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How To Solve It
''How to Solve It'' (1945) is a small volume by mathematician George Pólya, describing methods of problem solving. This book has remained in print continually since 1945. Four principles ''How to Solve It'' suggests the following steps when solving a mathematical problem: # First, you have to ''understand the problem''. # After understanding, ''make a plan''. pp. 8–12 # ''Carry out the plan''. # ''Look back'' on your work. How could it be better? If this technique fails, Pólya advises: "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?" First principle: Understand the problem "Understand the problem" is often neglected as being obvious and is not even mentioned in many mathematics classes. Yet students are often stymied in their efforts to solve it, simply because they don't understand it fully, or even in part. In order to remedy this oversight, Pólya taught teachers how to p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's ''Lectures on Moral Philosophy.'' History Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two already existing local publishers, that of the ''Princeton Alumni Weekly'' and the Princeton Press. The new press printed both local newspapers, university documents, '' The Daily Princetonian'', and later added book publishing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Special Case
In logic, especially as applied in mathematics, concept is a special case or specialization of concept precisely if every instance of is also an instance of but not vice versa, or equivalently, if is a generalization of .Brown, James Robert. Philosophy of Mathematics: An Introduction to a World of Proofs and Pictures'. United Kingdom, Taylor & Francis, 2005. 27. A limiting case is a type of special case which is arrived at by taking some aspect of the concept to the extreme of what is permitted in the general case. If is true, one can immediately deduce that is true as well, and if is false, can also be immediately deduced to be false. A degenerate case is a special case which is in some way qualitatively different from almost all of the cases allowed. Examples Special case examples include the following: * All squares are rectangles (but not all rectangles are squares); therefore the square is a special case of the rectangle. It is also a special case of the rhombus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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1945 Non-fiction Books
1945 marked the end of World War II, the fall of Nazi Germany, and the Empire of Japan. It is also the year concentration camps were liberated and the only year in which atomic weapons have been used in combat. Events World War II will be abbreviated as “WWII” January * January 1 – WWII: ** Germany begins Operation Bodenplatte, an attempt by the ''Luftwaffe'' to cripple Allied air forces in the Low Countries. ** Chenogne massacre: German prisoners are allegedly killed by American forces near the village of Chenogne, Belgium. * January 6 – WWII: A German offensive recaptures Esztergom, Hungary from the Soviets. * January 9 – WWII: American and Australian troops land at Lingayen Gulf on western coast of the largest Philippine island of Luzon, occupied by Japan since 1942. * January 12 – WWII: The Soviet Union begins the Vistula–Oder Offensive in Eastern Europe, against the German Army. * January 13 – WWII: The Soviet Union begins the East Prussian Offens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Inventor's Paradox
The inventor's paradox is a phenomenon that occurs in seeking a solution to a given problem. Instead of solving a specific type of problem, which would seem intuitively easier, it can be easier to solve a more general problem, which covers the specifics of the sought-after solution. The ''inventor's paradox'' has been used to describe phenomena in mathematics, programming, and logic, as well as other areas that involve critical thinking. History In the book ''How to Solve It'', Hungarian mathematician George Pólya introduces what he defines as the inventor's paradox: Or, in other words, to solve what one desires to solve, one may have to solve more than that in order to get a properly working flow of information. When solving a problem, the natural inclination typically is to remove as much excessive variability and produce limitations on the subject at hand as possible. Doing this can create unforeseen and intrinsically awkward parameters.Tate, et al., p. 110 The goal is to f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Prentice-Hall
Prentice Hall was a major American educational publisher. It published print and digital content for the 6–12 and higher-education market. It was an independent company throughout the bulk of the twentieth century. In its last few years it was owned by, then absorbed into, Savvas Learning Company. In the Web era, it distributed its technical titles through the Safari Books Online e-reference service for some years. History On October 13, 1913, law professor Charles Gerstenberg and his student Richard Ettinger founded Prentice Hall. Gerstenberg and Ettinger took their mothers' maiden names, Prentice and Hall, to name their new company. At the time the name was usually styled as Prentice-Hall (as seen for example on many title pages), per an orthographic norm for coordinate elements within such compounds (compare also ''McGraw-Hill'' with later styling as ''McGraw Hill''). Prentice-Hall became known as a publisher of trade books by authors such as Norman Vincent Peale; ele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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How To Solve It By Computer
''How to Solve it by Computer'' is a computer science book by R. G. Dromey, first published by Prentice-Hall in 1982. It is occasionally used as a textbook, especially in India. It is an introduction to the ''why''s of algorithms and data structures. Features of the book: #The design factors associated with problems #The creative process behind coming up with innovative solutions for algorithms and data structures #The line of reasoning behind the constraints, factors and the design choices made. The very fundamental algorithms portrayed by this book are mostly presented in pseudocode and/or Pascal notation. See also *''How to Solve It'', by George Pólya George Pólya (; ; December 13, 1887 – September 7, 1985) was a Hungarian-American mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributi ..., the author's mentor and inspiration for writing the book. References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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TRIZ
