3.6. Read the definitions and find the words/phrases in the text above.

1. 1) a measurement of the size of something in a particular direction, such as the length, width, height, or diameter; 2) the number of coordinates required to locate a point in space

2. 1) a collection of objects or a set; 2) a topological space having specific properties

3. a branch of theoretical physics in which the point-like particles of particle are replaced by one-dimensional objects called strings 

4. the antiparticle of the electron, having the same mass but an equal and opposite charge. It is produced in certain decay processes and in pair production, annihilation occurring when it collides with an electron

5. the theory that the origin of the universe was in a cataclysmic explosion in which all the matter of the universe, packed into a small superdense mass, was hurled in all directions

6. the branch of modern geometry in which certain axioms of Euclidean geometry are restated. It introduces fundamental changes into the concept of space

7. 1) an expression that can be assigned any of a set of values; 2) a symbol, esp x, y, or z, representing an unspecified member of a class of objects, numbers, etc

8. the theory of gravitation, developed by Einstein in 1916, extending the special theory of relativity to include acceleration and leading to the conclusion that gravitational forces are equivalent to forces caused by acceleration

3.7. Answer the questions.

1. What is the difference between Euclidian and non-Euclidian geometry?

2. What is Riemann’s geometry about?

3. How did Einstein’s equations influence the following discoveries?

4. What are positrons?

5. Why did physicists and mathematicians start losing touch with one another?

6. What is a fiber bundle?

7. What is string theory?

8. What do mathematics and physics have in common?

3.8. Translate the sentences.

1. Открытие антиматерии переросло в попытку совместить теорию относительности с квантово-механическим описанием электрона.

2. Изучение теории струн привело к нескольким важным внедрениям в математических науках, например, решение систем полиноминальных уравнений.

3. Бернхард Риман сделал еще один смелый шаг, описав пространства, в которых радиус кривизны мог меняться от точки к точке внутри этого пространства.

4. Математики начали интересоваться новым видом геометрического пространства, которое называется расслоенное пространство, которое, грубо говоря, напоминает искривленное пространство с колчаном стрел, прикрепленным к каждой точке.

5. Теория струн предполагает, что вселенная имеет шесть дополнительных невидимых измерений, которые свернуты в тугой клубок.

 

3.9. Match the distinct branches of mathematical physics with the corresponding historical periods. Translate the branches of science.

Mathematical physics

The Lagrangian mechanicsand theHamiltonian mechanicsare embodied in the so-calledanalytical mechanics. It leads, for instance, to discover the deep interplay of the notion of symmetry and that of conserved quantities during the dynamical evolution, stated within the most elementary formulation ofNoether's theorem. These approaches and ideas have been extended to other areas of physics asstatistical mechanics,continuum mechanics,classical field theoryandquantum field theory. Moreover they have provided several examples and basic ideas indifferential geometry(e.g. the theory ofvector bundlesand several notions insymplectic geometry).	Quantum theory
This theory developed almost concurrently with the mathematical fields of linear algebra, thespectral theoryofoperators,operator algebrasand more broadly,functional analysis. It has connections toatomic and molecular physics.Quantum informationtheory is another subspecialty.	Partial differential equations
The specialandgeneraltheories require a rather different type ofmathematics. This wasgroup theory, which played an important role in bothquantum field theoryanddifferential geometry. This was, however, gradually supplemented bytopologyandfunctional analysisin the mathematical description ofcosmologicalas well asquantum field theoryphenomena. In this area bothhomological algebraandcategory theoryare important nowadays.	Geometrically advanced formulations of classical mechanics
This theory forms a separate field, which includes the theory of phase transitions. It relies upon theHamiltonian mechanics(or its quantum version) and it is closely related with the more mathematicalergodic theoryand some parts ofprobability theory. There are increasing interactions betweencombinatorics and physics, in particular statistical physics.	Statistical mechanics
This theory (and the related areas of variational calculus, Fourier analysis, potential theory, and vector analysis) is perhaps most closely associated with mathematical physics. These were developed intensively from the second half of the eighteenth century (by, for example, D'Alembert, Euler, and Lagrange) until the 1930s. Physical applications of these developments include hydrodynamics, celestial mechanics, continuum mechanics, elasticitytheory, acoustics, thermodynamics,electricity, magnetism, and aerodynamics.	Relativity and Quantum Relativistic Theories