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Jennifer Balakrishnan
Jennifer Shyamala Sayaka Balakrishnan is an American mathematician known for leading a team that solved the problem of the "cursed curve", a Diophantine equation that was known for being "famously difficult". More generally, Balakrishnan specializes in algorithmic number theory and arithmetic geometry. She is the Clare Boothe Luce Associate Professor at Boston University. Education and career Balakrishnan was born in Mangilao, Guam to Narayana and Shizuko Balakrishnan; her father is a professor of chemistry at the University of Guam. As a junior at Harvest Christian Academy, Balakrishnan won an honorable mention in the 2001 Karl Menger Memorial Award competition, for the best mathematical project in the Intel International Science and Engineering Fair. Her project concerned elliptic coordinate systems. In the following year, she won the National High School Student Calculus Competition, given as part of the United States of America Mathematical Olympiad. Balakrishnan graduated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Coordinate System
In geometry, the elliptic coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae. The two foci F_ and F_ are generally taken to be fixed at -a and +a, respectively, on the x-axis of the Cartesian coordinate system. Basic definition The most common definition of elliptic coordinates (\mu, \nu) is : x = a \ \cosh \mu \ \cos \nu : y = a \ \sinh \mu \ \sin \nu where \mu is a nonnegative real number and \nu \in , 2\pi On the complex plane, an equivalent relationship is : x + iy = a \ \cosh(\mu + i\nu) These definitions correspond to ellipses and hyperbolae. The trigonometric identity : \frac + \frac = \cos^ \nu + \sin^ \nu = 1 shows that curves of constant \mu form ellipses, whereas the hyperbolic trigonometric identity : \frac - \frac = \cosh^ \mu - \sinh^ \mu = 1 shows that curves of constant \nu form hyperbolae. Scale factors In an orthogonal coordinate system the lengths of the bas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Curve
In number theory and algebraic geometry, a modular curve ''Y''(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular group of integral 2×2 matrices SL(2, Z). The term modular curve can also be used to refer to the compactified modular curves ''X''(Γ) which are compactifications obtained by adding finitely many points (called the cusps of Γ) to this quotient (via an action on the extended complex upper-half plane). The points of a modular curve parametrize isomorphism classes of elliptic curves, together with some additional structure depending on the group Γ. This interpretation allows one to give a purely algebraic definition of modular curves, without reference to complex numbers, and, moreover, prove that modular curves are defined either over the field of rational numbers Q or a cyclotomic field Q(ζ''n''). The latter fact and its generalization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Curve
In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If the field's characteristic is different from 2 and 3, then the curve can be described as a plane algebraic curve which consists of solutions for: :y^2 = x^3 + ax + b for some coefficients and in . The curve is required to be non-singular, which means that the curve has no cusps or self-intersections. (This is equivalent to the condition , that is, being square-free in .) It is always understood that the curve is really sitting in the projective plane, with the point being the unique point at infinity. Many sources define an elliptic curve to be simply a curve given by an equation of this form. (When the coefficient field has characteristic 2 or 3, the above equation is not quite general enough to include all non-singular cubic cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rational Number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all rational numbers, also referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by boldface , or blackboard bold \mathbb. A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example: ), or eventually begins to repeat the same finite sequence of digits over and over (example: ). This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones (see ). A real number that is not rational is called irrational. Irrational numbers include , , , and . Since the set of rational numbers is countable, and the set of real numbers is uncountable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute For Computational And Experimental Research In Mathematics
The Institute for Computational and Experimental Research in Mathematics (ICERM), founded in 2011, is an American research institute in mathematics at Brown University, funded beginning in 2010 by a grant from the National Science Foundation. About At the time of its founding, the institute was the eighth of its kind in the nation and the first in New England. It is located in downtown Providence, Rhode Island in a building it shares with the Brown University School of Public Health. The Institute for Computational and Experimental Research in Mathematics (ICERM), hold numerous events and workshops throughout the year. Workshops range from one day events all the way up to week-long conferences and conventions. A notable ICERM workshop was, "Illustrating Mathematics" (2016), which brought mathematicians and digital artist together. Directors of ICERM * Jill Pipher (2011–2016) * Brendan Hassett Brendan Edward Hassett is an American mathematician who works as a professor of ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Computation