TRIZ (; ) is a methodology that combines an organized, systematic method of problem-solving with analysis and forecasting techniques derived from the study of patterns of invention in global patent literature. The development and improvement of products and technologies in accordance with TRIZ are guided by the laws of technical systems evolution. Its development, by Soviet inventor and science-fiction author Genrich Altshuller and his colleagues, began in 1946. In English, TRIZ is typically rendered as the theory of inventive problem solving. TRIZ developed from a foundation of research into hundreds of thousands of inventions in many fields to produce an approach which defines patterns in inventive solutions and the characteristics of the problems these inventions have overcome. The research has produced three findings: # Problems and solutions are repeated across industries and sciences. # Patterns of technical evolution are replicated in industries and sciences. # The inn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Genrich Altshuller
Genrikh Saulovich Altshuller (, ; 15 October 1926 – 24 September 1998) was a Soviet engineer, inventor, and writer. He is most notable for creating the TRIZ, Theory of Inventive Problem Solving, better known by its Russian acronym TRIZ. He founded the Azerbaijan Public Institute for Inventive Creation and was the first President of the TRIZ Association. He also wrote science fiction under the penname Genrikh Altov. Early life Altshuller was born in Tashkent, Uzbekistan (formerly the USSR) to a family of journalists of Jewish background. He moved with his family to Baku, Azerbaijan, where he spent most of his life. After graduating from high school he was admitted to the Azerbaijan Industrial Institute. Altshuller enlisted in the Army in 1944 and was trained as a fighter pilot but did not see action. He joined the Soviet Navy at the age of twenty and attracted attention for his ability to fix engines, getting assigned to the Commission of Innovation of the Capian Navy Flotilla. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Mathematics Education
In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out Scholarly method, scholarly research into the transfer of mathematical knowledge. Although research into mathematics education is primarily concerned with the tools, methods, and approaches that facilitate practice or the study of practice, it also covers an extensive field of study encompassing a variety of different concepts, theories and methods. List of mathematical societies, National and international organisations regularly hold conferences and List of mathematics education journals, publish literature in order to improve mathematics education. History Ancient Elementary mathematics were a core part of education in many ancient civilisations, including ancient Egypt, Babylonia, ancient Babylonia, ancient Greece, ancient Rome, and Vedic civilization, Vedic Ancient India, India. In most cases, formal edu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Marvin Minsky
Marvin Lee Minsky (August 9, 1927 – January 24, 2016) was an American cognitive scientist, cognitive and computer scientist concerned largely with research in artificial intelligence (AI). He co-founded the Massachusetts Institute of Technology's AI laboratory and wrote extensively about AI and philosophy. Minsky received many accolades and honors, including the 1969 Turing Award. Early life and education Marvin Lee Minsky was born in New York City, to Henry, an eye surgeon, and Fannie (Reiser), a Zionism, Zionist activist. His family was Jewish. He attended the Ethical Culture Fieldston School and the Bronx High School of Science. He later attended Phillips Academy in Andover, Massachusetts, Andover, Massachusetts. He then served in the United States Navy, US Navy from 1944 to 1945. He received a B.A. in mathematics from Harvard University in 1950 and a Doctor of Philosophy, Ph.D. in mathematics from Princeton University in 1954. His doctoral dissertation was titled "Theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Diagrammatic Reasoning
Diagrammatic reasoning is reasoning by means of visual depiction, representations. The study of ''diagrammatic reasoning'' is about the understanding of concepts and ideas, visualized with the use of diagrams and imagery instead of by natural language, linguistic or algebraic means. Diagram A diagram is a 2D geometric symbolic depiction, representation of information according to some illustration, visualization technique. Sometimes, the technique uses a 3D space, 3D visualization which is then 3D projection, projected onto the 2D surface. The term diagram in common sense can have two meanings: * ''visual information device'': Like the term "illustration" the diagram is used as a collective term standing for the whole class of technical genres, including graphics, graphs, technical drawings and table (information), tables. * ''specific kind of visual display'': This is only the genre, that shows qualitative data with shapes that are connected by lines, arrows, or other visual link ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Backward Chaining
Backward chaining (or backward reasoning) is an inference method described colloquially as working backward from the goal. It is used in automated theorem provers, inference engines, proof assistants, and other artificial intelligence applications. In game theory, researchers apply it to (simpler) subgames to find a solution to the game, in a process called ''backward induction''. In chess, it is called retrograde analysis, and it is used to generate table bases for chess endgames for computer chess. Backward chaining is implemented in logic programming by SLD resolution. Both rules are based on the modus ponens inference rule. It is one of the two most commonly used methods of reasoning with inference rules and logical implications – the other is forward chaining. Backward chaining systems usually employ a depth-first search strategy, e.g. Prolog. Usage Backward chaining starts with a list of goals (or a hypothesis) and works backwards from the consequent to the antec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |