How To Use Algebraic In A Sentence

Baker, while on a visit to Göttingen, was inspired by Klein to study algebraic function theory.
Some indeed were revelling in the formulae of algebraical infinity and of twenty-four-dimensional space, like a child in the elementary class dealing with the four rules of arithmetic.
Mathematicians had regarded algebraic numbers as, in some sense, simpler than transcendental numbers.
Since we know that this distance is 260 miles, we can write the following algebraic equation to represent this information.
Omar Khayyam, known chiefly in Europe as a poet, combined trigonometry and approximation theory to solve algebraic equations using geometry.

His work led to considerable activity in the new area of algebraic combinatorics.
By means of this algebraic method of thinking, objects are grasped spatially, in the blink of an eye.
The first person known to have solved cubic equations algebraically was del Ferro but he told nobody of his achievement.
You dragged yourself to school, your mind seething with half-digested algebraic formulas. ABOUT THE AUTHOR
Putting those proportionalities together algebraically allows you deduce a relationship between speed and the number of rowers.
Vallée Poussin also worked on approximation to functions by algebraic and trigonometric polynomials from 1908 to 1918.
In 1873 he proved an important result on the intersection of two algebraic curves.
The underlying assumption of the project is that certain computer-based experiences can help pupils bridge the gap between arithmetical and algebraic thinking.
Vedic mathematics, which simplifies arithmetic and algebraic operations, has increasingly found acceptance the world over.
'catenary,' a line very simple in shape, but endowed with an algebraic symbol that has to resort to a kind of cabalistic number at variance with any sort of numeration, so much so that the unit refuses to express it, however much we subdivide the unit. The Life of the Spider
This ‘index theorem’ had antecedents in algebraic geometry and led to important new links between differential geometry, topology and analysis.
In 1952 Nash published Real Algebraic Manifolds in the Annals of Mathematics.
His research interests include topology, algebraic geometry, and Lie theory.
It takes neither differential equation nor Laplace transformation. Instead , some algebraic Methods: Will do.
The mathematical ballistics of 1918 was neither as refined as axiomatic geometry nor as theoretical as algebraic topology.
Algebraic topology is behind network theory which is used, among other things, to route circuits on CPUs. Matthew Yglesias » The Minerva Initiative
Or should they legitimately be applied only to continuous curves susceptible of being expressed by algebraic or transcendental equations?
Paniker not only played upon the abstraction of the words and scripts but also incorporated mathematical formulae, algebraic equations and diagrams of horoscopes.
Tarski made important contributions in many areas of mathematics: set theory, measure theory, topology, geometry, classical and universal algebra, algebraic logic, various branches of formal logic and metamathematics.
This does not present the same barrier to pupils use of algebraic ideas within computer programming environments.
The first person known to have solved cubic equations algebraically was del Ferro but he told nobody of his achievement.
Bromwich also made useful contributions to quadratic and bilinear forms and many consider his algebraic work to be his finest.
Al-Khwarizmi continues his study of algebra in Hisab al-jabr w'al-muqabala by examining how the laws of arithmetic extend to an arithmetic for his algebraic objects.
It has proved to be the computational method of choice for symbolic manipulation in algebraic geometry, differential equations, and combinatorics.
He developed a theory of automorphic functions, connecting algebraic and geometric results in his important 1884 book on the icosahedron.
His work followed that of Kronecker in the development of arithmetic in algebraic number fields.
His research interests include topology, algebraic geometry, and Lie theory.
It dealt with the sum of integrals of a given algebraic function.
This idea that there is some group of "logical functions" whose repeated application to some other entities yield complex propositions (and relations) is characteristic of what I am calling algebraic approaches. Structured Propositions
The first person to claim that equations of degree 5 could not be solved algebraically was Ruffini.
