1.
Nobel Prize
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The Nobel Prize is a set of annual international awards bestowed in a number of categories by Swedish and Norwegian institutions in recognition of academic, cultural, or scientific advances. The will of the Swedish inventor Alfred Nobel established the prizes in 1895, the prizes in Chemistry, Literature, Peace, Physics, and Physiology or Medicine were first awarded in 1901. Medals made before 1980 were struck in 23 carat gold, between 1901 and 2016, the Nobel Prizes and the Prize in Economic Sciences were awarded 579 times to 911 people and organisations. With some receiving the Nobel Prize more than once, this makes a total of 23 organisations, the prize ceremonies take place annually in Stockholm, Sweden. Each recipient, or laureate, receives a medal, a diploma. The Nobel Prize is widely regarded as the most prestigious award available in the fields of literature, medicine, physics, chemistry, peace, and economics. The prize is not awarded posthumously, however, if a person is awarded a prize and dies before receiving it, though the average number of laureates per prize increased substantially during the 20th century, a prize may not be shared among more than three people. Alfred Nobel was born on 21 October 1833 in Stockholm, Sweden and he was a chemist, engineer, and inventor. In 1894, Nobel purchased the Bofors iron and steel mill and this invention was a precursor to many smokeless military explosives, especially the British smokeless powder cordite. As a consequence of his patent claims, Nobel was eventually involved in a patent infringement lawsuit over cordite, Nobel amassed a fortune during his lifetime, with most of his wealth from his 355 inventions, of which dynamite is the most famous. In 1888, Nobel was astonished to read his own obituary, titled The merchant of death is dead, as it was Alfreds brother Ludvig who had died, the obituary was eight years premature. The article disconcerted Nobel and made him apprehensive about how he would be remembered and this inspired him to change his will. On 10 December 1896, Alfred Nobel died in his villa in San Remo, Italy, Nobel wrote several wills during his lifetime. He composed the last over a year before he died, signing it at the Swedish–Norwegian Club in Paris on 27 November 1895, Nobel bequeathed 94% of his total assets,31 million SEK, to establish the five Nobel Prizes. Because of skepticism surrounding the will, it was not until 26 April 1897 that it was approved by the Storting in Norway. The executors of Nobels will, Ragnar Sohlman and Rudolf Lilljequist, formed the Nobel Foundation to take care of Nobels fortune, Nobels instructions named a Norwegian Nobel Committee to award the Peace Prize, the members of whom were appointed shortly after the will was approved in April 1897. Soon thereafter, the other prize-awarding organisations were designated or established and these were Karolinska Institutet on 7 June, the Swedish Academy on 9 June, and the Royal Swedish Academy of Sciences on 11 June. The Nobel Foundation reached an agreement on guidelines for how the prizes should be awarded, and, in 1900, in 1905, the personal union between Sweden and Norway was dissolved

2.
Physics
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Physics is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental disciplines, the main goal of physics is to understand how the universe behaves. Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy, Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the mechanisms of other sciences while opening new avenues of research in areas such as mathematics. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs, the United Nations named 2005 the World Year of Physics. Astronomy is the oldest of the natural sciences, the stars and planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, according to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descended from late Babylonian astronomy. The most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn Al-Haitham, in which he was not only the first to disprove the ancient Greek idea about vision, but also came up with a new theory. In the book, he was also the first to study the phenomenon of the pinhole camera, many later European scholars and fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haythams Optics ranks alongside that of Newtons work of the same title, the translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the devices as what Ibn al-Haytham did. From this, such important things as eyeglasses, magnifying glasses, telescopes, Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics. Newton also developed calculus, the study of change, which provided new mathematical methods for solving physical problems. The discovery of new laws in thermodynamics, chemistry, and electromagnetics resulted from greater research efforts during the Industrial Revolution as energy needs increased, however, inaccuracies in classical mechanics for very small objects and very high velocities led to the development of modern physics in the 20th century. Modern physics began in the early 20th century with the work of Max Planck in quantum theory, both of these theories came about due to inaccuracies in classical mechanics in certain situations. Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger, from this early work, and work in related fields, the Standard Model of particle physics was derived. Areas of mathematics in general are important to this field, such as the study of probabilities, in many ways, physics stems from ancient Greek philosophy