''Mathematics of Computation'' is a bimonthly mathematics journal focused on computational mathematics. It was established in 1943 as ''Mathematical Tables and other Aids to Computation'', obtaining its current name in 1960. Articles older than five years are available electronically free of charge. Abstracting and indexing The journal is abstracted and indexed in Mathematical Reviews, Zentralblatt MATH, Science Citation Index, CompuMath Citation Index, and Current Contents/Physical, Chemical & Earth Sciences. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... of 2.417. References External links * Delayed open access journals English-language journals Mathematics journals Publications ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Research In Number Theory
''Research in Number Theory'' is a peer-reviewed mathematics journal covering number theory and arithmetic geometry. The editors-in-chief are Jennifer Balakrishnan (Boston University), Florian Luca (University of Witwatersrand), Ken Ono (University of Virginia), and Andrew Sutherland (Massachusetts Institute of Technology). It was established in 2015 as a full open access journal, but is now a hybrid open access journal, published by Springer Science+Business Media. Abstracting and indexing The journal is abstracted and indexed in EBSCO databases, Emerging Sources Citation Index, MathSciNet, Scopus, and Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructur .... References External links * English-language journals Hybrid open access journals Mathematics journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory Foundation
The Number Theory Foundation (NTF) is a non-profit organization based in the United States which supports research and conferences in the field of number theory, with a particular focus on computational aspects and explicit methods. The NTF funds the Selfridge prize awarded at each Algorithmic Number Theory Symposium (ANTS) and is a regular supporter of several conferences and organizations in number theory, including the Canadian Number Theory Association (CNTA), Women in Numbers (WIN), and the West Coast Number Theory (WCNT) conference. History The NTF was created in 1999 via a grant from John Selfridge with an initial board of directors including Paul Bateman, John Brillhart, Richard Blecksmith, Brian Conrey, Ronald Graham, Richard Guy, Carl Pomerance, John Selfridge, Sam Wagstaff, and Hugh Williams Hugh Anthony Glanmor Williams (6 March 1904 – 7 December 1969) was a British actor and dramatist of Welsh descent. Early life and career Hugh Anthony Glanmor William ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dartmouth College
Dartmouth College (; ) is a private research university in Hanover, New Hampshire. Established in 1769 by Eleazar Wheelock, it is one of the nine colonial colleges chartered before the American Revolution. Although founded to educate Native Americans in Christian theology and the English way of life, the university primarily trained Congregationalist ministers during its early history before it gradually secularized, emerging at the turn of the 20th century from relative obscurity into national prominence. It is a member of the Ivy League. Following a liberal arts curriculum, Dartmouth provides undergraduate instruction in 40 academic departments and interdisciplinary programs, including 60 majors in the humanities, social sciences, natural sciences, and engineering, and enables students to design specialized concentrations or engage in dual degree programs. In addition to the undergraduate faculty of arts and sciences, Dartmouth has four professional and graduate schools: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brown University
Brown University is a private research university in Providence, Rhode Island. Brown is the seventh-oldest institution of higher education in the United States, founded in 1764 as the College in the English Colony of Rhode Island and Providence Plantations. Brown is one of nine colonial colleges chartered before the American Revolution. Admissions at Brown is among the most selective in the United States. In 2022, the university reported a first year acceptance rate of 5%. It is a member of the Ivy League. Brown was the first college in the United States to codify in its charter that admission and instruction of students was to be equal regardless of their religious affiliation. The university is home to the oldest applied mathematics program in the United States, the oldest engineering program in the Ivy League, and the third-oldest medical program in New England. The university was one of the early doctoral-granting U.S. institutions in the late 19th century, adding masters ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Institute, University Of Oxford
The Mathematical Institute is the mathematics department at the University of Oxford in England. It is one of the nine departments of the university's Mathematical, Physical and Life Sciences Division. The institute includes both pure and applied mathematics (Statistics is a separate department) and is one of the largest mathematics departments in the United Kingdom with about 200 academic staff. It was ranked (in a joint submission with Statistics) as the top mathematics department in the UK in the 2021 Research Excellence Framework. Research at the Mathematical Institute covers all branches of mathematical sciences ranging from, for example, algebra, number theory, and geometry to the application of mathematics to a wide range of fields including industry, finance, networks, and the brain. It has more than 850 undergraduates and 550 doctoral or masters students. The institute inhabits a purpose-built building between Somerville College and Green Templeton College on Woodstoc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
