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2. Free algebra - Wikipedia

   en.wikipedia.org/wiki/Free_algebra

   Over a field, the free algebra on n indeterminates can be constructed as the tensor algebra on an n-dimensional vector space. For a more general coefficient ring, the same construction works if we take the free module on n generators. The construction of the free algebra on E is functorial in nature and satisfies an appropriate universal property.

3. Socratic (Google) - Wikipedia

   en.wikipedia.org/wiki/Socratic_(Google)

   Over months, millions of real student questions were analyzed and classified. Then the app uses that data to guess on future questions and provide specific education content. [5] [6] The app works by letting students take a photo of a homework question, [7] a feature that was later added to Google Lens.

4. MyMaths - Wikipedia

   en.wikipedia.org/wiki/MyMaths

   Several websites claim to offer 'hacks' to easily access answers on the site, although these merely involve opening several tabs or checking client side source code. [ 10 ] [ 11 ] A popular excuse amongst students completing homework was that they had forgotten to click the 'Checkout' tab, which resulted in the results of supposedly completed ...

5. Golod–Shafarevich theorem - Wikipedia

   en.wikipedia.org/wiki/Golod–Shafarevich_theorem

   Let A = K x 1, ..., x n be the free algebra over a field K in n = d + 1 non-commuting variables x i. Let J be the 2-sided ideal of A generated by homogeneous elements f j of A of degree d j with 2 ≤ d 1 ≤ d 2 ≤ ... where d j tends to infinity. Let r i be the number of d j equal to i. Let B=A/J, a graded algebra. Let b j = dim B j.

6. List of unsolved problems in mathematics - Wikipedia

   en.wikipedia.org/wiki/List_of_unsolved_problems...

   Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

7. Lists of mathematics topics - Wikipedia

   en.wikipedia.org/wiki/Lists_of_mathematics_topics

   Algebra includes the study of algebraic structures, which are sets and operations defined on these sets satisfying certain axioms. The field of algebra is further divided according to which structure is studied; for instance, group theory concerns an algebraic structure called group. Outline of algebra; Glossary of field theory; Glossary of ...