Even though their algebraic forms look different, one can verify that the antiderivatives differ by a piecewise constant: Wolfram Blog : Mathematica and the Fundamental Theorem of Calculus
Sernadas et al. 2002b, other examples of collapse were presented, and a solution to the problem was proposed by means of a controlled notion of algebraic fibring called modulated fibring. Combining Logics
The Mathematics Computation subtest assesses skills in computing with whole numbers, fractions, mixed numbers, decimals, and algebraic equations.
To do this, he advanced the study of differential equations from numbers, formulas, and the manipulation of algebraic equations to geometry, curves, and the visualization of flows.
His arithmetic setting of this result led eventually to the modern abstract theory of algebraic functions.
The algebraic approach to programming language semantics has several features to recommend it.
They thought they could just proceed from there, but things got messy (sorry) as they cut the pizza more times, or, as New Scientist puts it, “the solution still included a complicated set of sums of algebraic series involving tricky powers of trigonometric functions,” summed up more succinctly as “ugly.” The mathematics of pizza slicing
Wiseman, "Free Kirk and other rubbish" pitted against "Comtism, ghastliest of algebraic spectralities. Some Diversions of a Man of Letters
His work on algebra was an extension of Abel's work on algebraic functions and their integrals.
Then the embeddings correspond to the algebraic integers in a number field K form a subring denoted by order, this is, a ring which is finitely generated as a Z maximal order of K. Citizendium, the Citizens' Compendium - Recent changes [en]
This is an algebraic expression of the disjunctive normal form theorem of sentential logic.
Does Rijndael's algebraic formulation make the algorithm easier to crack than other cryptosystems not designed this way?
He wrote on algebraic integrals of certain differential equations.
Betti extended and gave proofs relating to the algebraic concepts of Galois theory.
The [[algebraic integer]] s in a number field '' K '' form a subring denoted by '' O '' Citizendium, the Citizens' Compendium - Recent changes [en]
For example, algebraic geometry, the field I am most familiar with, combines algebra, geometry, topology, and analysis.
In other work he looked at problems relating properties of algebraic number fields to algebraic K-theory.
As well as giving point to the subject, experience of algebraic representation is crucial if pupils are to understand and use precise algebraic language.
As spinor is a variable which has algebraic properties identical to that of angular momentum or spin. Einstein Still Rules, Says Fermi Telescope Team | Universe Today
Weil's work on bringing together number theory and algebraic geometry was highly fruitful.
On 4 November 1833 Hamilton read a paper to the Royal Irish Academy expressing complex numbers as algebraic couples, or ordered pairs of real numbers.
The minimal path sets (MPS) are achieved by Boolean algebraic simplification calculation. The authors put forward the analyzing result of the structural significance of the basic event.
His work in algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras.
His work on computational algebraic number theory seems to have started when he visited Caltec in 1959 and collaborated with Taussky-Todd.
It is based on the concept of indefinite admittance matrix, and uses an algebraic method of symbolic code in the generation of symbolic network functions.
The system of general language called algebraical notation does this. A System Of Logic, Ratiocinative And Inductive
From the categorial point of view, the process is the same as for algebraic fibring, the only difference being that the notion of morphism is stronger. Combining Logics
And if we go on in this way, with everybody, intellectuals, artists, government, industrialists and workers all frantically killing off the last human feeling, the last bit of their intuition, the last healthy instinct; if it goes on in algebraical progression, as it is going on: then ta-tah! to the human species! Lady Chatterley's Lover
This work initiates the algebraic theory of operators.
This led to several papers, culminating in a proof twelve years later of a conjecture of Siegel giving an asymptotic relationship satisfied by the class number, the regulator, and the discriminant of an algebraic number field.
From its true emergence, algebra can be seen as a theory of equations solved by means of radicals, and of algebraic calculations on related expressions.
The formal algebraic manipulation of series investigated by Lagrange and Laplace in the 1770s was put in the form of operator equalities by Arbogast in 1800 in Calcul des dérivations.
