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Міністерство освіти і науки, молоді та спорту України Сумський державний університет Збірник тематичних текстів та лексикограматичних вправ з дисципліни «Англійська мова професійного спілкування» для студентів спеціальності 080202 «Прикладна математика» спеціалізації «Моделювання складних систем» факультету ЕЛІТ денної форми навчання Суми Сумський державний університет 2011 Збірник тематичних текстів та лексикограматичних вправ з дисципліни «Англійська мова професійного спілкування» / укладач А.М.Дядечко. – Суми : Сумський державний університет, 2011. – 64 с. Кафедра іноземних мов Unit 1 1 Can you remember any ideas and views of modern science that go back to the 19^{th} century? Can you name the scientists who contributed to the development of science in the 19^{th} century? ^ gene confident assumption matter Euclidian geometry outgrowth fundamental constituents insight mutually core ideas in terms of heredity corpuscular germ to raise a question subjects and predicates to severe connection deductive reasoning to trace 3 Read the text. ^ ^{TH} CENTURY Twentiethcentury science is an evolutionary outgrowth of the 19^{th}century science: in terms of the theories scientists created and the new ideas underlying them; in its organization and conduct as professional practice; and in its relationship to society. From its 17^{th} – century birth, modern science has had two mutually influential “sides”: an “inside”, intellectual dimension, and an “outside”, social relationship dimension. The inside, the outside and the relationship between them all changed character in the course of the 20^{th} century. As 20^{th} –century physical, life, and social science are built on the 19^{th} –century science, identifying developments in the 19^{th} –century science that played key roles in the 20^{th} –century science is a precondition for appreciating the innovativeness of the 20^{th} – century science. A preview of the major theories and the core ideas that cut across the scientific disciplines will help orient us as we begin tracing the rise of these innovate theories and ideas. A In the 19^{th} century, the atom came to represent the view that natural phenomena consisted of fundamental building blocks that could be configured to produce the vast number of forms we find in nature. The atom in physics and chemistry is an example of that conception, as are the gene in the theory of heredity and the germ in the germ theory of disease. B In the 19^{th} century, a science of energy was created, called thermodynamics, which identified energy as a new dimension of reality. This science recognized that energy was a phenomenon in nature parallel to matter. C The 19^{th} century also saw the development of the idea of fields of energy and force. A field is an immaterial phenomenon obeying natural laws and capable of exercising forces on material objects. D Chemists in the 19^{th} century discovered that structure is the feature that differentiates one substance from another, as opposed to the fundamental constituents of substances and the properties of these constituents. E The fifth core idea of the 19^{th} century that would influence 20^{th} century science was the discovery of nonEuclidean geometry. For approximately 2,300 years before the mid19^{th} century, Western philosophy, science and mathematics were based on the confident assumption that deductive reasoning was closely linked to truth. In the mid19^{th} century, mathematicians discovered deductively perfect geometries that contradict Euclidean geometry, raising the question of which form of geometry is true of space and severing the critical connection between reasoning and reality. Another important development in mathematics in the 19^{th} century was the invention of symbolic logic. From this development, we learned that notation can have a significant impact on our thinking. Simply replacing words with symbols can lead to new insights. Further, symbolic logic undermined the notion that subjects had priority over predicates, that is, that things were the ultimate reality and relationships were a secondary consequence of the organization of things. Through the use of symbolism, relationships were found to have properties of their own. F The 19^{th} century also saw the replacement of Newton’s particle, or corpuscular, theory of light with the wave theory of light and the subsequent expansion of this theory with James Clerk Maxwell’s electromagnetic theory of energy. G Probability and statistics became important in the 19^{th} century, specifically, the idea that natural processes exist that require probability to describe them. H Finally, the 19^{th} –century theory of evolution was a foundational idea of the 20^{th} – century science. ^ a) What foundation did 19^{th} century science lay for 20^{th} century science? b) What two aspects of science development are considered in the text? c) What sciences are mentioned in the text? d) What do the terms “atom”, “gene” and “germ” have in common? e) What science is known for presenting energy in a new way? f) What is the impact of symbols on human thinking? g) What does light consist of? ^ diseaseproducing microorganism – physical matter or material – nearly identically – letter, figure or other conventional mark – supposition – basic unit of heredity – understanding  ^ nonmaterial to break (2 words) emergence characteristic product, result influence link to direct 4 Derive nouns from the following verbs: to assume – to replace to contradict to deduce to expand to identify to produce to influence to differentiate – ^ build, Euclid, cent, evolution, concept, intellect, relation, real, second, connect, chemist, symbol, foundation, approximate, material, place, view, condition, innovative. ^ a) … . . . . the atom came to represent the view that natural phenomena consisted