3.
Emmy Noether
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Amalie Emmy Noether was a German mathematician known for her landmark contributions to abstract algebra and theoretical physics. She was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, as one of the leading mathematicians of her time, she developed the theories of rings, fields, and algebras. In physics, Noethers theorem explains the connection between symmetry and conservation laws, Noether was born to a Jewish family in the Franconian town of Erlangen, her father was a mathematician, Max Noether. She originally planned to teach French and English after passing the examinations, but instead studied mathematics at the University of Erlangen. After completing her dissertation in 1907 under the supervision of Paul Gordan, at the time, women were largely excluded from academic positions. In 1915, she was invited by David Hilbert and Felix Klein to join the department at the University of Göttingen. The philosophical faculty objected, however, and she spent four years lecturing under Hilberts name and her habilitation was approved in 1919, allowing her to obtain the rank of Privatdozent. Noether remained a member of the Göttingen mathematics department until 1933. By the time of her address at the 1932 International Congress of Mathematicians in Zürich. The following year, Germanys Nazi government dismissed Jews from university positions, in 1935 she underwent surgery for an ovarian cyst and, despite signs of a recovery, died four days later at the age of 53. Noethers mathematical work has been divided into three epochs, in the first, she made contributions to the theories of algebraic invariants and number fields. In the second epoch, she began work that changed the face of algebra, in her classic paper Idealtheorie in Ringbereichen Noether developed the theory of ideals in commutative rings into a tool with wide-ranging applications. She made elegant use of the ascending chain condition, and objects satisfying it are named Noetherian in her honor, in the third epoch, she published works on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals. Emmys father, Max Noether, was descended from a family of traders in Germany. At 14, he had been paralyzed by polio and he regained mobility, but one leg remained affected. Largely self-taught, he was awarded a doctorate from the University of Heidelberg in 1868, after teaching there for seven years, he took a position in the Bavarian city of Erlangen, where he met and married Ida Amalia Kaufmann, the daughter of a prosperous merchant. Max Noethers mathematical contributions were to algebraic geometry mainly, following in the footsteps of Alfred Clebsch and his best known results are the Brill–Noether theorem and the residue, or AF+BG theorem, several other theorems are associated with him, see Max Noethers theorem. Emmy Noether was born on 23 March 1882, the first of four children and her first name was Amalie, after her mother and paternal grandmother, but she began using her middle name at a young age

4.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times

5.
Hermann Weyl
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Hermann Klaus Hugo Weyl, ForMemRS was a German mathematician, theoretical physicist and philosopher. His research has had significance for theoretical physics as well as purely mathematical disciplines including number theory. He was one of the most influential mathematicians of the century. Weyl published technical and some works on space, time, matter, philosophy, logic, symmetry. He was one of the first to conceive of combining general relativity with the laws of electromagnetism, while no mathematician of his generation aspired to the universalism of Henri Poincaré or Hilbert, Weyl came as close as anyone. Michael Atiyah, in particular, has commented that whenever he examined a mathematical topic, Weyl was born in Elmshorn, a small town near Hamburg, in Germany, and attended the gymnasium Christianeum in Altona. From 1904 to 1908 he studied mathematics and physics in both Göttingen and Munich and his doctorate was awarded at the University of Göttingen under the supervision of David Hilbert whom he greatly admired. In September 1913 in Göttingen, Weyl married Friederike Bertha Helene Joseph who went by the name Helene, Helene was a daughter of Dr. Bruno Joseph, a physician who held the position of Sanitätsrat in Ribnitz-Damgarten, Germany. Helene was a philosopher and also a translator of Spanish literature into German and it was through Helenes close connection with Husserl that Hermann became familiar with Husserls thought. Hermann and Helene had two sons, Fritz Joachim Weyl and Michael Weyl, both of whom were born in Zürich, Switzerland, Helene died in Princeton, New Jersey on September 5,1948. A memorial service in her honor was held in Princeton on September 9,1948, speakers at her memorial service included her son Fritz Joachim Weyl and mathematicians Oswald Veblen and Richard Courant. In 1950 Hermann married sculptress Ellen Bär, who was the widow of professor Richard Josef Bär of Zürich, einstein had a lasting influence on Weyl, who became fascinated by mathematical physics. In 1921 Weyl met Erwin Schrödinger, a theoretical physicist who at the time was a professor at the University of Zürich and they were to become close friends over time. Weyl left Zürich in 1930 to become Hilberts successor at Göttingen, leaving when the Nazis assumed power in 1933, particularly as his wife was Jewish. He had been offered one of the first faculty positions at the new Institute for Advanced Study in Princeton, New Jersey, as the political situation in Germany grew worse, he changed his mind and accepted when offered the position again. He remained there until his retirement in 1951, together with his second wife Ellen, he spent his time in Princeton and Zürich, and died from a heart attack on December 8,1955 while living in Zürich. Hermann Weyl was cremated in Zurich on December 12,1955 and his cremains remained in private hands until 1999, at which time they were interred in an outdoor columbarium vault in the Princeton Cemetery, located at 29 Greenview Avenue, Princeton, New Jersey. The remains of Hermanns son Michael Weyl are interred next to Hermanns ashes in the same columbarium vault in the Princeton Cemetery

