|
Hendrik Lenstra
Hendrik Willem Lenstra Jr. (born 16 April 1949, Zaandam) is a Dutch mathematician. Biography Lenstra received his doctorate from the University of Amsterdam in 1977 and became a professor there in 1978. In 1987 he was appointed to the faculty of the University of California, Berkeley; starting in 1998, he divided his time between Berkeley and the University of Leiden, until 2003, when he retired from Berkeley to take a full-time position at Leiden. Three of his brothers, Arjen Lenstra, Andries Lenstra, and Jan Karel Lenstra, are also mathematicians. Jan Karel Lenstra is the former director of the Netherlands Centrum Wiskunde & Informatica (CWI). Hendrik Lenstra was the Chairman of the Program Committee of the International Congress of Mathematicians in 2010. Scientific contributions Lenstra has worked principally in computational number theory. He is well known for: * Co-discovering of the Lenstra–Lenstra–Lovász lattice basis reduction algorithm (in 1982); * Developing a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zaandam
Zaandam () is a city in the Provinces of the Netherlands, province of North Holland, Netherlands. It is the main city of the municipality of Zaanstad, and received City rights in the Netherlands, city rights in 1811. It is located on the river Zaan, just north of Amsterdam. The statistical district Zaandam, which covers the city and the surrounding countryside, has a population of around 76,804.Municipality of Zaanstad, ''Zaanstad in cijfers' As of 1 January 2017. Zaandam was a separate municipality until 1974, when it became a part of the new municipality of Zaanstad. History The history of Zaandam (formerly called ''Saenredam'') and the surrounding Zaan River region (the Zaanstreek) is intimately tied to industry. In the Dutch Golden Age, Zaandam served as a large milling centre. Thousands of windmills powered saws that processed Scandinavian wood for the shipbuilding and paper industries. A statue that commemorates this industry was commissioned from sculptor Slavomir Miletić ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spinoza Prize
The Spinoza Prize ( nl, Spinozapremie) is an annual award of 2.5 million euro, to be spent on new research given by the Dutch Research Council (NWO). The award is the highest scientific award in the Netherlands. It is named after the philosopher Baruch de Spinoza Baruch (de) Spinoza (born Bento de Espinosa; later as an author and a correspondent ''Benedictus de Spinoza'', anglicized to ''Benedict de Spinoza''; 24 November 1632 – 21 February 1677) was a Dutch philosopher of Portuguese-Jewish origin, b .... The prize is awarded to researchers in the Netherlands who belong to the best in their field. Academics can nominate each other and an international commission evaluates the submissions. It is sometimes referred to as the Dutch Nobel Prize. List of winners The following persons have received the Spinoza Prize: References External links * {{Official website, http://www.nwo.nl/en/research-and-results/programmes/spinoza+prize, name = Spinoza Prize Awards establis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class Number Problem
In mathematics, the Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each ''n'' ≥ 1 a complete list of imaginary quadratic fields \mathbb(\sqrt) (for negative integers ''d'') having class number (number theory), class number ''n''. It is named after Carl Friedrich Gauss. It can also be stated in terms of Discriminant of an algebraic number field, discriminants. There are related questions for real quadratic fields and for the behavior as d \to -\infty. The difficulty is in effective computation of bounds: for a given discriminant, it is easy to compute the class number, and there are several ineffective lower bounds on class number (meaning that they involve a constant that is not computed), but effective bounds (and explicit proofs of completeness of lists) are harder. Gauss's original conjectures The problems are posed in Gauss's Disquisitiones Arithmeticae of 1801 (Section V, Articles 303 and 304). are a set of mor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been known since antiquity to have infinitely many solutions.Singh, pp. 18–20. The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of '' Arithmetica''. Fermat added that he had a proof that was too large to fit in the margin. Although other statements claimed by Fermat without proof were subsequently proven by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to doubt that Fermat ever had a correct proof. Consequently the proposition became known as a conjecture rather than a theorem. After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles and form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Curve Factorization
The Lenstra elliptic-curve factorization or the elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer factorization, which employs elliptic curves. For general-purpose factoring, ECM is the third-fastest known factoring method. The second-fastest is the multiple polynomial quadratic sieve, and the fastest is the general number field sieve. The Lenstra elliptic-curve factorization is named after Hendrik Lenstra. Practically speaking, ECM is considered a special-purpose factoring algorithm, as it is most suitable for finding small factors. , it is still the best algorithm for divisors not exceeding 50 to 60 digits, as its running time is dominated by the size of the smallest factor ''p'' rather than by the size of the number ''n'' to be factored. Frequently, ECM is used to remove small factors from a very large integer with many factors; if the remaining integer is still composite, then it has only large factors and is factored ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Programming