of fundamental building blocks… b) … . relations were found to have properties of their own. c) … natural processes require probability to describe them. ^ a) Structure is a feature that differentiates one substance ____ another , as opposed ____ the fundamental constituents of substances and properties of these substances. b) We learned that notation can have a significant impact ____ our thinking. c) The relationship ______ them all changed character _____ the course of the 20^{th} century. d) Simply replacing words _____ symbols can lead _____ new insights. e) A field is capable _____ exercising forces on material objects. ^ 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. legacy fluid mechanics emergence numerical analysis simulation data set cryptology neural networks domain to spawn advent to change over time probability to spawn lattice theory to arise out of differential equations to cover approximation theory applicable 5 Read the text ^ Applied mathematics is a branch of mathematics that concerns itself with the mathematical technique typically used in the application of mathematical knowledge to other domains. There is no consensus of what the various branches of applied mathematics are. Such categorizations are made difficult by the way mathematics and science change over time, and also by the way universities organize departments, courses, and degrees. Historically, applied mathematics consisted principally of applied analysis, most notably differential equations, approximation theory (broadly construed to include representations, asymptotic methods, variational methods, and numerical analysis), and applied probability. These areas of mathematics were intimately tied to the development of Newtonian Physics, and in fact the distinction between mathematicians and physicists was not sharply drawn before the mid19^{th} century. This history left legacy as well; until the early 20^{th} century subjects such as classical mechanics were often taught in applied mechanics departments at American universities rather than in physics departments, and fluid mechanics may still be taught in applied mathematics departments. Today, the term applied mathematics is used in a broader sense. It includes the classical areas above, as well as other areas that have become increasingly important in applications. Even fields such as number theory that are part of pure mathematics are now important in applications (such as cryptology), though they are not generally considered to be a part of the fields of applied mathematics. Sometimes the term applicable mathematics is used to distinguish between the traditional field of applied mathematics and the many more areas of mathematics that are applicable to real world problems. Mathematicians distinguish between applied mathematics, which is concerned with mathematical methods, and the applications of mathematics within science and engineering. A biologist using a population model and applying known mathematics would not be doing applied mathematics, but rather using it. Industrial mathematics is used to solve industrial problems. It is sometimes split in two branches: technomathematics (covering problems coming from technology) and economathematics (for problems in economy and finance). The success of modern numerical mathematical methods and software has led to the emergence of computational mathematics, computational science, and computational engineering, which use high performance computing for the simulation of phenomena and solution of problems in the science and engineering. Historically mathematics was most important in the natural sciences and engineering. However, after World War II, fields outside of the physical sciences have spawned the creations of new areas of mathematics, such as game theory, which grew out of economic considerations, or neural networks, which arose out of the study of the brain in neuroscience, or bioinformatics, from the importance of analyzing large data sets in biology. The advent of the computer has created new applications, both in studying and using the new computer technology itself (computer science, which uses combinatorics, formal logic, and lattice theory), as well as using computers to study problems arising in other areas of science (computational science), and of course studying the mathematics of computation (numerical analysis). Statistics is probably the most widespread application of mathematics in the social sciences, but other areas of mathematics are proving increasingly useful in these disciplines, especially in economics and management sciences. ^ a) Do you agree with the definition of applied mathematics given in the text? If not, give the one you consider more appropriate. b) Is it easy to distinguish between physics and applied mathematics? c) What was the role of Newtonian physics in the development of applied mathematics? d) Can we consider applied mathematics as a purely theoretical science? e) In what way did the development of computer software broadened the applied mathematics area? f) What areas of applied mathematics appeared in the 20^{th} century? ^ mathematics, history, chemistry, management, biology, mechanics, physics, nervous system ? 3 Find in the text and make a list of 6 adverbs that end in –ly and 12 nouns that end in –tion. 4 Complete the sentences a) High performance computers make it possible to simulate …………………………… b) ……………… is important in cryptology. c) …………………covers problems coming from technology. d) The problems in economy and finance are covered by ……………………….. e) Statistics is widely used in ……………………………………… ^ a) Classical mechanics _______________( teach) in applied mathematics departments. b) Industrial mathematics _______________( split) in two branches: technomathematics and economathematics. c) These areas of mathematics ___________(tie) to the development of Newtonian Physics. d) Such categorizations ________________( make) difficult by the way mathematics and science change over time. ^ 1 What are typical features of a complex system? 