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Manuel Blum Manuel Blum Manuel Blum (Caracas, 26 April 1938) is a Venezuelan computer scientist who received the Turing Award Turing Award in 1995 "In recognition of his contributions to the foundations of computational complexity theory and its application to cryptography and program checking".[2][3][4][5][6][7][8]Contents1 Education 2 Career 3 Research 4 See also 5 ReferencesEducation[edit] Blum was educated at MIT, where he received his bachelor's degree and his master's degree in EECS in 1959 and 1961 respectively, and his Ph.D. in mathematics in 1964 supervised by Marvin Minsky.[1][7] Career[edit] He worked as a professor of computer science at the University of California, Berkeley until 1999 [...More...]  "Manuel Blum" on: Wikipedia Yahoo 

Microsoft Academic Microsoft Microsoft Academic is a free public search engine for academic publications and literature, developed by Microsoft Microsoft Research. Relaunched in 2016, the tool features an entirely new data structure and search engine using semantic search technologies. It currently indexes over 375 million entities [1], 170 million of which are academic papers [1] [...More...]  "Microsoft Academic" on: Wikipedia Yahoo 

Thesis A thesis or dissertation[1] is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings.[2] In some contexts, the word "thesis" or a cognate is used for part of a bachelor's or master's course, while "dissertation" is normally applied to a doctorate, while in other contexts, the reverse is true.[3] The term graduate thesis is sometimes used to refer to both master's theses and doctoral dissertations.[4] The required complexity or quality of research of a thesis or dissertation can vary by country, university, or program, and the required minimum study period may thus vary significantly in duration. The word "dissertation" can at times be used to describe a treatise without relation to obtaining an academic degree [...More...]  "Thesis" on: Wikipedia Yahoo 

Computer Scientist A computer scientist is a scientist who has acquired the knowledge of computer science, the study of the theoretical foundations of information and computation and their application.[1] Computer scientists typically work on the theoretical side of computer systems, as opposed to the hardware side that computer engineers mainly focus on (although there is overlap) [...More...]  "Computer Scientist" on: Wikipedia Yahoo 

Doctor Of Philosophy A Doctor of Philosophy Philosophy (PhD, Ph.D., DPhil, or Dr. phil.; Latin Philosophiae doctor) is the highest academic degree awarded by universities in most countries. PhDs are awarded for programs across the whole breadth of academic fields. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy Philosophy degree may, in most jurisdictions, use the title Doctor (often abbreviated "Dr") or, in nonEnglish speaking countries, variants such as "Dr. phil." with their name, and may use postnominal letters such as "Ph.D.", "PhD" (depending on the awarding institute). The requirements to earn a PhD degree vary considerably according to the country, institution, and time period, from entrylevel research degrees to higher doctorates [...More...]  "Doctor Of Philosophy" on: Wikipedia Yahoo 

United States National Academy Of Sciences The National Academy of Sciences National Academy of Sciences (NAS) is a United States United States nonprofit, nongovernmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering Engineering (NAE) and the National Academy of Medicine (NAM). As a national academy, new members of the organization are elected annually by current members, based on their distinguished and continuing achievements in original research. Election to the National Academies is one of the highest honors in the scientific field. Members serve pro bono as "advisers to the nation" on science, engineering, and medicine [...More...]  "United States National Academy Of Sciences" on: Wikipedia Yahoo 

Gödel Numbering In mathematical logic, a Gödel numbering is a function that assigns to each symbol and wellformed formula of some formal language a unique natural number, called its Gödel number. The concept was used by Kurt Gödel Kurt Gödel for the proof of his incompleteness theorems [...More...]  "Gödel Numbering" on: Wikipedia Yahoo 

Compression Theorem In computational complexity theory the compression theorem is an important theorem about the complexity of computable functions. The theorem states that there exists no largest complexity class, with computable boundary, which contains all computable functions. Compression theorem[edit] Given a Gödel numbering φ displaystyle varphi of the computable functions and a Blum complexity measure Φ displaystyle Phi where a complexity class for a boundary function f displaystyle f is defined as C ( f ) := φ i ∈ R ( 1 ) ( ∀ ∞ x ) Φ i ( x [...More...]  "Compression Theorem" on: Wikipedia Yahoo 

