Open AccessBook
Basic Algebraic Geometry
TLDR
The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds as discussed by the authors, and is suitable for beginning graduate students.Abstract:
The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with first volume the author has revised the text and added new material. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum making the book accessible to non-specialists. It can be read independently of the first volume and is suitable for beginning graduate students.read more
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Book
The Arithmetic of Elliptic Curves
TL;DR: It is shown here how Elliptic Curves over Finite Fields, Local Fields, and Global Fields affect the geometry of the elliptic curves.
Book
Discriminants, Resultants, and Multidimensional Determinants
TL;DR: The Cayley method of studying discriminants was used by Cayley as discussed by the authors to study the Cayley Method of Discriminants and Resultants for Polynomials in One Variable and for forms in Several Variables.
Journal ArticleDOI
On the mathematical foundations of learning
TL;DR: A main theme of this report is the relationship of approximation to learning and the primary role of sampling (inductive inference) and relations of the theory of learning to the mainstream of mathematics are emphasized.
Book
4-manifolds and Kirby calculus
TL;DR: In this article, the authors introduce surfaces in 4-manifolds complex surfaces and Kirby calculus, a calculus based on handelbodies and Kirby diagrams, which is used for handel bodies and kirby diagrams.
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The quantum method of the inverse problem and the heisenberg xyz model
TL;DR: In this article, the six-vertex model is used to generate vectors and permutation relations for a two-dimensional lattice and quantum mechanics on a chain, and the Bethe Ansatz general Bethe-Anatz method is used for the inverse problem.
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