2 Give examples of complex systems from different spheres of human activities. 3 Make sure that you can read and understand the words and word combinations below. Try to memorize them. consensus to encompass attribute to seek neuroscience to constrain hallmark to exhibit aspiration to brandish chaos spontaneous a weak fit dispersed coupling rules ominous pattern prediction essentially precise prediction notably linear equations reciprocal dependence 4 Read the text ^ Complex systems is a scientific field which studies the common properties of systems that are considered fundamentally complex. Such systems are used to model processes in biology, economics, physics and many other fields. The scientific field under discussion is also called complex systems theory, complexity science, study of complex systems, sciences of complexity, nonequilibrium physics, and historical physics. The key problems of complex systems are difficulties with their formal modeling and simulation. At present, the consensus related to one universal definition of complex systems does not exist yet. In different research contexts complex systems are defined on the base of their different attributes. The study of complex systems is bringing an old approach to many scientific questions that are a weak fit for the usual mechanistic view of reality present in science. Complex systems encompass an approach in many diverse disciplines including anthropology, artificial life, chemistry, computer science, economics, evolutionary computation, earthquake prediction, meteorology, molecular biology, neuroscience, physics, psychology and sociology. Scientists often seek simple nonlinear coupling rules which lead to complex phenomena. Human societies and probably human brains are complex systems in which neither the components nor the couplings are simple. Nevertheless, they exhibit many of the hallmarks of complex systems. It is worth remarking that nonlinearity is not a necessary feature of complex systems modeling: macroanalyses that concern unstable equilibrium and evolution processes of certain biological/social/economic systems can usefully be carried out also by sets of linear equations, which do nevertheless entail reciprocal dependence between variable parameters. Complex systems is a new approach to science that studies how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment. The earliest precursor to modern complex systems theory can be found in the classical political economy of the Scottish Enlightenment, late developed by the Austrian school of economics, which says that order in market systems is spontaneous and that it is the result of human action, but not the execution of any human design. Upon this the Austrian school developed from the 19^{th} to the early 20^{th} century the economic calculation problem, along with the concept of dispersed knowledge, which were to fuel debates against the thendominant Keynesian economics. This debate would lead economists, politicians and others to explore the question of computational complexity. A pioneer in the field, and inspired by Karl Popper’s and Warren Weaver’s works, Novel prize economist and philosopher Friedrich Hayek dedicated much of his work, from early to the late 20^{th} century, to the study of complex phenomena, not constraining his work to human economies but to other fields such as psychology, biology and cybernetics. Further Steven Strogatz stated that “every decade or so, a grandiose theory comes along, bearing similar aspirations and often brandishing an ominoussounding Cname. In the 1960s it was cybernetics. In the 70s it was catastrophe theory. Then came chaos theory in the 80s and complexity theory in the 90s.” One of Hayek’s main contributions to early complexity theory is his distinction between the human capacity to predict the behavior of simple systems and its capacity to predict the behavior of complex systems through modeling. He believed that economics and the sciences of complex phenomena in general (biology, psychology and so on) could not be modeled after the sciences that deal with essentially simple phenomena like physics. Hayek would notably explain that complex phenomena, through modeling, can only allow pattern predictions, compared with the precise predictions that can be made out of noncomplex phenomena. ^ a) Complex systems theory development needed new approaches. b) Complex systems are not easy to simulate. c) Complex systems approach fits weather forecasting. d) People can design market system order. e) Warren Weaver was awarded a Nobel prize in economics. f) Complexity theory came after cybernetics but prior to catastrophe theory. ^ a) Where can complex systems be applied? Give examples. b) What doesn’t mechanical approach fit today? c) Are complex systems easy to define and model? d) Can you consider human brain and a society as a complex system? e) Do complex systems need linearity or nonlinearity? f) What is the main concept of a complex system? g) When and where were the complex system applied first? h) What are “ctheories” that the humanity gained in the 2^{nd} half of the 20^{th} century? i) What was the role of Friedrich Hayek in the complexity theory development? j) Can complex systems be predicted? ^ simulation, definition, computation, prediction, equation, execution, distinction, action. 