An integer programming problem is a mathematical optimization or Constraint satisfaction problem, feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are Linear function (calculus), linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems. If some decision variables are not discrete, the problem is known as a mixed-integer programming problem. Canonical and standard form for ILPs In integer linear programming, the ''canonical form'' is distinct from the ''standard form''. An integer linear program in canonical form is expressed thus (note that it is the \mathbf vector which is to be decided): : \begin & \text && \math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Number Theory
In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry. Computational number theory has applications to cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the modularity conjecture, the Sato-Tate conjecture, and explicit aspects of the Langlands program. Software packages * Magma computer algebra system * SageMath * Number Theory Library * PARI/GP * Fast Library for Number Theory Further reading * * * * * * * * * * * References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centrum Wiskunde & Informatica
The (abbr. CWI; English: "National Research Institute for Mathematics and Computer Science") is a research centre in the field of mathematics and theoretical computer science. It is part of the institutes organization of the Dutch Research Council (NWO) and is located at the Amsterdam Science Park. This institute is famous as the creation site of the programming language Python. It was a founding member of the European Research Consortium for Informatics and Mathematics (ERCIM). Early history The institute was founded in 1946 by Johannes van der Corput, David van Dantzig, Jurjen Koksma, Hendrik Anthony Kramers, Marcel Minnaert and Jan Arnoldus Schouten. It was originally called ''Mathematical Centre'' (in Dutch: ''Mathematisch Centrum''). One early mission was to develop mathematical prediction models to assist large Dutch engineering projects, such as the Delta Works. During this early period, the Mathematics Institute also helped with designing the wings of the Fokker F27 F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Karel Lenstra
Jan Karel Lenstra (born 19 December 1947, in Zaandam) is a Dutch mathematician and operations researcher, known for his work on scheduling algorithms, local search, and the travelling salesman problem. Lenstra received his Ph.D. from the University of Amsterdam in 1976, advised by Gijsbert de Leve. He then became a researcher at the Centrum Wiskunde & Informatica, where he remained until 1989. After taking positions at the Eindhoven University of Technology (where he became Dean of the Faculty of Mathematics and Computer Science) and the Georgia Institute of Technology, he returned to CWI as its director in 2003. He stepped down in 2011, and at that time became a CWI Fellow.. He was editor-in-chief of '' Mathematics of Operations Research'' from 1993 to 1998, and is editor-in-chief of ''Operations Research Letters'' since 2002.Faculty profile CWI, r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arjen Lenstra
Arjen Klaas Lenstra (born 2 March 1956, in Groningen) is a Dutch mathematician, cryptographer and computational number theorist. He is currently a professor at the École Polytechnique Fédérale de Lausanne (EPFL) where he heads of the Laboratory for Cryptologic Algorithms. Career He studied mathematics at the University of Amsterdam. He is currently a professor at the EPFL (Lausanne), in the Laboratory for Cryptologic Algorithms, and previously worked for Citibank and Bell Labs. Research Lenstra is active in cryptography and computational number theory, especially in areas such as integer factorization. With Mark Manasse, he was the first to seek volunteers over the internet for a large scale volunteer computing project. Such projects became more common after the Factorization of RSA-129 which was a high publicity distributed factoring success led by Lenstra along with Derek Atkins, Michael Graff and Paul Leyland. He was also a leader in the successful factorizations o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctorate
A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism ''licentia docendi'' ("licence to teach"). In most countries, a research degree qualifies the holder to teach at university level in the degree's field or work in a specific profession. There are a number of doctoral degrees; the most common is the Doctor of Philosophy (PhD), awarded in many different fields, ranging from the humanities to scientific disciplines. In the United States and some other countries, there are also some types of technical or professional degrees that include "doctor" in their name and are classified as a doctorate in some of those countries. Professional doctorates historically came about to meet the needs of practitioners in a variety of disciplines. Many universities also award honorary doctorates to individuals d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