Steven Rudich Steven Rudich Steven Rudich (born October 4, 1961) is a professor in the Carnegie Mellon School of Computer Science. In 1994, he and Alexander Razborov proved that a large class of combinatorial arguments, dubbed natural proofs were unlikely to answer many of the important problems in computational complexity theory [...More...]  "Steven Rudich" on: Wikipedia Yahoo 

Gap Theorem In computational complexity theory the Gap Theorem, also known as the BorodinTrakhtenbrot Gap Theorem, is a major theorem about the complexity of computable functions.[1] It essentially states that there are arbitrarily large computable gaps in the hierarchy of complexity classes. For any computable function that represents an increase in computational resources, one can find a resource bound such that the set of functions computable within the expanded resource bound is the same as the set computable within the original bound. The theorem was proved independently by Boris Trakhtenbrot[2] and Allan Borodin.[3][4] Although Trakhtenbrot's derivation preceded Borodin's by several years, it was not known nor recognized in the West until after Borodin's work was published. Gap theorem[edit] The general form of the theorem is as follows.Suppose Φ is an abstract (Blum) complexity measure [...More...]  "Gap Theorem" on: Wikipedia Yahoo 

MIT The Massachusetts Institute of Technology Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts, United States. Founded in 1861 in response to the increasing industrialization of the United States, MIT adopted a European polytechnic university model and stressed laboratory instruction in applied science and engineering. The Institute is traditionally known for its research and education in the physical sciences and engineering, but more recently in biology, economics, linguistics and management as well [...More...]  "MIT" on: Wikipedia Yahoo 

Mathematics Genealogy Project The Mathematics Mathematics Genealogy Project is a webbased database for the academic genealogy of mathematicians.[1][2][3] By 3 January 2018, it contained information on 222,193 mathematical scientists who contributed to researchlevel mathematics [...More...]  "Mathematics Genealogy Project" on: Wikipedia Yahoo 

Doctoral Advisor A doctoral advisor (also dissertation director or dissertation advisor) is a member of a university faculty whose role is to guide graduate students who are candidates for a doctorate, helping them select coursework, as well as shaping, refining and directing the students' choice of subdiscipline in which they will be examined or on which they will write a dissertation.[1] Students generally choose advisors based on their areas of interest within their discipline, their desire to work closely with particular graduate faculty, and the willingness and availability of those faculty to work with them. In some countries, the student's advisor serves as the chair of the doctoral examination or dissertation committees. In some cases, though, the person who serves those roles may be different from the faculty member who has most closely advised the student [...More...]  "Doctoral Advisor" on: Wikipedia Yahoo 

Cryptography Cryptography Cryptography or cryptology (from Greek κρυπτός kryptós, "hidden, secret"; and γράφειν graphein, "to write", or λογία logia, "study", respectively[1]) is the practice and study of techniques for secure communication in the presence of third parties called adversaries.[2] More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages;[3] various aspects in information security such as data confidentiality, data integrity, authentication, and nonrepudiation[4] are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, electrical engineering, communication science, and physics [...More...]  "Cryptography" on: Wikipedia Yahoo 

Carnegie Mellon University Coordinates: 40°26′36″N 79°56′37″W / 40.443322°N 79.943583°W / 40.443322; 79.943583 Carnegie Mellon University Carnegie Mellon University (Carnegie Mellon or CMU /ˈkɑːrnɪɡi ˈmɛlən/ or /kɑːrˈneɪɡi ˈmɛlən/) is a private research university in Pittsburgh, Pennsylvania. Founded in 1900 by Andrew Carnegie Andrew Carnegie as the Carnegie Technical Schools, the university became the Carnegie Institute of Technology in 1912 and began granting fouryear degrees. In 1967, the Carnegie Institute of Technology merged with the Mellon Institute of Industrial Research Mellon Institute of Industrial Research to form Carnegie Mellon University. The university's 140acre (57 ha) main campus is 3 miles (5 km) from Downtown Pittsburgh [...More...]  "Carnegie Mellon University" on: Wikipedia Yahoo 

Computer Science Computer science Computer science is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. It is the scientific and practical approach to computation and its applications and the systematic study of the feasibility, structure, expression, and mechanization of the methodical procedures (or algorithms) that underlie the acquisition, representation, processing, storage, communication of, and access to, information. An alternate, more succinct definition of computer science is the study of automating algorithmic processes that scale. A computer scientist specializes in the theory of computation and the design of computational systems.[1] Its fields can be divided into a variety of theoretical and practical disciplines [...More...]  "Computer Science" on: Wikipedia Yahoo 