4 Fill in the gaps with the proper prepositions: a) The scientific field ______ discussion is also called complex systems theory. b) The consensus related ______ one universal definition of complex systems doe not exist yet. c) Scientists often seek simple nonlinear rules which lead ____ complex phenomena. d) The evolution processes of certain economic systems can be carried _____ also _____ sets of linear equations. e) Complex systems is a new approach ____ science that studies how relationships ____ parts give rise _____ the collective behaviors of the system. f) People can predict the behavior of complex systems _____ modeling. ^ a) Keynesian economics b) Karl Popper’s and Warren Weaver’s main ideas and views c) cybernetics d) catastrophe theory e) chaos theory. ^ 1What basic principles of synergetics do you remember? Give some examples of synergetic approach . 2 Make sure that you can read and understand the words and word combinations below. Memorize them. cybernetics qualitative changes bifurcation theory emergence macroscopic scales chaos theory neuron strong interplay catastrophe theory hormone cooperative behavior stochastic process fluctuation paradigmic example instability point variable theoretical treatment to obey cognition macroscopic state to elaborate interdisciplinary order parameters macroscopically spatial slaving principle irrespective of temporal circular causality spontaneous phase transition 3 Read the text SYNERGETICS Synergetics (Greek: ‘working together”) is an interdisciplinary field of research originated by Hermann Haken in 1969.The term “synergetics”is widely used, but still not generally accepted. Instead, “theory of selforganization” is used as a more traditional term. Synergetics can be considered as a modern stage of development within the traditions of cybernetics (N.Weiner, W.R.Ashby) and systemstructural analysis (attempts to elaborate the general theory of systems). However, while cybernetics investigates the functioning of complex using an abstract model of “black box”, synergetics studies some physical mechanisms of the complex structures formation, i.e. it tries to look into the “black box”. Synergetics deals with material or immaterial systems, composed of, in general, many individual parts. It focuses its attention on the spontaneous, i.e. selforganized emergence of new qualities which may be structures, processes or functions. The basic question dealt with by Synergetics is: are there general principles of selforganization irrespective of the nature of the individual parts of a system? In spite of the great variety of the individual parts, which may be atoms, molecules, neurons (nerve cells), up to individuals in a society, this question could not be answered in the positive for large classes of systems, provided attention is focused on qualitative changes on macroscopic scales. Here “macroscopic scales” means spatial and temporal scales that are large compared to those of the elements. “Working together” may take place between parts of a system, between systems or even between scientific disciplines. Characteristic of synergetics is the strong interplay between experiment and theory. The development of the theory of cooperative behaviour, made by H.Haken and called by himself synergetics proper, originated from the investigation of the coherent radiation of lasers. Lasers became a paradigmic example of synergetics. The systems under experimental or theoretical treatment are subject to control parameters which may be fixed from the outside or may be generated by part of the system considered. An example for an external control parameter is the power input into a gas laser by an electric current. An example for an internally generated control parameter is hormones in the human body or neurotransmitters in the brain. When control parameters reach specific critical values the system may become unstable and adopt a new macroscopic state. Close to such instability points, a new set of collective variables can be identified: the order parameters. They obey, at least in general, low dimensional dynamics and characterize the system macroscopically. According to the slaving principle, the order parameters determine the behavior of the individual parts which may be still be subject to fluctuations. Their origin may be internal or external. Because the cooperation of the individual parts enables the existence of order parameters that in turn determine the behavior of the individual parts, one speaks of circular causality. At a critical point, a single order parameter may undergo a nonequilibrium phase transition with symmetry breaking, critical slowing down and critical fluctuations. Synergetics has a number of connections with to other disciplines, such as complexity theory, dynamic systems theory, bifurcation theory, chaos theory, catastrophe theory, the theory of stochastic processes. The connection with chaos theory and catastrophe theory is in particular established by the concept of order parameters and the slaving principle, according to which close to instabilities the dynamics even of complex systems is governed by few variables only. Synergetics goes beyond the framework of strict mathematical models and narrow applications. Scholars are trying to apply synergetics not only to new fields of natural sciences, but also to humanities. There are some attempts to use synergetic models in understanding human artistic and scientific creativity, cognition, health, education, communication, etc. ^ a) The term “synergetics” is still being discussed today. b) Synergetics is being developed and applied by mathematicians. c) Lasers happened to become quite important for synergetics development. d) Fluctuations are typically caused from outside. e) Synergetics can help investigate human abilities and behavior. ^ a) What is the origin of the term “synergetics”? b) How is synergetics related to cybernetics? c) What is synergetics focused on? d) What meaning does the term “macroscopic scales” acquire in the synergetic context? e) What systems can be investigated by means of synergetics? f) What is the contribution of Hermann Haken into synergetics development? g) What is the difference between types of control parameters? h) What are order