Sumner was informed that a learned mathematician had discovered an algebraical demonstration of the existence of God and would present it before the audience.
The presentation then went through the "binomial" break apart strategy that's supposed to be teaching kids "algebraic principles in 4th grade", the "change it and make it easier problem" using 98 x 15 as an example (ok change it to 100×15 - 2×15 = 1500 - 30 = 1470). Citizen Tom
It also meant that Wiles' earlier work in algebraic number theory would be helpful, and that he would probably generate some interesting problems-whether or not he found a proof.
‘We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves’ - Lovelace describing the Analytical Engine in the ‘Notes’.
Refactoring, a process of simplifying code in an almost algebraic way, is guided by rules and leads to a predictable result.
Three century Diophantine one of the outstanding contribution that Greece algebra simplify, simplify algebraic created.
He also published results on algebras which were fundamental in the study of algebraic number fields.
It has allowed major progress in classical areas of algebraic geometry such as invariant theory and the moduli of curves. AvaxHome RSS:
He also classified real and complex numbers into classes which are algebraically independent.
Even his analytical work was guided by algebraic and linear algebraic methods.
He had a distinguished career as a math professor, specializing in algebra, algebraic geometry and number theory.
Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.
One of Weil's major achievements was his proof of the Riemann hypothesis for the congruence zeta functions of algebraic function fields.
His work in algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras.
The expressions were ordered in a random way rather than in blocks of expressions with the same algebraic structure.
He replaced the differential operator d/dx by a variable p transforming a differential equation into an algebraic equation.
Bromwich also made useful contributions to quadratic and bilinear forms and many consider his algebraic work to be his finest.
This is, indeed, what they are, if we take the word algebraic in a loose enough sense. The Life of Reason
This is part of a very broad-reaching theme in algebraic topology in which functors represented and corepresented by various spaces are used in analyzing geometry and topology.
He is also remembered by those working in algebraic geometry for his discovery of an involution, now named after him.
This work gave an algebraic classification of maps from polyhedra to spheres.
Neile's parabola was the first algebraic curve to have its arc length calculated; only the arc lengths of transcendental curves such as the cycloid and the logarithmic spiral had been calculated before this.
He replaced the differential operator d/dx by a variable p transforming a differential equation into an algebraic equation.
It dealt with the sum of integrals of a given algebraic function.
His contributions to algebraic symbolism were in using short Arabic words, or just their initial letters, as mathematical symbols.
In [[algebra]], the '' 'continuant' '' of a sequence of terms is an algebraic expression which has applications in [[generalized continued fraction]] s and as the determinant of a Citizendium, the Citizens' Compendium - Recent changes [en]
Omar Khayyam combined the use of trigonometry and approximation theory to provide methods of solving algebraic equations by geometrical means.
He restudied and generalised the mathematical theories of Kummer fields and of cyclotomic fields from the standpoint of abelian varieties over algebraic number fields.
But the last, justice, at least as between the Infinite and the finite, has been so utterly dehumanized, disintegrated, decomposed, and diabolized in passing through the minds of the half-civilized banditti who have peopled and unpeopled the world for some scores of generations, that it has become a mere algebraic x, and has no fixed value whatever as Complete Project Gutenberg Oliver Wendell Holmes, Sr. Works
The control of a specific flip - flop which stores the algebraic sign of numbers.
To summarize, then, the upshot of this discussion is this: if we take a purely algebraic approach to the axioms of set theory, then many basic set-theoretic notions ” including the notions of countability and uncountability ” will turn out to be relative. Skolem's Paradox
Herbrand also worked on field theory considering abelian extensions of algebraic number fields.
