What is an algebraic variety? - Mathematics Stack Exchange
Dec 30, 2019 · A projective k-variety is a Zariski closed (zero set of some family of homogeneous polynomials) subset of Pn. The definition of an algebraic (k -)variety is somewhat more delicate. According to Milne's Algebraic Geometry notes, an affine k-variety is any locally ringed space isomorphic to some (V, OV) where V is affine algebraic and OV(U) is ...
Why study Algebraic Geometry? - Mathematics Stack Exchange
Dec 10, 2012 · So when any software plots a transcendental surface (or manifold), it is actually displaying a polynomial approximation (an algebraic variety). So the study of algebraic geometry in the applied and computational sense is fundamental for the rest of geometry. From a pure mathematics perspective, the case of projective complex algebraic geometry ...
abstract algebra - Algebraic structure cheat sheet anyone ...
Dec 1, 2010 · Division algebra : This is like a group object in the category of abelian groups except there can't be an inverse for zero, or rather the additive identity. So R R is a division algebra if x ∈ R ∖ 0 x ∈ R ∖ 0 has an inverse for all a ∈ R a ∈ R. Note here R R must have a multiplicative identity. Essentially R R is a ring and R ∖ 0 ...
Best Algebraic Topology book/Alternative to Allen Hatcher free …
BUT, another part of algebraic topology is in the new jointly authored book Nonabelian Algebraic Topology: filtered spaces, crossed complexes, cubical homotopy groupoids (NAT) published in 2011 by the European Mathematical Society. The print version is not cheap, but seems to me good value for 703 pages, and a pdf is available on my web page ...
Newest 'algebraic-topology' Questions - Mathematics Stack …
Questions tagged [algebraic-topology] Questions about algebraic methods and invariants to study and classify topological spaces: homotopy groups, (co)-homology groups, fundamental groups, covering spaces, and beyond. Learn more….
Where to learn algebraic analysis - Mathematics Stack Exchange
Jan 1, 2013 · 7. Here's a link to Foundations of Algebraic Analysis by Masaki Kashiwara, Takahiro Kawai, and Tatsuo Kimura. It's not available from, new, from Amazon, but is available as a used book for purchase. You might want to search a university library for the text, to see if it meets your needs before considering purchasing it.
Newest 'algebraic-geometry' Questions - Mathematics Stack …
Questions tagged [algebraic-geometry] The study of geometric objects defined by polynomial equations, as well as their generalizations: algebraic curves, such as elliptic curves, and more generally algebraic varieties, schemes, etc. Problems under this tag typically involve techniques of abstract algebra or complex-analytic methods. This tag ...
How to know if you are "tough enough" to study Algebraic Topology
Jun 17, 2016 · Algebraic topology, by it's very nature,is not an easy subject because it's really an uneven mixture of algebra and topology unlike any other subject you've seen before.However,how difficult it can be to me depends on how you present algebraic topology and the …
Books for algebraic geometry, algebraic topology [duplicate]
A very beautiful introduction to algebraic geometry is the book "Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra" in the Springer undergraduate texts in mathematics series. (It only requires basic abstract algebra as a prerequisite). The second "half" of Munkres' 2000 Topology ...
algebraic geometry - what is a "section" exactly? - Mathematics …
Apr 6, 2018 · This definition has the obvious generalization to very arbitrary situations; e.g. the definition you cite from basic algebra. More generally we can consider local sections; given an open subset U ⊆ B U ⊆ B, a section of the bundle E→π B E → π B over U U is a continuous map s: U → E s: U → E such that π ∘ s π ∘ s is the ...