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George B. Purdy
George Barry Purdy (20 February 1944 – 30 December 2017) was a mathematician and computer scientist who specialized in cryptography, combinatorial geometry, and number theory. Purdy received his Ph.D. from the University of Illinois at Urbana–Champaign in 1972, officially under the supervision of Paul T. Bateman, but his de facto adviser was Paul Erdős. He was on the faculty in the mathematics department at Texas A&M University for 11 years, and was appointed the Geier Professor of computer science at the University of Cincinnati in 1986. Purdy had Erdős number one and coauthored many papers with Paul Erdős, who regarded him as his own student. He is the "P" in G.W. Peck, a pseudonym for the group of mathematicians that also included Ronald Graham, Douglas West, Paul Erdős, Fan Chung, and Daniel Kleitman. Purdy polynomial In 1971, Purdy was asked by Larry Roberts, the director of the DARPA Information Processing Techniques Office, to develop a secure hash function to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
San Francisco
San Francisco (; Spanish language, Spanish for "Francis of Assisi, Saint Francis"), officially the City and County of San Francisco, is the commercial, financial, and cultural center of Northern California. The city proper is the List of California cities by population, fourth most populous in California and List of United States cities by population, 17th most populous in the United States, with 815,201 residents as of 2021. It covers a land area of , at the end of the San Francisco Peninsula, making it the second most densely populated large U.S. city after New York City, and the County statistics of the United States, fifth most densely populated U.S. county, behind only four of the five New York City boroughs. Among the 91 U.S. cities proper with over 250,000 residents, San Francisco was ranked first by per capita income (at $160,749) and sixth by aggregate income as of 2021. Colloquial nicknames for San Francisco include ''SF'', ''San Fran'', ''The '', ''Frisco'', and '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object. Discrete geometry has a large overlap with convex geometry and computational geometry, and is closely related to subjects such as finite geometry, combinatorial optimization, digital geometry, discrete differential geometry, geometric graph theory, toric geometry, and combinatorial topology. History Although polyhedra and tessellations had been studied for many years by people such as Kepler and Cauchy, modern discrete geometry has its origins in the late 19th century. Early topics studied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Exponentiation
Modular exponentiation is exponentiation performed over a modulus. It is useful in computer science, especially in the field of public-key cryptography, where it is used in both Diffie-Hellman Key Exchange and RSA public/private keys. Modular exponentiation is the remainder when an integer (the base) is raised to the power (the exponent), and divided by a positive integer (the modulus); that is, . From the definition of division, it follows that . For example, given , and , dividing by leaves a remainder of . Modular exponentiation can be performed with a ''negative'' exponent by finding the modular multiplicative inverse of modulo using the extended Euclidean algorithm. That is: :, where and . Modular exponentiation is efficient to compute, even for very large integers. On the other hand, computing the modular discrete logarithm – that is, finding the exponent when given , , and – is believed to be difficult. This one-way function behavior makes modular ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ARPANET
The Advanced Research Projects Agency Network (ARPANET) was the first wide-area packet-switched network with distributed control and one of the first networks to implement the TCP/IP protocol suite. Both technologies became the technical foundation of the Internet. The ARPANET was established by the Advanced Research Projects Agency (ARPA) of the United States Department of Defense. Building on the ideas of J. C. R. Licklider, Bob Taylor initiated the ARPANET project in 1966 to enable access to remote computers. Taylor appointed Larry Roberts as program manager. Roberts made the key decisions about the network design. He incorporated Donald Davies' concepts and designs for packet switching, and sought input from Paul Baran. ARPA awarded the contract to build the network to Bolt Beranek & Newman who developed the first protocol for the network. Roberts engaged Leonard Kleinrock at UCLA to develop mathematical methods for analyzing the packet network technology. The first ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Function
A hash function is any function that can be used to map data of arbitrary size to fixed-size values. The values returned by a hash function are called ''hash values'', ''hash codes'', ''digests'', or simply ''hashes''. The values are usually used to index a fixed-size table called a ''hash table''. Use of a hash function to index a hash table is called ''hashing'' or ''scatter storage addressing''. Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval. They require an amount of storage space only fractionally greater than the total space required for the data or records themselves. Hashing is a computationally and storage space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and structured trees, and the often exponential storage requirements of direct access of state spaces of large or variable-length keys. Use of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Processing Techniques Office
