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Julia Robinson
Julia Hall Bowman Robinson (December 8, 1919July 30, 1985) was an American mathematician noted for her contributions to the fields of computability theory and computational complexity theory—most notably in decision problems. Her work on Hilbert's tenth problem (now known as Matiyasevich's theorem or the MRDP theorem) played a crucial role in its ultimate resolution. Robinson was a 1983 MacArthur Fellow. Early years Robinson was born in St. Louis, Missouri, the daughter of Ralph Bowers Bowman and Helen (Hall) Bowman. Her father owned a machine equipment company while her mother was a school teacher before marriage. Her mother died when Robinson was 2 years old and her father remarried. Her older sister was the mathematical popularizer and biographer Constance Reid and her younger sister is Billie Comstock. When she was 9 years old, she was diagnosed with scarlet fever which was shortly followed by rheumatic fever. This caused her to miss two years of school. When she was w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Missouri
Missouri is a U.S. state, state in the Midwestern United States, Midwestern region of the United States. Ranking List of U.S. states and territories by area, 21st in land area, it is bordered by eight states (tied for the most with Tennessee): Iowa to the north, Illinois, Kentucky and Tennessee to the east, Arkansas to the south and Oklahoma, Kansas and Nebraska to the west. In the south are the Ozarks, a forested highland, providing timber, minerals, and recreation. The Missouri River, after which the state is named, flows through the center into the Mississippi River, which makes up the eastern border. With more than six million residents, it is the List of U.S. states and territories by population, 19th-most populous state of the country. The largest urban areas are St. Louis, Kansas City, Missouri, Kansas City, Springfield, Missouri, Springfield and Columbia, Missouri, Columbia; the Capital city, capital is Jefferson City, Missouri, Jefferson City. Humans have inhabited w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert's Tenth Problem
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm which, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values. For example, the Diophantine equation 3x^2-2xy-y^2z-7=0 has an integer solution: x=1,\ y=2,\ z=-2. By contrast, the Diophantine equation x^2+y^2+1=0 has no such solution. Hilbert's tenth problem has been solved, and it has a negative answer: such a general algorithm does not exist. This is the result of combined work of Martin Davis, Yuri Matiyasevich, Hilary Putnam and Julia Robinson which spans 21 years, with Matiyasevich completing the theorem in 1970. The theorem is now known as Matiyasevich's theorem or the MRDP theorem (an initialism for the surnames of the four principal contribut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pell's Equation
Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form x^2 - ny^2 = 1, where ''n'' is a given positive nonsquare integer, and integer solutions are sought for ''x'' and ''y''. In Cartesian coordinates, the equation is represented by a hyperbola; solutions occur wherever the curve passes through a point whose ''x'' and ''y'' coordinates are both integers, such as the trivial solution with ''x'' = 1 and ''y'' = 0. Joseph Louis Lagrange proved that, as long as ''n'' is not a perfect square, Pell's equation has infinitely many distinct integer solutions. These solutions may be used to accurately approximate the square root of ''n'' by rational numbers of the form ''x''/''y''. This equation was first studied extensively in India starting with Brahmagupta, who found an integer solution to 92x^2 + 1 = y^2 in his ''Brāhmasphuṭasiddhānta'' circa 628. Bhaskara II in the 12th century and Narayana Pandit i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RAND Corporation
The RAND Corporation (from the phrase "research and development") is an American nonprofit global policy think tank created in 1948 by Douglas Aircraft Company to offer research and analysis to the United States Armed Forces. It is financed by the Federal government of the United States, U.S. government and private Financial endowment, endowment, corporations, university, universities and private individuals. The company assists other governments, international organizations, private companies and foundations with a host of defense and non-defense issues, including healthcare. RAND aims for interdisciplinary and quantitative problem solving by translating theory, theoretical concepts from formal economics and the Outline of physical science, physical sciences into novel applications in other areas, using applied science and operations research. Overview RAND has approximately 1,850 employees. Its American locations include: Santa Monica, California (headquarters); Arlington ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incompleteness Theorem
Complete may refer to: Logic * Completeness (logic) * Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable Mathematics * The completeness of the real numbers, which implies that there are no "holes" in the real numbers * Complete metric space, a metric space in which every Cauchy sequence converges * Complete uniform space, a uniform space where every Cauchy net in converges (or equivalently every Cauchy filter converges) * Complete measure, a measure space where every subset of every null set is measurable * Completion (algebra), at an ideal * Completeness (cryptography) * Completeness (statistics), a statistic that does not allow an unbiased estimator of zero * Complete graph, an undirected graph in which every pair of vertices has exactly one edge connecting them * Complete category, a category ''C'' where every diagram from a small category to ''C'' has a limit; it is ''cocomplete'' if every such functor ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kurt Gödel