The algebraic strength of GEM, and of its weaker finitary and infinitary variants, is worth emphasizing, but it also reflects substantive mereological postulates whose philosophical underpinnings leave room for controversy. Wild Dreams Of Reality, 3
Given this algebraic conception of axiomatization, then, Skolem appeals to the LÃ¶wenheim-Skolem theorems to argue that the axioms of set theory lack the resources to pin down the notion of uncountability. Skolem's Paradox
+s denote a set of complex embeddings of K into algebraic integers in a number field K form a subring denoted by order, this is, a ring which is finitely generated as a Z maximal order of K. Citizendium, the Citizens' Compendium - Recent changes [en]
His derivation of the estimates is a tour de force and the applications in algebraic geometry are beautiful.
Todd generalised the arithmetic genus and the invariants of the canonical system on an algebraic variety to a system of invariants of every codimension.
According to Rotman, the justification of homological algebra is that it eventually proved useful in solving purely algebraic problems.
He divided his course into two parts, the first part being a general overview of mathematics while the second part was on the theory of plane algebraic curves.
He also published results on algebras which were fundamental in the study of algebraic number fields.
There is, of course, a tension in this topic between the totally geometric approach and the algebraic approach.
Other topics he worked on include algebraic geometry, number theory and integral equations.
Le Paige studied the generation of plane cubic and quartic curves, developing further Chasles's work on plane algebraic curves and Steiner's results on the intersection of two projective pencils.
Some rate Severi's discovery of a base of algebraically independent curves on any surface as his most important contribution.
Since the algebraic expressions for the roots z are rather complicated, we use numerical approximations from here on.
His derivation of the estimates is a tour de force and the applications in algebraic geometry are beautiful.
Baldwin - Lomax algebraic turbulent model is corrected to adapt the feature of the base flow.
They can solve a variety of two-step problems using variables, identify equivalent algebraic expressions, and solve linear equations and inequalities.
After all, it's still a theorem that set-theoretic notions like countability and uncountability come out relative on the algebraic conception. Skolem's Paradox
This text attempted to unify many existing algebraic systems.
Real numbers that are solutions of polynomial equations with integer coefficients are called algebraic, and the search was on for numbers that are not algebraic. Set Theory
Ritt-Wu's method of characteristic sets is an effective method to solve algebraic equations by computer, while one cannot get the multiplicity of an isolated solution by this method so far.
The papers look at algebraic curves, the Riemann Roch theorem and algebraic polynomials.
Khayyam also wrote that he hoped to give a full description of the algebraic solution of cubic equations in a later work.
He represented subspaces of a space by coordinates leading to point mapping of an algebraic manifold now called the Grassmannian.
The papers look at algebraic curves, the Riemann Roch theorem and algebraic polynomials.
Some details must be ironed out: for example, the investigation of loops which are very similar gives no insight into the structure of the space, so we work instead with sets of loops called homotopy classes One of the most useful tools in algebraic topology is the [[fundamental group]], Conservapedia - Recent changes [en]
Herbrand also worked on field theory considering abelian extensions of algebraic number fields.
Few have had the simultaneous grasp of topology, algebraic geometry and K-theory that Thomason did.
This does not present the same barrier to pupils use of algebraic ideas within computer programming environments.
Geometrically the resolvent enables us to resolve the whole spread represented by any given set of algebraic equations into definite irreducible spreads.
His aim was to bring together point-set topology and algebraic topology with his 1932 paper.
Hensel was interested in the exact power of a prime which divides the discriminant of an algebraic number field.
The underlying assumption of the project is that certain computer-based experiences can help pupils bridge the gap between arithmetical and algebraic thinking.
In his doctoral studies, his main area of interest was in algebraic geometry and its interactions with symplectic geometry, mathematical physics and differential geometry. The Times Today's News
The idea was to start a pendulum from several different heights in order to cover a range of velocities and then to use simultaneous algebraic equations to fit a two or three term polynomial to two or three lost-arc data-points, changing the exponents until the polynomial achieved good agreement with the other lost-arc data points. Newton's Philosophiae Naturalis Principia Mathematica
And many of the notions which form a part of the train of our thoughts are hardly realized by us at the time, but, like numbers or algebraical symbols, are used as signs only, thus lightening the labour of recollection. Theaetetus
This gave powerful results such as a purely algebraic proof of the Riemann Roch theorem.