parameters? i) When does circular causality take place? j) What are connections and newest trends of synergetics? ^ interdisciplinary field phase transition coherent radiation spatial/temporal scales instability point stochastic process 4 Complete the chart by forming nouns and adverbs from the adjectives enlisted: Noun Adjective Adverb __________ qualitative ____________ ___________ traditional ____________ ___________ stochastic ____________ ___________ critical ____________ ___________ artistic ____________ ___________ creative ____________ ___________ natural ____________ ___________ cooperative ____________ ___________ paradigmatic ____________ ^ in im ir instability immaterial irrespective regular, possible, moral, finite, migrant, dependent, capable, movable, mobile, rational, adequate, accurate, resistible, responsive ^ a) Synergetics tries to look _______ the black box”. b) Synergetics focuses its attention ______ the spontaneous emergence of new qualities. c) Synergetics proper originated _______ the investigation of the coherent radiation of lasers. d) According _____ the slaving principle, the order parameters determine the behavior of the individual parts. e) _____ a critical point, a single order parameter may undergo a nonequilibrium phase transition. f) Close ____ instabilities the dynamics even of complex systems is governed by few variables only. g) Scholars are trying to apply synergetics not only _____ new fields of natural sciences, but also ____ humanities. ^ 1 Say what you remember about fractals. Give examples of fractals. 2 What scientists investigated fractals? Try to remember names and countries. 3 Make sure that you can read and understand the words and the word combinations below. Memorize them: magnification reduced copy Brownian motion snowflake Hausdoff dimension Levy flight coastline mountain range fractal landscape artifact lightning bolt aggregation cluster triangle true fractals blood vessel set iterated functions pulmonary vessel sponge recurrence relation to derive aggregation complex plane to exhibit broccoli replacement rule to denote replica deterministic process to take shape to coin 4 Read the text FRACTALS A fractal is generally “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced copy of the whole,” a property called selfsimilarity. The term was coined by Benoit Mandelbrot in 1975 and was derived from the Latin fractus meaning “broken”. A fractal often has the following features: It has a fine structure at arbitrary small scales. It is too irregular to be easily described in traditional Euclidian geometric language. It is selfsimilar (at least approximately or stochastically). It has a Hausdorff dimension which is greater than its topological dimensions. It has a simple and recursive definition. Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex. Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snowflakes. However, not all selfsimilar objects are fractals – for example, the real line (a straight Euclidean line) is formally selfsimilar but fails to have other fractal characteristics. Images of fractals can be created using fractal generating software. Images produced by such software are normally referred to as being fractals even if they do not have the above characteristics, such as when it is possible to zoom into a region of the fractal that does not exhibit any fractal properties. Also, these may include calculation or display artifacts which are not characteristics of true fractals. The mathematics behind fractals began to take shape in the 17^{th} century when mathematician and philosopher Leibniz considered recursive selfsimilarity (although he made the mistake of thinking that only the straight line was selfsimilar in this sense). It took until 1872 before a function appeared whose graph would today be considered fractal, when Karl Weierstrass gave an example of a function with the nonintuitive property of being everywhere continuous but nowhere differentiable. In 1904, Helge von Koch, dissatisfied with Weierstrass’s very abstract and analytic definition, gave a more geometric definition of a similar function, which is now called the Koch snowflake. In 1915,Waclaw Sierpiski constructed his triangle and, one year later, his carpet. Originally these geometric fractals were described as curves rather than 2D shapes that they are known as in their modern constructions. The idea of selfsimilar curves was taken further by Paul Pierrre Levy, who, in his 1938 paper “Space Curves and Surfaces Consisting of Parts Similar to the Whole” described a new fractal curve, the Levy C curve. George Cantor also gave examples of subsets of the real line with unusual properties – these Cantor sets are also now recognized as fractals. Iterated functions in the complex plane were investigated in the late 19^{th} and early 20^{th} centuries by Henri Poincare, Felix Klein, Pierre Fatou and Gaston Julia. However, without the aid of modern computer graphics, they lacked the means to visualize the beauty of many of the objects that they had discovered. In the 1960s, Benoit Mandelbrot started investigating selfsimilarity in papers such as How Long Is the Coast of Britain? Statistical SelfSimilarity and Fractional Dimension, which was built on earlier work by Lewis Fry Richardson. Finally, in 1975 Mandelbrot coined the word “fractal” to denote an object whose HausdorffBesicovitch dimension is greater than its topological dimension. He illustrated this mathematical definition with striking computerconstructed visualizations. These images captured the popular imagination; many of them were based on recursion, leading to the popular meaning of the term “fractal”. Four common techniques for generating fractals are: ^ (also known as “orbits” fractals ) are defined by a recurrence relation at each point in a space (such as the complex plane). Examples of this type are the Mandelbrot