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‘In other work he looked at problems relating properties of algebraic number fields to algebraic K-theory.’
‘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.’
‘In 1874 he submitted this doctoral dissertation on algebraic integers and was awarded the degree.’
‘According to Rotman, the justification of homological algebra is that it eventually proved useful in solving purely algebraic problems.’
‘He tried, with great success, to show why the introduction of algebraic notation was necessary and inevitable.’
‘Fermat preferred the algebraic techniques that he used to such devastating effect in number theory.’
‘Albanese's research involved examining curves on algebraic surfaces and the genus of an algebraic variety.’
‘Bromwich also made useful contributions to quadratic and bilinear forms and many consider his algebraic work to be his finest.’
‘Baker, while on a visit to Göttingen, was inspired by Klein to study algebraic function theory.’
‘The papers look at algebraic curves, the Riemann Roch theorem and algebraic polynomials.’
‘Remak made important contributions to algebraic number theory.’
‘His work in algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras.’
‘Even his analytical work was guided by algebraic and linear algebraic methods.’
‘He also published results on algebras which were fundamental in the study of algebraic number fields.’
‘Back in Berlin he worked on his doctoral thesis on algebraic number theory under Dirichlet's supervision.’
‘It dealt with the sum of integrals of a given algebraic function.’
‘Does Rijndael's algebraic formulation make the algorithm easier to crack than other cryptosystems not designed this way?’
‘Herbrand also worked on field theory considering abelian extensions of algebraic number fields.’
‘Betti extended and gave proofs relating to the algebraic concepts of Galois theory.’
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.
‘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.’
‘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.’
‘Vedic mathematics, which simplifies arithmetic and algebraic operations, has increasingly found acceptance the world over.’
‘Few have had the simultaneous grasp of topology, algebraic geometry and K-theory that Thomason did.’
‘Over the years, mathematicians have developed a variety of such invariants, often expressed in the form of a polynomial algebraic expression.’
‘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.’
‘After writing a thesis on algebraic functions and equations, he worked on space curves.’
‘The main innovation was Playfair's use of algebraic notation to abbreviate the proofs which he taught in his class.’
‘His arithmetic setting of this result led eventually to the modern abstract theory of algebraic functions.’
‘Naimark's first work for his candidate's thesis was on the separation of roots of algebraic equations.’
‘Paniker not only played upon the abstraction of the words and scripts but also incorporated mathematical formulae, algebraic equations and diagrams of horoscopes.’
‘In his lectures Sylow explained Abel's and Galois's work on algebraic equations.’
‘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.’
‘They can solve a variety of two-step problems using variables, identify equivalent algebraic expressions, and solve linear equations and inequalities.’
‘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.’
‘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.’
‘Omar Khayyam, known chiefly in Europe as a poet, combined trigonometry and approximation theory to solve algebraic equations using geometry.’
‘It has proved to be the computational method of choice for symbolic manipulation in algebraic geometry, differential equations, and combinatorics.’