Rademacher also wrote important papers on Dedekind sums and investigated many problems relating to algebraic number fields.
He did publish a number of papers, however, which arose through the various courses such as algebraic topology, functional analysis, and geometry, which he taught.
Since most functions defined by simple algebraic expressions are differentiable, on a sufficiently fine scale the points will appear to fall on a straight line.
This was the time when Brauer made his fundamental contribution to the algebraic theory of simple algebras.…
For my Ph.D. 1 was required to study analysis, algebra, and algebraic topology.
Albanese's research involved examining curves on algebraic surfaces and the genus of an algebraic variety.
The singular position of similar platform 3UPU reached by algebraical method is identical to the position of general 3UPU analysized by vector method.
Omar Khayyam, known chiefly in Europe as a poet, combined trigonometry and approximation theory to solve algebraic equations using geometry.
This is where elliptic curves come into play: they induce algebraical groups, some of them suitable for DH and ElGamal crypto systems. Phrack Issue #63 (The Lost Circle of Hackers)
Moreover, multivariate splines also have certain relations with pure mathematics, such as, abstract algebra, algebraic geometry combinatorics and so forth.
Our greatest debt to Lefschetz lies in the fact that he showed us that a study of topology was essential for all algebraic geometers.
He conjectured results about the number of solutions to polynomial equations over the integers using intuition on how algebraic topology should apply in this novel situation.
algebraic geometry
Lagrange's main object was to find out why cubic and quartic equations could be solved algebraically.
The algebraic solution of general equations of degree greater than four is always impossible.
Two algebraic varieties are said to be equivalent if there is a one-to-one correspondence between them with both the map and its inverse regular.
Algebraic laws alone only allow us to prove one occam program equal to another.
He also used letters to replace numbers and was able to state general algebraic theorems but this early use of algebraic notation was not used by subsequent writers.
We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves. Ada Lovelace
He tried, with great success, to show why the introduction of algebraic notation was necessary and inevitable.
He pointed out the analogy between algebraic symbols and those that represent logical forms.
Modern, Sixteenth-Century attention to this ancient matter, as by Cardano and his followers, introduced the modern issues of cubic and biquadratic algebraic functions in an attempted algebraic form. LaRouche's Latest
It takes neither differential equation nor Laplace transformation. Instead , some algebraic Methods: Will do.
I always suspected that if Poetry is inherently a matter of interconnections (what we Pinoys also call pakikiramdam and what I lately have been calling algebraic as a result of three months of tutoring a 13-year-old boy in four years worth of math), such a book can hold together -- also recall Gertrude Stein's observation (I paraphrase) about how a word arbitrarily placed next to another word will rub together for some unexpected frisson if not generate some meaning. THE TEST OF THE UNCOLLECTED
It has proved to be the computational method of choice for symbolic manipulation in algebraic geometry, differential equations, and combinatorics.
Waring also wrote on algebraic curves, classifying quartic curves into 12 main divisions with 84551 subdivisions.
His arithmetic setting of this result led eventually to the modern abstract theory of algebraic functions.
zero fulfills a central role in algebraic structures
The apparatus of algebraic geometry is built upon polars, and these upon distances.
- Presents a number of applications of Galois theory, including symmetric functions, finite fields, cyclotomic fields, algebraic number fields, solvability of equations by radicals, and the impossibility of solution of the three geometric problems of Greek antiquity. AvaxHome RSS:
It was unfortunate for him that already in the 1920's the fashion in algebraical research had drastically changed, and his original work on invariants did not receive the recognition which it would have found two decades earlier.
The OR gates and AND gates you can read about in books that describe how computers work correspond directly to Boole's algebraic operations of addition and multiplication.