set, Julia set, the Burning Ship fractal, the Nova fractal and the Lyapunov fractal. The 2D vector fields that are generated by one or two iterations of escapetime formulae also give rise to a fractal form when points (or pixel data ) are passed through this field repeatedly. ^ have a fixed geometric replacement rule. Cantor set, Sierpinski carpet, Peano curve, Koch snowflake, HarterHeighway dragon curve, Menger sponge, are some examples of such fractals. Random fractals are generated by stochastic rather than deterministic processes, for example, trajectories of the Brownian motion, Levy flight, fractal landscapes and the Brownian tree. The latter yields socalled mass or dendritic fractals, for example, diffusionlimited aggregation or reactionlimited aggregation clusters. ^ are generated by iteration of the solution of a system of initialvalue differential equations that exhibit chaos. Fractals can also be classified according to their selfsimilarity. There are three types of selfsimilarity found in fractals: Exact selfsimilarity is the strongest type of selfsimilarity; the fractal appears identical at different scales. Fractals defined by iterated function systems often display exact selfsimilarity. Quasiselfsimilarity is a loose form of selfsimilarity; the fractal appears approximately (but not exactly ) identical at different scales. Quasiselfsimilarity fractals contain small copies of the entire fractal in distorted and degenerate forms. Fractals defined by recurrence relations are usually quasiselfsimilar but not exactly selfsimilar. ^ is the weakest type of selfsimilarity; the fractal has numerical or statistical measures which are preserved across scales. Most reasonable definitions of “fractal” trivially imply some form of statistical selfsimilarity.(Fractal dimension itself is a numerical measure which is preserved across scales.) Random fractals are examples of fractals which are statistically selfsimilar, but neither exactly nor quasiselfsimilar. Approximate fractals are easily found in nature. These objects display selfsimilar structure over an extended, but finite, scale range. Examples include clouds, snowflakes, crystals, mountain ranges, lightning, river networks, broccoli, and systems of blood vessels and pulmonary vessels. Coastlines may be loosely considered fractal in nature. Trees and ferns are fractal in nature and can be modeled on a computer by using a recursive algorithm. This recursive nature is obvious in these examples a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature. Fractal patterns have been found in the paintings. They are also prevalent in African art and architecture. Such patterns can also be found in African textiles, sculpture, and even cornrow hairstyles. ^ a) If translated from Latin, “fractal” means “breaking”. b) The term “fractal” was introduced by B. Mandelbrot in the 20^{th} century. c) Any fractal can be characterized by 4 features. d) Fractals are often viewed as very complex. e) Today lots of fractal examples are introduced artificially. f) Leibniz thought that only the straight line was selfsimilar. g) Koch is known for constructing his triangle. h) By “orbits” we mean random fractals. i) Selfsimilarity ranges from the strongest to the weakest type. ^ a) How can you define a fractal? b) What are 5 typical characteristics of fractals? c) What were the roles of Leibniz and Mandelbrot in the fractal theory development? d) Whose views did Mandelbrot follow? e) What helps fractals capture everyone’s imagination? f) What are the techniques used to generate fractals? ^ a) plane figure with three straight sides; b) line of which no part is straight and which changes direction without angles; c) crystals of frozen vapour falling from the sky; d) coming, happening again, repeated; e) number of things of the same kind that belong together. 4 Complete the table with the derivatives. Noun Adjective Verb ___________ visual ______________ relation ______________ ______________ ____________ ______________ function ____________ xxxxxxxxxxxxxx exhibit ____________ topological xxxxxxxxxxxxxx ____________ ______________ include origin _______________ ______________ dimension _______________ xxxxxxxxxxxxxx imagination _______________ ______________ curve xxxxxxxxxxxxxxx ______________ ^ 1 Tell as much as you remember about game theory. Give names, facts, main concepts. 2 What film deals closely with game theory? 3 Make sure that you can read and understand the words and word combinations from the text: equilibrium to attempt explicitly payoff to capture unilaterally move to expand outcome to mitigate insight to come into being Nash equilibrium solution concept current set equilibrium strategy strategic interaction hostile situation traffic flow game semantics multiagent system 4 Read the text ^ Game theory is a branch of applied mathematics that is used in the social sciences, most notably in economics, as well as in biology, engineering, political science, international relations, computer science, and philosophy. Game theory attempts to mathematically capture behavior in strategic situations, in which an individual’s success in making choices depends on the choices of others. While initially developed to analyze competitions in which one individual does better at another’s expense (zero sum games), it has been expanded to treat a wide class of interactions, which are classified according to several criteria. Welldefined mathematically, a game consists of a set of players, a set of moves (or strategies ) available to those players, and a specification of payoffs for each combination of strategies. Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games. Traditional applications of game theory attempt to find equilibria in these games. In an equilibrium, each player of the game has adopted a strategy that they are unlikely to change. Many equilibrium concepts have been developed (most famously the Nash equilibrium) in an attempt to capture this idea. These equilibrium concepts are motivated differently depending on the field of application, although they often overlap or coincide. Although some developments occurred before it, the field of game theory came into being with the 1944 book “Theory of Games and Economic Behavior” by John von Neumann and Oskar Morgenstern. This theory was developed extensively in the 1950s by many scholars. Game theory was later explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important tool in many fields. Eight game theorists have won Nobel prizes in economics, and John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology. In the game, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium. The Nash equilibrium concept is used to analyze the outcome of the strategic interaction of several decision makers. In other words, it is a way of predicting what will happen if several people or several institutions are making decisions at the same time, and if the decision of each one depends on the decision of the others. The simple insight underlying John Nash’s idea is that we cannot predict the result of the choices of multiple decision makers if we analyze those decisions in isolation. Instead, we must ask what each player would do, taking into account the decisionmaking of the others. Nash equilibrium has been used to analyze hostile situations like war and arms races (see Prisoner’s dilemma), and also how conflict may be mitigated by repeated interaction (see Titfortat). It has also been used to study to what extent people with different preferences can cooperate (see Battle of the sexes), and whether they will take risks to achieve a cooperative outcome (see Stag hunt). It has been used to study the adoption of technical standards, and also the occurrence of bank runs and currency crises (see Coordination game). Other applications include traffic flow (see Wardrop’s principle), how to organize auctions (see Auction theory), and even penalty kicks in soccer (see Matching pennies). Game theory has been used to study a wide variety of human or animal behaviors. It was initially developed in economics to understand a large collection of economic behaviors, including behaviors of firms, markets, and consumers. The use of game theory in the social sciences has expanded, and the game theory has been applied to political, sociological, and psychological behaviors as well. Game theory analysis was initially used to study animal behavior by Ronald Fisher in the 1930s (although even Charles Darwin makes a few informal game theoretic statements). The developments in economics were later applied to biology largely by John Maynard Smith in his book “Evolution and the Theory of Games”. Game theory has come to play an increasingly important role in logic and in computer science. Several logical theories have a basis in game semantics. In addition, computer scientists have used games to model interactive computations. Also, game theory provides a theoretical basis to the field of multiagent systems. The field of algorithmic game theory combines computer science concepts of complexity and algorithm design with game theory and economic theory. The emergence of the internet has motivated the development of algorithms for finding equilibria in games, markets, computational auctions, peertopeer systems, and security and information markets. ^ a) Any player depends on other players’ choices. b) The equilibrium concept differs from one field of science to another. c) Game theory came into being when the book by J. F. Nash appeared. d) Game theorists have been welcomed by the Nobel prize committee. e) Nash equilibrium cannot be applied to the military. f) Both humans and animals can be described by game theory. ^ a) What is a game from a mathematical and logical point of view? b) What do you know about the history of game theory development? c) What is the idea of the Nash equilibrium concept? d) Who may benefit from the Nash equilibrium concept? e) In what way did Charles Darwin contribute to the game theory evolution? f) In what field the demand for game theory is increasingly high today? ^ ___________ data equilibrium ___________ formulae ___________ ___________ criteria ___________ axes ___________ quanta ^ hostile explicitly cooperative normal informal extensive to expand to mitigate 5 Use synonyms to explain the following words: outcome insight standard scholar currency concept to occur unilaterally ^ a) An individual success ____ making choices depends ____ the choices ____ others. b) Game theory has been widely recognized ____ an important tool in many fields. c) No player can benefit ____ changing his or her strategy. d) Eight game theorists have won Nobel prizes ____ economics. e) The developments ___ economics were later applied ____ biology largely ____ John Maynard Smith. ^ 1 Do you often wait in a queue? When and where do you queue? How do you feel when waiting in a queue? 2 What is the main idea of queuing theory? Where can it be applied? 