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- •Contents
- •Пояснительная записка
- •Vocabulary
- •Careers in Mathematics and Physics
- •Job Description
- •Vocabulary
- •2.1. What do you know about the latest inventions in mathematics and physics? Do these inventions help mankind? Why / Why not?
- •2.2. Read the text. What is the main idea of the text? What all the "God particle" hoopla was all about?
- •2.3. Сhoose the correct answer.
- •2.6. Match the following words in a with the words of the similar meaning in b.
- •2.7. Search the Internet and find more information about different Nobel prizes in Physics. Make a presentation. (See Appendix 1)
- •2.8. Read the text. What is the main idea of the text? The world's smallest electric motor
- •2.9. Decide if the statements are true (t) or false (f).
- •2.10. Find the following phrases in the text.
- •2.11. Translate the words. Match the words with the similar meaning.
- •2.12. Read the summary of the text above. Put the words (on the right) into the gaps (on the left).
- •2.13. Search the Internet and find out more about Dr Sykes’ nanotechnology device. Share what you discover with your partner. Make a presentation about nanotechnology. (See Appendix 1)
- •2.14. Answer the questions.
- •2.15. Make a summary of the texts. (See Appendix 4)
- •Vocabulary
- •The mathematical sciences in everyday life
- •Shanghai students are the world's best at maths
- •3.4. Translate the words. Find the words with the similar meaning on the right.
- •3.5. Read the text and translate the words and phrases in bold. Geometry and Physics Interactions
- •3.6. Read the definitions and find the words/phrases in the text above.
- •3.7. Answer the questions.
- •3.8. Translate the sentences.
- •Mathematical physics
- •3.10. Make a translation of the texts.
- •Famous Puzzles
- •Weighing the Baby Puzzle
- •A Question of Time Puzzle
- •Outwitting the Weighing Machine Puzzle
- •1) Weighing the Baby Puzzle
- •A Question of Time Puzzle
- •Outwitting the Weighing Machine Puzzle
- •Welcoming
- •Introducing yourself
- •Introducing your presentation
- •Explaining that there will be time for questions at the end
- •Interests:
- •Bibliography
- •Web-sources
- •Recommended sources
- •625003, Г. Тюмень, ул. Семакова 10
3.5. Read the text and translate the words and phrases in bold. Geometry and Physics Interactions
The secrets of the universe are still written in geometric terms, although the figures Galileo wrote about have now been replaced by more exotic and abstract ones: manifolds, fiber bundles, and Calabi-Yau spaces.
In the early 1800s, it was shown that the familiar Euclidean geometry, which has been taught since the ancient Greeks and is still taught in high schools today, is only one of an infinite variety of possible geometries. Euclidean geometry is flat - it is the geometry of a tabletop, infinitely extended. By contrast, non-Euclidean geometries are curved. They may have the positive curvature of a sphere, or they may have negative curvature, which is harder to visualize but may be compared to the frilly surface of some leafy vegetables.
In the 1850s, Bernhard Riemann took another bold step forward, describing spaces in which the curvature could change from point to point within the space. Riemann’s geometry also allows space to take on any number of dimensions - two, three, or even more. He called these curved spaces “manifolds”.
For some time these new geometries remained just a mathematical curiosity. But in the early 1900s, Albert Einstein used Riemann’s mathematics as a language to express his dimensional space-time. A long list of profound discoveries followed from the equations that Einstein wrote down in 1915: black holes, the expanding universe, the big bang, and dark energy. To understand any of these ideas fully, you have to learn Riemannian geometry. Somewhere, Galileo must be smiling.
But Einstein’s general relativity was only the beginning. Similar geometric constructions underlie the field theories that describe particle physics. The discovery of antimatter, in 1932, grew directly out of an attempt to reconcile relativity with the quantum-mechanical description of the electron. The equations predicted extra solutions that seemed like positively charged electrons. We now call them positrons. They are the key ingredients in positron emission tomography, or PET scans, which are used to study the workings of the human brain.
In the later 1930s and 1940s, physicists and mathematicians started losing touch with one another. Physicists started thinking about fields that permeate all of space, which they called “gauge fields.” (Examples include the electromagnetic field and the weak and strong nuclear forces.) Meanwhile mathematicians, for different reasons, became very interested in a new kind of geometric space, called a fiber bundle, which is roughly like a curved space with a quiver of arrows attached at every point. It wasn’t until the 1970s that mathematicians and physicists realized that they were doing the same thing.
The physicists’ gauge fields were like individual arrows in the mathematicians’ quiver of arrows. The cross-fertilization of ideas between the mathematical sciences and theoretical physics continues to this day. In the late 20th and early 21st centuries, string theory was formulated as an approach to unifying gravity and quantum physics into a theory of everything. Like all other theories in physics, it is highly mathematical - but the necessary mathematics has not yet been invented. There is still no rigorous context for the calculations that string theorists do, nor do mathematical scientists know the extent to which these techniques are valid.
However, the study of string theory has led to some important applications of the mathematical sciences. For example, since the 1800s, mathematicians have studied the solution sets of polynomial equations, such as a fifth degree polynomial in four variables. An example of such a polynomial is x5 + y5 + z5 + s5 + t5 = 0, which is known as a “quintic hypersurface”. These surfaces contain figures that Galileo would have recognized. And why did string theorists care about quintic hypersurfaces? Because string theory postulates that the universe has six extra, unseen dimensions that are curled up into a tight ball. Except that “ball” is not really the correct word. They actually form a manifold - a type of space discovered by mathematical scientists. The list of interactions between geometry and physics could go on and on. It is difficult to speculate where it will lead next, but it is virtually certain that unexpected ideas for both disciplines will continue to grow out of the interaction. Galileo’s words continue to hold true: Geometry is still the language spoken by the universe.