After all, it's still a theorem that set-theoretic notions like countability and uncountability come out relative on the algebraic conception. Skolem's Paradox
First interpret it combinatorially, and then derive it algebraically from the multinomial theorem.
His main mathematical interests were in algebraic geometry and differential geometry.
In 1874 he submitted this doctoral dissertation on algebraic integers and was awarded the degree.
At Bath, he will be working with Professor Gregory Sankaran in the branch of mathematics known as algebraic geometry. Media Newswire
First interpret it combinatorially, and then derive it algebraically from the multinomial theorem.
Arabic mathematicians learned to manipulate polynomials, to solve certain algebraic equations, and more.
FOOTNOTES TO ALGEBRA whose title was inspired by Marne Kilates who once published some of my poems in his lovely poets Picturebook and called them "algebraic" should come out later this year. THEN THERE WAS THE SPIRITUALLY-DERIVED BOOK...
The theorem states that all central division algebras over algebraic number fields are cyclic algebras.
The Mathematics Computation subtest assesses skills in computing with whole numbers, fractions, mixed numbers, decimals, and algebraic equations.
You dragged yourself to school, your mind seething with half-digested algebraic formulas. ABOUT THE AUTHOR
Since most functions defined by simple algebraic expressions are differentiable, on a sufficiently fine scale the points will appear to fall on a straight line.
Bobillier is best known for his work on polars of curves and of algebraic surfaces.
Computers operate with semiconductor switches known as logic gates that perform binary algebraic processes to yield an output of either zero or one.
After writing a thesis on algebraic functions and equations, he worked on space curves.
Back in Berlin he worked on his doctoral thesis on algebraic number theory under Dirichlet's supervision.
This work led to a thesis on algebraic geometry in which he introduced rings which are now named after him.
In the 1830s Charles Babbage got serious about automating the computation and printing of mathematical tables, and started imagining a kind of universal “analytical engine”, which, as Ada Lovelace described it, could “weave algebraical patterns just as the Jacquard loom weaves flowers and leaves”. Wolfram Blog : Stephen Wolfram on the Quest for Computable Knowledge
the general term of an algebraic equation of the n-th degree
It's for a so-called "Poetry and Math" issue and Marne thought my poems were "algebraic"...then notes in his Editor's Intro that I have an M.B.A. Archive 2008-08-01
The algebraic strength of GEM, and of its weaker finitary and infinitary variants, is worth emphasizing, but it also reflects substantive mereological postulates whose philosophical underpinnings leave room for controversy. Wild Dreams Of Reality, 3
Remak made important contributions to algebraic number theory.
OrangeMath: Supports research in algebra, including algebraic structures, general algebra, and linear algebra; number theory, including algebraic, analytic number theory, arithmetic geometry, quadratic forms, and automorphic forms; combinatorics, … Read more Feeds4all documents in category 'SEO'
We see how algebraic laws allow us to give a precise and succinct description of each operator.
Sometimes when going through a long algebraic derivation, I will ask each student in turn: ‘Clara, what is the next step in solving for [lambda]?’
He also worked on functions that changed celestial mechanics, helped pioneer algebraic topology and co-discovered the special theory of relativity.
The issue of how to help students get started learning algebraic geometry is a question that almost every practicing algebraic geometer would answer differently.
Instead of taking an algebraic approach, however, Halton used a shortcut inspired by the geometry of paths traced by rays of light.
Paniker not only played upon the abstraction of the words and scripts but also incorporated mathematical formulae, algebraic equations and diagrams of horoscopes.
He had a distinguished career as a math professor, specializing in algebra, algebraic geometry and number theory.
Lagrange's main object was to find out why cubic and quartic equations could be solved algebraically.
And first to derive the transformation matrix D by using "Linear algebraic method". And then obtain an incidence submatrix A.
Moreover, multivariate splines also have certain relations with pure mathematics, such as, abstract algebra, algebraic geometry combinatorics and so forth.

How To Use Algebraic In A Sentence

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