Control theory, Aero-space engineering, optimal planning, math finance. There is a fuzzy boundary between applied math and engineering and at the other side, between applied and pure mathematics. Applied math discovers new problems which could become subjects of pure math (like geodesics), or develop to become a new engineering discipline (like elasticity theory). Study of applied math requires expertise in many areas of mathematics and science, physical intuition and common sense, and collaboration skills. Applied math allows for many approaches to the problem, a choice of objectives, and variety of methods.
In the majority of applied problems, one need to build mathematical model of a phenomenon, solve this model, and develop the recommendations for improvement of the performance.

Math modeling

Typically we deal with large systems (thousands of variables, equations and inequalities). A clever model separates the main phenomenon from the noise and allows for analytic treatment of the problem, followed by extensive numerical development. There may be several models suggested for the same phenomena with various level of details: No one need a one-to-one geographical map. The art of simplification is to make the problem solvable but not trivial. All models have ranges of applicability (Take for example the ideal gas model, compare with the black hole model).