Langlands' conjectures have dominated the field since they were proposed, and their proof would unify large areas of algebra, number theory, and analysis, but proving them was exceptionally difficult.
His conjectures have dominated the field since they were proposed, and their proof would unify large areas of algebra, number theory, and analysis, but proving them has been exceptionally difficult.
In the areas of algebra and geometry, for example, there are the Cognitive Tutors (Aleven et al. 2009; Koedinger et al. 1997; Ritter et al. 2007) and ALEKS (Falmagne et al. 2013); one assessment compared these two systems on learning gains and resulted in a virtual tie (Sabo et al. 2013).
German mathematician Emmy Noether worked in the area of abstract algebra and developed a theorem -- Noether's Theorem -- that became important in theoretical physics.
When he joined the fledgling university, he concentrated initially on three core areas of mathematics, algebra, analysis and topology, inviting several key figures to join him in the new venture.
Lethbridge, Alberta--I am a mathematician, working in the research areas of universal algebra and semigroup theory.
Matrix multiplication is one of the most common numerical operations, especially in the area of dense linear algebra, where it forms the core of many important algorithms, including solvers of linear systems of equations, least square problems, and singular and eigenvalue computations.