The Information Processing Techniques Office (IPTO), originally "Command and Control Research",Lyon, Matthew; Hafner, Katie (1999-08-19). ''Where Wizards Stay Up Late: The Origins Of The Internet'' (p. 39). Simon & Schuster. Kindle Edition. was part of the Defense Advanced Research Projects Agency of the United States Department of Defense. Origin According to an ARPA-sponsored history of the organization, IPTO grew from a distinctly unpromising beginning: the Air Force had a large, expensive computer ( AN/FSQ 321A) which was intended as a backup for the SAGE air defense program, but no longer needed; and it also had too few required tasks to maintain the desired staffing level at its main software contractor, the System Development Corporation (SDC). Accordingly, the Under Secretary of Defense for Research and Engineering decided to capitalize on these "sunk costs" and SDC expertise by standing up an ARPA program in Command & Control Research. It was accordingly begun in June 1961 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DARPA
The Defense Advanced Research Projects Agency (DARPA) is a research and development agency of the United States Department of Defense responsible for the development of emerging technologies for use by the military. Originally known as the Advanced Research Projects Agency (ARPA), the agency was created on February 7, 1958, by President Dwight D. Eisenhower in response to the Soviet Union, Soviet launching of Sputnik 1 in 1957. By collaborating with academia, industry, and government partners, DARPA formulates and executes research and development projects to expand the frontiers of technology and science, often beyond immediate U.S. military requirements.Dwight D. Eisenhower and Science & Technology, (2008). Dwight D. Eisenhower Memorial CommissionSource ''The Economist'' has called DARPA the agency "that shaped the modern world," and pointed out that "Moderna COVID-19 vaccine, Moderna's COVID-19 vaccine sits alongside weather satellites, Global Positioning System, GPS, Unmann ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lawrence Roberts (scientist)
Lawrence Gilman Roberts (December 21, 1937 – December 26, 2018) was an American engineer who received the Draper Prize in 2001 "for the development of the Internet", and the Principe de Asturias Award in 2002. As a program manager and later office director at the Advanced Research Projects Agency, Roberts and his team created the ARPANET using packet switching techniques invented by British computer scientist Donald Davies and American Paul Baran. The ARPANET, which was built by the Massachusetts-based company Bolt Beranek and Newman (BBN), was a predecessor to the modern Internet. He asked Leonard Kleinrock to apply mathematical models to simulate the performance of the network. Roberts later served as CEO of the commercial packet-switching network Telenet. Early life and education Roberts, who was known as Larry, was born and raised in Westport, Connecticut. He was the son of Elizabeth (Gilman) and Elliott John Roberts, both of whom had doctorates in chemistry. It is said t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Kleitman
Daniel J. Kleitman (born October 4, 1934)article availableon Douglas West's web page, University of Illinois at Urbana–Champaign)."Kleitman, Daniel J.," in: ''Who's Who in Frontier Science and Technology'', 1, 1984, p. 396. is an American mathematician and professor of applied mathematics at MIT. His research interests include combinatorics, graph theory, genomics, and operations research. Biography Kleitman was born in 1934 in Brooklyn, New York, the younger of Bertha and Milton Kleitman's two sons. His father was a lawyer who after WWII became a commodities trader and investor. In 1942 the family moved to Morristown, New Jersey,. and he graduated from Morristown High School in 1950. Kleitman then attended Cornell University, from which he graduated in 1954, and received his PhD in Physics from Harvard University in 1958 under Nobel Laureates Julian Schwinger and Roy Glauber. He is the "k" in G. W. Peck, a pseudonym for a group of six mathematicians that includes Kleitman. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fan Chung
Fan-Rong King Chung Graham (; born October 9, 1949), known professionally as Fan Chung, is a Taiwanese-born American mathematician who works mainly in the areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdős–Rényi model for graphs with general degree distribution (including power-law graphs in the study of large information networks). Since 1998, Chung has been the Paul Erdős Professor in Combinatorics at the University of California, San Diego (UCSD). She received her doctorate from the University of Pennsylvania in 1974, under the direction of Herbert Wilf. After working at Bell Laboratories and Bellcore for nineteen years, she joined the faculty of the University of Pennsylvania as the first female tenured professor in mathematics. She serves on the editorial boards of more than a dozen international journals. Since 2003 she has been the editor-in-chief of ''Internet Mathematics''. She has been invited to give lec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Douglas West (mathematician)
Douglas Brent West is a professor of graph theory at University of Illinois at Urbana-Champaign. He received his Ph.D. from Massachusetts Institute of Technology in 1978; his advisor was Daniel Kleitman. He is the "W" in G. W. Peck, a pseudonym for a group of six mathematicians that includes West.. He is the editor of the journal ''Discrete Mathematics''. Selected work Books * ''Introduction to Graph Theory'' - Second edition, Douglas B. West. Published by Prentice Hall 1996, 2001. * ''Mathematical Thinking: Problem-Solving and Proofs'' Second edition, John P D'Angelo and Douglas West. Published by Prentice Hall 1999. Research work * Spanning trees with many leaves, DJ Kleitman, DB West - SIAM Journal on Discrete Mathematics, 1991. * Class of Solutions to the Gossip Problem, Part II, DB West - Discrete Mathematics, 1982. * The interval number of a planar graph: three intervals suffice, ER Scheinerman, DB West - Journal of combinatorial theory. Series B, 1983. See also *Er ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
