User:Purabi zafar/sandbox


 * Cosmology
 * Cosmology is the study of the origins and eventual fate of the universe. Physical cosmology is the scholarly and scientific study of the origin, evolution, structure, dynamics, and ultimate fate of the universe, as well as the natural laws that keep it in order. Religious cosmology (or mythological cosmology) is a body of beliefs based on the historical, mythological, religious, and esoteric literature and traditions of creation and eschatology.Physical cosmology is studied by scientists, such as astronomers, and theoretical physicists; and academic philosophers, such as metaphysicians, philosophers of physics, and philosophers of space and time. Modern cosmology is dominated by the Big Bang theory, which attempts to bring together observational astronomy and particle physics. Although the word cosmology is recent (first used in 1730 in Christian Wolff's Cosmologia Generalis), the study of the universe has a long history involving science, philosophy, esotericism and religion. Related studies include cosmogony, which focuses on the origin of the Universe, and cosmography, which maps the features of the Universe. Cosmology is also connected to astronomy, but while the former is concerned with the Universe as a whole, the latter deals with individual celestial objects.


 * Physical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the Universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion. Cosmology as a science originated with the Copernican principle, which implies that celestial bodies obey identical physical laws to those on Earth, and Newtonian mechanics, which first allowed us to understand those laws.Physical cosmology, as it is now understood, began with the 20th century development of Albert Einstein's general theory of relativity, and better astronomical observations of extremely distant objects. These advances made it possible to speculate about the origin of the Universe, and allowed scientists to establish the Big Bang Theory as the leading cosmological model. Some researchers still advocate a handful of alternative cosmologies; however, cosmologists generally agree that the Big Bang theory best explains observations.Cosmology draws heavily on the work of many disparate areas of research in theoretical and applied physics. Areas relevant to cosmology include particle physics experiments and theory, including astrophysics, general relativity, quantum mechanics, and plasma physics. Thus, cosmology unites the physics of the largest structures in the Universe with the physics of the smallest structures in the Universe.


 * History of Physical cosmology . In 1916, Albert Einstein published his theory of general relativity, which provided a unified description of gravity as a geometric property of space and time. At the time, Einstein believed in a static universe, but found that his original formulation of the theory did not permit it. This is because masses distributed throughout the Universe gravitationally attract, and move toward each other over time. However, he realized that his equations permitted the introduction of a constant term which could counteract the attractive force of gravity on the cosmic scale. Einstein published his first paper on relativistic cosmology in 1917, in which he added this cosmological constant to his field equations in order to force them to model a static universe. However, this so-called Einstein model is unstable to small perturbations—it will eventually start to expand or contract.[4] The Einstein model describes a static universe; space is finite and unbounded (analogous to the surface of a sphere, which has a finite area but no edges). It was later realized that Einstein's model was just one of a larger set of possibilities, all of which were consistent with general relativity and the cosmological principle. The cosmological solutions of general relativity were found by Alexander Friedmann in the early 1920s. His equations describe the Friedmann-Lemaître-Robertson-Walker universe, which may expand or contract, and whose geometry may be open, flat, or closed.In the 1910s, Vesto Slipher (and later Carl Wilhelm Wirtz) interpreted the red shift of spiral nebulae as a Doppler shift that indicated they were receding from Earth. However, it is difficult to determine the distance to astronomical objects. One way is to compare the physical size of an object to its angular size, but a physical size must be assumed to do this. Another method is to measure the brightness of an object and assume an intrinsic luminosity, from which the distance may be determined using the inverse square law. Due to the difficulty of using these methods, they did not realize that the nebulae were actually galaxies outside our own Milky Way, nor did they speculate about the cosmological implications. In 1927, the Belgian Roman Catholic priest Georges Lemaître independently derived the Friedmann-Lemaître-Robertson-Walker