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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. 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 prompt each student with appropriate questions, depending on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 to it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divide And Conquer Algorithm
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem. The divide-and-conquer technique is the basis of efficient algorithms for many problems, such as sorting (e.g., quicksort, merge sort), multiplying large numbers (e.g., the Karatsuba algorithm), finding the closest pair of points, syntactic analysis (e.g., top-down parsers), and computing the discrete Fourier transform (FFT). Designing efficient divide-and-conquer algorithms can be difficult. As in mathematical induction, it is often necessary to generalize the problem to make it amenable to a recursive solution. The correctness of a divide-and-conquer algorithm is usually proved by mathematical induction, and its computational cost is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heuristics
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, short-term goal or approximation. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision. Examples that employ heuristics include using trial and error, a rule of thumb or an ansatz, educated guess. Heuristics are the strategies derived from previous experiences with similar problems. These strategies depend on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines and abstract issues. When an individual applies a heuristic in practice, it generally performs as expected. However it can alternati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1945 Non-fiction Books
1945 marked the end of World War II and the fall of Nazi Germany and the Empire of Japan. It is also the only year in which nuclear weapons have been used in combat. Events Below, the events of World War II have the "WWII" prefix. 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 Russians. * 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 Offensive, to eliminate German forces in East Prussia. * January 16 – WWII: Adolf Hitler takes residence in the ''Führerbunker'' in Berlin. * January 17 ** WWII: The Soviet Union occupies Warsaw, Po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, short-term goal or approximation. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision. Examples that employ heuristics include using trial and error, a rule of thumb or an educated guess. Heuristics are the strategies derived from previous experiences with similar problems. These strategies depend on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines and abstract issues. When an individual applies a heuristic in practice, it generally performs as expected. However it can alternatively cre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prentice-Hall
Prentice Hall was an American major educational publisher owned by Savvas Learning Company. Prentice Hall publishes print and digital content for the 6–12 and higher-education market, and distributes its technical titles through the Safari Books Online e-reference service. 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. Prentice Hall became known as a publisher of trade books by authors such as Norman Vincent Peale; elementary, secondary, and college textbooks; loose-leaf information services; and professional books. Prentice Hall acquired the training provider Deltak in 1979. Prentice Hall was acquired by Gulf+Western in 1984, and became part of that company's publishing division Simon & Schuster. S&S sold several Prentice Hall subsidiaries: Deltak and Resource Systems were sold to National Education ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 (; hu, Pólya György, ; December 13, 1887 – September 7, 1985) was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamenta ..., the author's mentor and inspiration for writing the book. References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TRIZ
TRIZ (; russian: теория решения изобретательских задач, ', lit. "theory of inventive problem solving") is “the next evolutionary step in creating an organized and systematic approach to problem solving. The development and improvement of products and technologies according to TRIZ are guided by the objective Laws of Engineering System Evolution. TRIZ Problem Solving Tools and Methods are based on them.” In another description, TRIZ is "a problem-solving, analysis and forecasting tool derived from the study of patterns of invention in the global patent literature". It was developed by the Soviet inventor and science-fiction author Genrich Altshuller (1926-1998) and his colleagues, beginning in 1946. In English the name is typically rendered as the theory of inventive problem solving, and occasionally goes by the English acronym TIPS. Following Altshuller's insight, the theory developed on a foundation of extensive research covering hundreds of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genrich Altshuller
Genrikh Saulovich Altshuller (Ге́нрих Сау́лович Альтшу́ллер, ) (born Tashkent, Uzbek SSR, USSR, 15 October 1926; died Petrozavodsk, Russia, 24 September 1998), was a Soviet engineer, inventor, and writer. He is most notable for the creation of the Theory of Inventive Problem Solving, better known by its Russia 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 pen-name Genrikh Altov. Early life Working as a clerk in a patent office, Altshuller embarked on finding some generic rules that would explain creation of new, inventive, patentable ideas. He eventually created the ''Teoriya Resheniya Izobreatatelskikh Zadach'' (Theory of Inventive Problem Solving or TRIZ)). Arrest and imprisonment During Joseph Stalin's political purges of members of the Communist Party in 1950, he was imprisoned for political reasons and continued his s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 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. National and international organisations regularly hold conferences and 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, ancient Babylonia, ancient Greece, ancient Rome and Vedic India. In most cases, formal education was only available to male children with sufficiently high status, wealth or caste. The oldest known mathematics textbook is the Rh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marvin Minsky
Marvin Lee Minsky (August 9, 1927 – January 24, 2016) was an American cognitive and computer scientist concerned largely with research of artificial intelligence (AI), co-founder of the Massachusetts Institute of Technology's AI laboratory, and author of several texts concerning AI and philosophy. Minsky received many accolades and honors, including the 1969 Turing Award. Biography Marvin Lee Minsky was born in New York City, to an eye surgeon father, Henry, and to a mother, Fannie (Reiser), who was a 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. He then served in the US Navy from 1944 to 1945. He received a B.A. in mathematics from Harvard University in 1950 and a Ph.D. in mathematics from Princeton University in 1954. His doctoral dissertation was titled "Theory of neural-analog reinforcement systems and its application to the brain- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