6.
Yeshiva University
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Yeshiva University is a private university in New York City, with four campuses in New York City. Founded in 1886, it is a research university, while the majority of students at the University are of the Jewish faith, many students, especially at School of Law and the School of Business, are not Jewish. Yeshiva University is an independent institution chartered by New York State and it is accredited by the Commission on Higher Education of the Middle States Association of Colleges and Schools and by several professional agencies. It conferred 1,822 degrees in 2007 and offers community service projects serving New York, Jewish communities, the university has run an operating deficit for seven consecutive years. In 2014 it lost $84 million, and in 2013 suffered a loss of $64 million, in March 2015, the faculty of Yeshiva College passed a no-confidence motion against Richard Joel, the university president. A1928 plan to build a spacious Moorish Revival campus around several gardens, building continued after the Depression in modern style and by the acquisition of existing neighborhood buildings. It has campuses and facilities in Manhattan, the Bronx, Queens, the Yeshiva University Museum is a teaching museum and the cultural arm of Yeshiva University. The Brookdale Center in the Greenwich Village neighborhood of downtown Manhattan contains the Benjamin Cardozo School of Law, law clinics and office, the Center for Jewish History, which includes the Yeshiva University Museum along with other institutions, is nearby in the Chelsea neighborhood. The Azrieli School has classes on campus as well. The Wilf Campus is centered around the area of Amsterdam Ave, Yeshiva Universitys main office is located within the Wilf Campus, at 500 185th St. and Wilf is considered the main campus. The high school for girls is located in the Holliswood neighborhood of eastern Queens, the universitys building in Jerusalem, in the Bayit VeGan neighborhood, contains a branch of the rabbinical seminary and an office coordinating the S. While studying in Israel, students study Jewish subjects while learning firsthand about Israels land, people, history, Yeshiva University Israel advisers visit each school regularly to offer academic guidance, career planning, and personal counseling. In addition, the program sponsors lectures and activities students can gather under the auspices of Yeshiva University. Yeshiva University also cosponsors events for American students in Israel, such as the Battle of the Bands and Inter-Seminary Choir Competition, the program is headquartered at the Student Center at Yeshiva Universitys Israel Campus in the Bayit Vegan neighborhood of Jerusalem. Mrs. Stephanie Strauss serves as director of the program, clubs and activities are maintained by the students in each school, generally under the auspices of a student government. Activities are funded by a student activities fee collected by the school, each graduate school maintains a student council, such as the Student Bar Association at Cardozo, which, in turn, supports the many clubs and publications in each school. At the undergraduate level, there are separate student governments on the two campuses, although the two student governments are separate, they work closely in coordinating joint events. There are also individual councils for each class, council committees, a Student Court, on the Wilf Campus, the Yeshiva Student Union, run by Aryeh Minsky oversees most of student life on campus