equations and proposed, on the basis of the recession of spiral nebulae, that the Universe began with the "explosion" of a "primeval atom"—which was later called the Big Bang. In 1929, Edwin Hubble provided an observational basis for Lemaître's theory. Hubble showed that the spiral nebulae were galaxies by determining their distances using measurements of the brightness of Cepheid variable stars. He discovered a relationship between the redshift of a galaxy and its distance. He interpreted this as evidence that the galaxies are receding from Earth in every direction at speeds proportional to their distance. This fact is now known as Hubble's law, though the numerical factor Hubble found relating recessional velocity and distance was off by a factor of ten, due to not knowing about the types of Cepheid variables.Given the cosmological principle, Hubble's law suggested that the Universe was expanding. Two primary explanations were proposed for the expansion. One was Lemaître's Big Bang theory, advocated and developed by George Gamow. The other explanation was Fred Hoyle's steady state model in which new matter is created as the galaxies move away from each other. In this model, the Universe is roughly the same at any point in time.For a number of years, support for these theories was evenly divided. However, the observational evidence began to support the idea that the Universe evolved from a hot dense state. The discovery of the cosmic microwave background in 1965 lent strong support to the Big Bang model, and since the precise measurements of the cosmic microwave background by the Cosmic Background Explorer in the early 1990s, few cosmologists have seriously proposed other theories of the origin and evolution of the cosmos. One consequence of this is that in standard general relativity, the Universe began with a singularity, as demonstrated by Stephen Hawking and Roger Penrose in the 1960s.


 * The importance ofmathematicsPrepared by Md. Zafaruddin
 * 1) The word mathematicscomes from the Greek μάθημα (máthēma), which, in theancient Greek language, means "what one learns", "what one getsto know", Hence it is sayed Mathematics means "knowledge,study, learning". Though It is the abstract study of topics encompassing quantity, structure, space, change, andother properties but it also helps  to use logical thought, to formulate a problem in a way which     allows for computation and decision, to make deductions from assumption, to use advanced concepts,  Mathematicsarises from many different kinds of problems. At first these were found in commerce, landmeasurement, architecture and later astronomy;today, all sciences suggest problems studied by mathematicians. Many mathematicians talk about the elegance ofmathematics, its intrinsic aesthetics and inner beauty. It is the gate and key of the All kind of knowledge.Considering the importance mathematics inscience, it is said that Mathematics is the mother of the Science. If some one ask `WHY ISMATHEMATICS IMPORTANT?’ Answer is given by quoting Galileo: "The greatbook of nature can be read only by those who know the language in which it waswritten. And that language is mathematics.", So it is said "Math isthe way to understand all sorts of things in the world around us." According to the famous Philosopher Kant,"A Science is exact only in so far as it employs Mathematics". So,all scientific education which does not commence with Mathematics is said to bedefective at its foundation. Neglect of mathematics works injury to allknowledge.One who is ignorant of mathematics cannotknow other things of the World. Again, what is worse, who are thus ignorant areunable to perceive their own ignorance and do not seek any remedy. So Kantsays, "A natural Science is a Science in so far as it ismathematical". And Mathematics has played a very important role inbuilding up modern Civilization by perfecting all Science.In this modern age of Science and Technology,emphasis is given on Science such as Physics, Chemistry, Biology, Medicine andEngineering. Mathematics, which is a Science by any criterion, also is anefficient and necessary tool being employed by all these Sciences. As a matterof fact, all these Sciences progress only with the aid of Mathematics. So it isaptly remarked, "Mathematics is a Science of all Sciences and art of allarts."  Because the conception ofMathematics is requiredto lighten the every corner ofknowledge.  