Kurt Friedrich Gödel ( , ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an immense effect upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell,For instance, in their "Principia Mathematica' (''Stanford Encyclopedia of Philosophy'' edition). Alfred North Whitehead, and David Hilbert were using logic and set theory to investigate the foundations of mathematics, building on earlier work by the likes of Richard Dedekind, Georg Cantor and Frege. Gödel published his first incompleteness theorem in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The first incompleteness theorem states that for any ω-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undecidable Problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether arbitrary programs eventually halt when run. Background A decision problem is any arbitrary yes-or-no question on an infinite set of inputs. Because of this, it is traditional to define the decision problem equivalently as the set of inputs for which the problem returns ''yes''. These inputs can be natural numbers, but also other values of some other kind, such as strings of a formal language. Using some encoding, such as a Gödel numbering, the strings can be encoded as natural numbers. Thus, a decision problem informally phrased in terms of a formal language is also equivalent to a set of natural numbers. To keep the formal definition simple, it is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jerzy Neyman
Jerzy Neyman (April 16, 1894 – August 5, 1981; born Jerzy Spława-Neyman; ) was a Polish mathematician and statistician who spent the first part of his professional career at various institutions in Warsaw, Poland and then at University College London, and the second part at the University of California, Berkeley. Neyman first introduced the modern concept of a confidence interval into statistical hypothesis testing and co-revised Ronald Fisher's null hypothesis testing (in collaboration with Egon Pearson). Life and career He was born into a Polish family in Bendery, in the Bessarabia Governorate of the Russian Empire, the fourth of four children of Czesław Spława-Neyman and Kazimiera Lutosławska. His family was Roman Catholic and Neyman served as an altar boy during his early childhood. Later, Neyman would become an agnostic. Neyman's family descended from a long line of Polish nobles and military heroes. He graduated from the Kamieniec Podolski gubernial gymnasium for boys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bachelor Of Arts
Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four years, depending on the country and institution. * Degree attainment typically takes four years in Afghanistan, Armenia, Azerbaijan, Bangladesh, Brazil, Brunei, China, Egypt, Ghana, Greece, Georgia, Hong Kong, Indonesia, Iran, Iraq, Ireland, Japan, Kazakhstan, Kenya, Kuwait, Latvia, Lebanon, Lithuania, Mexico, Malaysia, Mongolia, Myanmar, Nepal, Netherlands, Nigeria, Pakistan, the Philippines, Qatar, Russia, Saudi Arabia, Scotland, Serbia, South Korea, Spain, Sri Lanka, Taiwan, Thailand, Turkey, Ukraine, the United States and Zambia. * Degree attainment typically takes three years in Albania, Australia, Bosnia and Herzegovina, the Caribbean, Iceland, India, Israel, Italy, New Zealand, Norway, South Africa, Switzerland, the Canadian province of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
San Diego State University
San Diego State University (SDSU) is a public research university in San Diego, California. Founded in 1897 as San Diego Normal School, it is the third-oldest university and southernmost in the 23-member California State University (CSU) system. In Fall 2022, SDSU hit an all time high enrollment record student body of nearly 37,000 and an alumni base of more than 300,000. It is classified among "R2: Doctoral Universities – High research activity". In the 2015–16 fiscal year, the university obtained $130 million in public and private funding—a total of 707 awards—up from $120.6 million the previous fiscal year. As reported by the Faculty Scholarly Productivity Index released by the Academic Analytics organization of Stony Brook, New York, SDSU had the highest research output of any small research university in the United States in 2006 and 2007. SDSU sponsors the second-highest number of Fulbright Scholars in the State of California, just behind UC Berkeley. Since 2005, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
San Diego High School
San Diego High School (SDHS) is an urban public high school located on the southern edge of Balboa Park, in San Diego, California, United States. It is the oldest high school in the San Diego Unified School District, one of the oldest public schools in all of California, and the oldest still on its original site. History Russ High (1882–1907) The school was established in 1882, initially named Russ School after lumberman Joseph Russ, who donated the lumber to build the school. The school was built in the Italian Villa style with a low-hip roof, ironwork parapet, and open-bell tower. It consisted of two stories and eight rooms. It initially served elementary students. In 1888 a high school was added, with three teachers. The high school students took over the upper floor; elementary and primary students occupied the lower floor. The first commencement was held in 1889, with four students graduating. In 1893 high school students took over the entire school, which was renamed Rus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
