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1Relating to or involving algebra.

*‘The papers look at algebraic curves, the Riemann Roch theorem and algebraic polynomials.’**‘Betti extended and gave proofs relating to the algebraic concepts of Galois theory.’**‘Fermat preferred the algebraic techniques that he used to such devastating effect in number theory.’**‘His work in algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras.’**‘This gave powerful results such as a purely algebraic proof of the Riemann Roch theorem.’**‘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.’**‘Does Rijndael's algebraic formulation make the algorithm easier to crack than other cryptosystems not designed this way?’**‘Remak made important contributions to algebraic number theory.’**‘Back in Berlin he worked on his doctoral thesis on algebraic number theory under Dirichlet's supervision.’**‘In other work he looked at problems relating properties of algebraic number fields to algebraic K-theory.’**‘Herbrand also worked on field theory considering abelian extensions of algebraic number fields.’**‘Even his analytical work was guided by algebraic and linear algebraic methods.’**‘It dealt with the sum of integrals of a given algebraic function.’**‘Bromwich also made useful contributions to quadratic and bilinear forms and many consider his algebraic work to be his finest.’**‘In 1874 he submitted this doctoral dissertation on algebraic integers and was awarded the degree.’**‘Albanese's research involved examining curves on algebraic surfaces and the genus of an algebraic variety.’**‘He tried, with great success, to show why the introduction of algebraic notation was necessary and inevitable.’**‘According to Rotman, the justification of homological algebra is that it eventually proved useful in solving purely algebraic problems.’**‘Baker, while on a visit to Göttingen, was inspired by Klein to study algebraic function theory.’**‘He also published results on algebras which were fundamental in the study of algebraic number fields.’*

- 1.1Denoting a mathematical expression or equation in which a finite number of symbols are combined using only the operations of addition, subtraction, multiplication, division, and exponentiation with constant rational exponents.Compare with transcendental
*‘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.’**‘It has proved to be the computational method of choice for symbolic manipulation in algebraic geometry, differential equations, and combinatorics.’**‘Paniker not only played upon the abstraction of the words and scripts but also incorporated mathematical formulae, algebraic equations and diagrams of horoscopes.’**‘Omar Khayyam, known chiefly in Europe as a poet, combined trigonometry and approximation theory to solve algebraic equations using geometry.’**‘These books allowed new generations of mathematicians to learn algebraic topology and homological algebra directly in the categorical language and to master the method of diagrams.’**‘Vedic mathematics, which simplifies arithmetic and algebraic operations, has increasingly found acceptance the world over.’**‘Arabic mathematicians learned to manipulate polynomials, to solve certain algebraic equations, and more.’**‘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.’**‘In his lectures Sylow explained Abel's and Galois's work on algebraic equations.’**‘Over the years, mathematicians have developed a variety of such invariants, often expressed in the form of a polynomial algebraic expression.’**‘Her mother always reminded her of how she was doing long division when she was three and complex algebraic equations by the time she was five.’**‘After writing a thesis on algebraic functions and equations, he worked on space curves.’**‘They can solve a variety of two-step problems using variables, identify equivalent algebraic expressions, and solve linear equations and inequalities.’**‘In this book, Boole showed how to apply ordinary algebra to human thought processes, writing down algebraic equations in which the unknowns denoted not numbers but human thoughts.’**‘Since we know that this distance is 260 miles, we can write the following algebraic equation to represent this information.’**‘His research interests include topology, algebraic geometry, and Lie theory.’**‘Few have had the simultaneous grasp of topology, algebraic geometry and K-theory that Thomason did.’**‘Naimark's first work for his candidate's thesis was on the separation of roots of algebraic equations.’**‘His arithmetic setting of this result led eventually to the modern abstract theory of algebraic functions.’**‘The main innovation was Playfair's use of algebraic notation to abbreviate the proofs which he taught in his class.’*

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