For example, thefollowing areas require good knowledge of Mathematics and : the physical sciences (like Chemistry, Physics,     Engineering), the life and health sciences (like Biology,     Psychology, Pharmacy, Nursing, Optometry), the social sciences (including Anthropology,     Communications, Economics, Linguistics, Education, Geography) the tech sciences (like Computer Science,     Networking, Software development), Business and Commerce, Actuarial science (used by insurance companies) Medicine Mathematics is a creation of human mindconcerned chiefly with ideas, processes and reasoning. It is much more thanArithmetic, more than Algebra more than Geometry. Also it is much more thanTrigonometry, Statistics, and Calculus.Mathematics includes all of them. Primarilymathematics is a way of thinking, a way of organizing a logical proof. As a wayreasoning, it gives an insight into the power of human mind, so this forms avery valuable discipline of teaching-learning programmes of school subjectseverywhere in the world of curious children. So the pedagogy of Mathematicsshould very carefully be built in different levels of school education.In the pedagogical study of mathematics wemainly concern ourselves with two things; the manner in which the subjectmatter is arranged or the method the way in which it is presented to the pupilsor the mode of presentation. Mathematics is intimately connected with everydaylife and necessary to successful conduct of affairs. It is an instrument ofeducation found to be in conformity with the needs of human mind.The everyday use of arithmetic and thedisplay of information by means of graphs, are an everyday commonplace. Theseare the elementary aspects of mathematics. Advanced mathematics is widely used,but often in an unseen and unadvertised way. The     mathematics of error-correcting codes is applied to CD players and to     computers. The     stunning pictures of far away planets sent by Voyager II could not have     had their crispness and quality without such mathematics. Voyager's     journey to the planets could not have been calculated without the     mathematics of differential equations. Whenever     it is said that advances are made with supercomputers, there has to be a     mathematical theory which instructs the computer what is to be done, so     allowing it to apply its capacity for speed and accuracy. The     development of computers was initiated in this country by mathematicians     and logicians, who continue to make important contributions to the theory     of computer science. The     next generation of software requires the latest methods from what is     called category theory, a theory of mathematical structures which     has given new perspectives on the foundations of mathematics and on logic.     The     physical sciences (chemistry, physics, oceanography, astronomy) require     mathematics for the development of their theories. In     ecology, mathematics is used when studying the laws of population change. Statistics     provides the theory and methodology for the analysis of wide varieties of     data. Statistics     is also essential in medicine, for analysing data on the causes of illness     and on the utility of new drugs. . Travel     by aeroplane would not be possible without the mathematics of airflow and     of control systems. Body     scanners are the expression of subtle mathematics, discovered in the 19th     century, which makes it possible to construct an image of the inside of an     object from information on a number of single X-ray views of it. Thus     mathematics is often involved in matters of life and death. These applications have often developed fromthe study of general ideas for their own sake: numbers, symmetry, area andvolume, rate of change, shape, dimension, randomness and many others.Mathematics makes an especial contribution to the study of these ideas, namelythe methods of precise     definitions; careful     and rigorous argument; representation of ideas by many methods, including     symbols and formulae, pictures and graphics; means     of calculation; and     the obtaining of precise solutions to clearly stated problems, or clear     statements of the limits of knowledge. These features allow mathematics to provide asolid foundation to many aspects of daily life, and to give a comprehension ofthe complexities inherent in apparently quite simple situations. For these reasons, mathematics andcalculation have been associated from earliest times. In modern times, theneed to perform rapid mathematical calculations in war time, particularly inballistics, and in decoding, was a strong stimulus to the development of theelectronic computer. The existence of high speed computers has now helpedmathematicians to calculate and to make situations visual as never before. Alsothis calculation has developed from numerical calculation, to symboliccalculation, and currently to calculation with the mathematicalstructures themselves. This last is very recent, and is likely to lead to amajor transformation. These capacities change, not the nature of mathematics,but the power of the mathematican, which increases perhaps a millionfold thepossibility to comprehend, to argue, to explore.Teaching of mathematics has its aims andobjectives to be incorporated in the school curricula. If and when Mathematicsis removed, the back-bone of our material civilization would collapse. So isthe importance of Mathematics.