7.
Set theory
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Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics, the language of set theory can be used in the definitions of nearly all mathematical objects. The modern study of set theory was initiated by Georg Cantor, Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Beyond its foundational role, set theory is a branch of mathematics in its own right, contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals. Mathematical topics typically emerge and evolve through interactions among many researchers, Set theory, however, was founded by a single paper in 1874 by Georg Cantor, On a Property of the Collection of All Real Algebraic Numbers. Since the 5th century BC, beginning with Greek mathematician Zeno of Elea in the West and early Indian mathematicians in the East, especially notable is the work of Bernard Bolzano in the first half of the 19th century. Modern understanding of infinity began in 1867–71, with Cantors work on number theory, an 1872 meeting between Cantor and Richard Dedekind influenced Cantors thinking and culminated in Cantors 1874 paper. Cantors work initially polarized the mathematicians of his day, while Karl Weierstrass and Dedekind supported Cantor, Leopold Kronecker, now seen as a founder of mathematical constructivism, did not. This utility of set theory led to the article Mengenlehre contributed in 1898 by Arthur Schoenflies to Kleins encyclopedia, in 1899 Cantor had himself posed the question What is the cardinal number of the set of all sets. Russell used his paradox as a theme in his 1903 review of continental mathematics in his The Principles of Mathematics, in 1906 English readers gained the book Theory of Sets of Points by William Henry Young and his wife Grace Chisholm Young, published by Cambridge University Press. The momentum of set theory was such that debate on the paradoxes did not lead to its abandonment, the work of Zermelo in 1908 and Abraham Fraenkel in 1922 resulted in the set of axioms ZFC, which became the most commonly used set of axioms for set theory. The work of such as Henri Lebesgue demonstrated the great mathematical utility of set theory. Set theory is used as a foundational system, although in some areas category theory is thought to be a preferred foundation. Set theory begins with a binary relation between an object o and a set A. If o is a member of A, the notation o ∈ A is used, since sets are objects, the membership relation can relate sets as well. A derived binary relation between two sets is the relation, also called set inclusion. If all the members of set A are also members of set B, then A is a subset of B, for example, is a subset of, and so is but is not. As insinuated from this definition, a set is a subset of itself, for cases where this possibility is unsuitable or would make sense to be rejected, the term proper subset is defined

8.
Percy Williams Bridgman
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Percy Williams Bridgman was an American physicist who won the 1946 Nobel Prize in Physics for his work on the physics of high pressures. He also wrote extensively on the method and on other aspects of the philosophy of science. Known to family and friends as Peter, Bridgman was born in Cambridge, Massachusetts, Bridgmans parents were both born in New England. His father, Raymond Landon Bridgman, was religious and idealistic. His mother, Mary Ann Maria Williams, was described as more conventional, sprightly, Bridgman attended both elementary and high school in Auburndale, where he excelled at competitions in the classroom, on the playground, and while playing chess. Described as both shy and proud, his life consisted of family music, card games, and domestic. The family was religious, reading the Bible each morning and attending a Congregational Church. Bridgman entered Harvard University in 1900, and studied physics through to his Ph. D, from 1910 until his retirement, he taught at Harvard, becoming a full professor in 1919. In 1905, he began investigating the properties of matter under high pressure, a machinery malfunction led him to modify his pressure apparatus, the result was a new device enabling him to create pressures eventually exceeding 100,000 kgf/cm2. This was an improvement over previous machinery, which could achieve pressures of only 3,000 kgf/cm2. Bridgman is also known for his studies of electrical conduction in metals and he developed the Bridgman seal and is the eponym for Bridgmans thermodynamic equations. Bridgman made many improvements to his pressure apparatus over the years. His philosophy of science book The Logic of Modern Physics advocated operationalism, in 1938 he participated in the International Committee composed to organise the International Congresses for the Unity of Science. He was also one of the 11 signatories to the Russell–Einstein Manifesto, Bridgman married Olive Ware, of Hartford, Connecticut, in 1912. Wares father, Edmund Asa Ware, was the founder and first president of Atlanta University, the couple had two children and were married for 50 years, living most of that time in Cambridge. The family also had a home in Randolph, New Hampshire. Bridgman was a penetrating analytical thinker with a fertile mechanical imagination and he was a skilled plumber and carpenter, known to shun the assistance of professionals in these matters. He was also fond of music and played the piano, and took pride in his flower, Bridgman committed suicide by gunshot after suffering from metastatic cancer for some time