3 Make sure that you can read and understand the following words and word combinations from the text. Memorize them. iteration finite to abandon switchboard infinite to grant entity discrete to exceed customer viable to balk server excessive to jockey congestion manually simulation randomly 4 Read the text ^ Queuing theory deals with problems which involve queuing (or waiting). Typical examples might be: banks/supermarkets (waiting for service), computers (waiting for a response), failure situations (waiting for a failure to occur e.g. in a piece of machinery), public transport (waiting for a train or a bus). As we know queues are a common everyday experience. They form because resources are limited. It makes economic sense to have queues just to know for example how many supermarket tills you would need to avoid queuing or how many buses or trains would be needed to avoid queues. The first to develop a viable queuing theory was the French mathematician S. D. Poisson (17811840). He created a distribution function to describe the probability of a prescribed outcome after repeated iterations of independent trials. Poisson used a statistical approach. His distributions could be applied to any situation where excessive demands are made on a limited resource. The most important application of queuing theory occurred during the late 1800s, when telephone companies were faced with the problem of how many operators to place on duty at a given time. At the time, all calls were switched manually by an operator who physically connected a wire to a switchboard. A Danish mathematician named A.K Erlang developed a different approach to traffic engineering based on Poisson’s work. He established formulas for calls that are abandoned (called ErlangB) and for those that are held until service is granted (ErlangC). All queuing systems can be broken into individual subsystems consisting of entities queuing for some activity. To analyze these subsystems we need information related to: arrival process:  how many customers arrive singly or in groups;  how the arrivals are distributed in time (what is the probability distribution of time between successive arrivals – the interarrival time distribution);  whether there is a finite population of customers or an infinite number. service mechanism:  a description of the resources needed for service to begin;  how long the service will take (the service time distribution);  the number of severs available;  whether the servers are in series (each server has a separate queue) or in parallel (on queue for all servers);  whether preemtion is allowed (a server can stop processing a customer to deal with another “emergency” customer). queue characteristics:  how, from a set of customers waiting for service, do we choose the one to be served next (FIFO firstin firstout also known as FCFS –firstcome firstserved, LIFO – lastin first out, randomly);  do we have balking (customers deciding not to join the queue if it is too long), reneging (customers leave the queue if they have waited too long for a service), jockeying (customers switch between queues if they think they will get faster by doing so); a queue of finite capacity or of infinite capacity. Changing the queue discipline (the rule by which we select the next customer to be served) can often reduce congestion. In terms of the analysis of queuing situations the types of questions typically concerned with measures of system performance include:  How long does a customer expect to wait in the queue before they are served, and how long will they have to wait before the service is complete?  What is the probability of a customer having to wait longer than a given time interval before they are served?  What is the average length of the queue?  What is the probability that the queue will exceed a certain length? –  What is the expected utilization of the server and the expected time period during which he will be fully occupied (servers cost money so we need them to keep busy). In order to get answers to the above questions there are two basic approaches: analytic methods or formula based queuing theory and simulation or computer based queuing theory. Analytic methods are only available for relatively simple queuing systems. Complex queuing systems are almost always analyzed using simulation (more technically known as discreteevent simulation). ^ a) Queuing is still a problem today. b) The French scientist made the theoretical basis for queuing theory. c) A. K. Erlang’s approach helped many telephone stations to solve their problems. d) To solve a queuing problem one must build up its simplified model. e) The customers are often served randomly. f) Congestion is the result of an effective management. g) Computation of queuing problems means their simulation. ^ a) Why is queuing theory in such demand today? b) What did S. D. Poisson create? c) What big application did queuing theory occur in 1800s? d) What aspects must be considered when analyzing a queuing subsystem? e) What parameters can arrival process include? f) What does service mechanism consist of? h) What do abbreviations FIFO and LIFO stand for? i) What is the difference between balking, reneging and jockeying? j) What is a queue discipline? k) What points are especially important for any service manager? l) What are two basic approaches in queuing theory? ^ a) the person who receives a service entity b) done with hands viable c) pretence, imitation customer d) the state of being too full, overcrowded distribution e) to go away from, not intending to return to congestion f) to do again and again h) the device for making or breaking connection infinite i) endless, without limits j) putting, giving or sending out parts of a to iterate set of things k) moneyregister to abandon l) able to exist manually m) something that really exists simulation ^ iteration, distribution, application, population, simulation, utilization 5 Find in the text the phrases or sentences that make the context for the following adverbs: relatively, technically, physically, randomly, manually, typically 6 Practice prepositions: a) All calls were switched manually _____ an operator who connected a wire _____ a switchboard. b) Telephone companies were faced _____ a problem of how many operators to place ____ duty _____ a given time. c) Poisson’s distributions could be applied ____ any situation. d) The queue discipline is the rule _____ which we select the next customer to be served. e) All queuing systems can be broken _____ individual systems consisting _____ entities queuing _____ some activity. 7 Speak about your own queuing experiences. 
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