Mathstack

Answers are validated before they are marked, mathstack, so students are not mathstack for poor programming skills. Students are given feedback that refers to their specific answer and mistake, as if marked by hand.

In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of the main constructions of descent theory , and to construct fine moduli stacks when fine moduli spaces do not exist. Descent theory is concerned with generalisations of situations where isomorphic , compatible geometrical objects such as vector bundles on topological spaces can be "glued together" within a restriction of the topological basis. In a more general set-up the restrictions are replaced with pullbacks ; fibred categories then make a good framework to discuss the possibility of such gluing. The intuitive meaning of a stack is that it is a fibred category such that "all possible gluings work". The specification of gluings requires a definition of coverings with regard to which the gluings can be considered.

Mathstack

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Grothendieck's letter to Serre, mathstack, Nov 5. STACK can generate random questions so students are shown different variants of questions, and can repeat quizzes with new mathstack.

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Mi hivatkozik erre? EC-8 3 — DOI : ISSN A new way of making logarithms. London: J. Beecroft Perle-nek vagy a lapot Component Designnak nevezik. Krieger Publishing Company, , —, —

Mathstack

CORDIC and closely related methods known as pseudo-multiplication and pseudo-division or factor combining are commonly used when no hardware multiplier is available e. As such, they all belong to the class of shift-and-add algorithms. In computer science, CORDIC is often used to implement floating-point arithmetic when the target platform lacks hardware multiply for cost or space reasons. Volder at the aeroelectronics department of Convair out of necessity to replace the analog resolver in the B bomber 's navigation computer with a more accurate and faster real-time digital solution. His research led to an internal technical report proposing the CORDIC algorithm to solve sine and cosine functions and a prototypical computer implementing it. Daggett, a colleague of Volder at Convair, developed conversion algorithms between binary and binary-coded decimal BCD. In , Convair finally started to build a demonstration system to solve radar fix -taking problems named CORDIC I , completed in without Volder, who had left the company already. Meggitt IBM [18] had proposed as pseudo-multiplication and pseudo-division in Osborne 's prototypical Green Machine , a four-function, floating-point desktop calculator he had completed in DTL logic [17] in December John Stephen Walther at Hewlett-Packard generalized the algorithm into the Unified CORDIC algorithm in , allowing it to calculate hyperbolic functions , natural exponentials , natural logarithms , multiplications , divisions , and square roots.

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Contents move to sidebar hide. Tools Tools. Differentiable stacks and topological stacks are defined in a way similar to algebraic stacks, except that the underlying category of affine schemes is replaced by the category of smooth manifolds or topological spaces. Keys Action? More generally one can define the notion of an n -sheaf or n —1 stack, which is roughly a sort of sheaf taking values in n —1 categories. This is because these are the points where the cover ramifies. Case Studies. If A is a quasi-coherent sheaf of graded algebras in an algebraic stack X over a scheme S , then there is a stack Proj A generalizing the construction of the projective scheme Proj A of a graded ring A. It is also possible to use finer topologies. In the same way, moduli spaces of curves, vector bundles, or other geometric objects are often best defined as stacks instead of schemes. The concept of stacks has its origin in the definition of effective descent data in Grothendieck There are several inequivalent ways of doing this. Read Edit View history. For example, take a projective morphism. Most reasonable "sufficiently large" Grothendieck topologies seem to lead to equivalent categories of quasi-coherent sheaves, but the larger a topology is the harder it is to handle, so one generally prefers to use smaller topologies as long as they have enough open sets.

Our fun, hands-on learning systems were designed by a Master of Mathematics Education to promote:. Download this free version of Math Stackers and start building math thinkers today! Does your school or district need a quote in order to request a purchase order?

Annals of Mathematics. In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. The Grothendieck topology should be strong enough so that the stack is locally affine in this topology: schemes are locally affine in the Zariski topology so this is a good choice for schemes as Serre discovered, algebraic spaces and Deligne—Mumford stacks are locally affine in the etale topology so one usually uses the etale topology for these, while algebraic stacks are locally affine in the smooth topology so one can use the smooth topology in this case. Main article: Algebraic stack. Stacks are used to formalise some of the main constructions of descent theory , and to construct fine moduli stacks when fine moduli spaces do not exist. Thus a stack is formally given as a fibred category over another base category, where the base has a Grothendieck topology and where the fibred category satisfies a few axioms that ensure existence and uniqueness of certain gluings with respect to the Grothendieck topology. A quasi-coherent sheaf is roughly one that looks locally like the sheaf of a module over a ring. JSTOR Most reasonable "sufficiently large" Grothendieck topologies seem to lead to equivalent categories of quasi-coherent sheaves, but the larger a topology is the harder it is to handle, so one generally prefers to use smaller topologies as long as they have enough open sets. Roughly speaking, Deligne—Mumford stacks can be thought of as algebraic stacks whose objects have no infinitesimal automorphisms.