9.
Paradox
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A paradox is a statement that, despite apparently sound reasoning from true premises, leads to a self-contradictory or a logically unacceptable conclusion. A paradox involves contradictory yet interrelated elements that exist simultaneously and persist over time, some logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking. Some paradoxes have revealed errors in definitions assumed to be rigorous, others, such as Currys paradox, are not yet resolved. Examples outside logic include the Ship of Theseus from philosophy, paradoxes can also take the form of images or other media. Escher featured perspective-based paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, and staircases that appear to climb endlessly. In common usage, the word often refers to statements that may be both true and false i. e. ironic or unexpected, such as the paradox that standing is more tiring than walking. Common themes in paradoxes include self-reference, infinite regress, circular definitions, patrick Hughes outlines three laws of the paradox, Self-reference An example is This statement is false, a form of the liar paradox. The statement is referring to itself, another example of self-reference is the question of whether the barber shaves himself in the barber paradox. One more example would be Is the answer to this question No, contradiction This statement is false, the statement cannot be false and true at the same time. Another example of contradiction is if a man talking to a genie wishes that wishes couldnt come true, vicious circularity, or infinite regress This statement is false, if the statement is true, then the statement is false, thereby making the statement true. Another example of vicious circularity is the group of statements. Other paradoxes involve false statements or half-truths and the biased assumptions. This form is common in howlers, for example, consider a situation in which a father and his son are driving down the road. The car crashes into a tree and the father is killed, the boy is rushed to the nearest hospital where he is prepared for emergency surgery. On entering the suite, the surgeon says, I cant operate on this boy. The apparent paradox is caused by a hasty generalization, for if the surgeon is the boys father, the paradox is resolved if it is revealed that the surgeon is a woman — the boys mother. Paradoxes which are not based on a hidden error generally occur at the fringes of context or language, paradoxes that arise from apparently intelligible uses of language are often of interest to logicians and philosophers. Russells paradox, which shows that the notion of the set of all sets that do not contain themselves leads to a contradiction, was instrumental in the development of modern logic

10.
Academic journal
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An academic or scholarly journal is a periodical publication in which scholarship relating to a particular academic discipline is published. Academic journals serve as permanent and transparent forums for the presentation, scrutiny and they are usually peer-reviewed or refereed. Content typically takes the form of articles presenting original research, review articles, the term academic journal applies to scholarly publications in all fields, this article discusses the aspects common to all academic field journals. Upon receipt of an article, editors at the journal determine whether to reject the submission outright or begin the process of peer review. In the latter case, the submission becomes subject to review by scholars of the editors choosing who typically remain anonymous. Though these reports are confidential, some journals and publishers also practice public peer review. The editors either choose to reject the article, ask for a revision and resubmission, even accepted articles are often subjected to further editing by journal editorial staff before they appear in print. The peer review can take several weeks to several months. Review articles, also called reviews of progress, are checks on the published in journals. Some journals are devoted entirely to review articles, some contain a few in each issue, such reviews often cover the research from the preceding year, some for longer or shorter terms, some are devoted to specific topics, some to general surveys. Some journals are enumerative, listing all significant articles in a subject, others are selective. Yet others are evaluative, judging the state of progress in the subject field, some journals are published in series, each covering a complete subject field year, or covering specific fields through several years. Unlike original research articles, review articles tend to be solicited submissions and they are typically relied upon by students beginning a study in a given field, or for current awareness of those already in the field. Reviews of scholarly books are checks upon the books published by scholars, unlike articles. Journals typically have a book review editor determining which new books to review. If an outside scholar accepts the book review editors request for a book review, publishers send books to book review editors in the hope that their books will be reviewed. The length and depth of research book reviews varies much from journal to journal, as does the extent of textbook, an academic journals prestige is established over time, and can reflect many factors, some but not all of which are expressible quantitatively. In each academic discipline there are dominant journals that receive the largest number of submissions, yet, not only the largest journals are of excellent quality