Alexandru Buium - Böcker
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6 produkter
6 produkter
1 604 kr
Skickas inom 11-20 vardagar
This monograph contains exciting original mathematics that will inspire new directions of research in algebraic geometry. Developed here is an arithmetic analog of the theory of ordinary differential equations, where functions are replaced by integer numbers, the derivative operator is replaced by a 'Fermat quotient operator', and differential equations (viewed as functions on jet spaces) are replaced by 'arithmetic differential equations'. The main application of this theory concerns the construction and study of quotients of algebraic curves by correspondences with infinite orbits.Any such quotient reduces to a point in algebraic geometry. But many of the above quotients cease to be trivial (and become quite interesting) if one enlarges algebraic geometry by using arithmetic differential equations in place of algebraic equations. This book, in part, follows a series of papers written by the author. However, a substantial amount of the material has never been published before. For most of the book, the only prerequisites are the basic facts of algebraic geometry and algebraic number theory. It is suitable for graduate students and researchers interested in algebraic geometry and number theory.
2 770 kr
Skickas inom 10-15 vardagar
Bridging the gap between procedural mathematics that emphasizes calculations and conceptual mathematics that focuses on ideas, Mathematics: A Minimal Introduction presents an undergraduate-level introduction to pure mathematics and basic concepts of logic. The author builds logic and mathematics from scratch using essentially no background except natural language. He also carefully avoids circularities that are often encountered in related books and places special emphasis on separating the language of mathematics from metalanguage and eliminating semantics from set theory.The first part of the text focuses on pre-mathematical logic, including syntax, semantics, and inference. The author develops these topics entirely outside the mathematical paradigm. In the second part, the discussion of mathematics starts with axiomatic set theory and ends with advanced topics, such as the geometry of cubics, real and p-adic analysis, and the quadratic reciprocity law. The final part covers mathematical logic and offers a brief introduction to model theory and incompleteness.Taking a formalist approach to the subject, this text shows students how to reconstruct mathematics from language itself. It helps them understand the mathematical discourse needed to advance in the field.
748 kr
Skickas inom 10-15 vardagar
Bridging the gap between procedural mathematics that emphasizes calculations and conceptual mathematics that focuses on ideas, Mathematics: A Minimal Introduction presents an undergraduate-level introduction to pure mathematics and basic concepts of logic. The author builds logic and mathematics from scratch using essentially no background except natural language. He also carefully avoids circularities that are often encountered in related books and places special emphasis on separating the language of mathematics from metalanguage and eliminating semantics from set theory.The first part of the text focuses on pre-mathematical logic, including syntax, semantics, and inference. The author develops these topics entirely outside the mathematical paradigm. In the second part, the discussion of mathematics starts with axiomatic set theory and ends with advanced topics, such as the geometry of cubics, real and p-adic analysis, and the quadratic reciprocity law. The final part covers mathematical logic and offers a brief introduction to model theory and incompleteness.Taking a formalist approach to the subject, this text shows students how to reconstruct mathematics from language itself. It helps them understand the mathematical discourse needed to advance in the field.
955 kr
Kommande
This book provides an introduction to the new field of δ-geometry and its applications to the construction of certain quotient spaces that cannot be approached within usual algebraic geometry, specifically quotients of Siegel moduli spaces by the action of Hecke correspondences. δ-geometry is a geometry obtained from usual algebraic geometry by ‘adjoining’ a Fermat quotient operator; the latter morally plays the role of an ‘arithmetic differentiation’ with respect to a prime integer. The book assumes some basic knowledge of the algebraic geometry of schemes, including abelian schemes, but it is otherwise self-contained. Its intended audience includes mathematics graduate students and researchers interested in algebraic geometry and number theory.
Del 1226 - Lecture Notes in Mathematics
Differential Function Fields and Moduli of Algebraic Varieties
Häftad, Engelska, 1986
270 kr
Skickas inom 10-15 vardagar
Del 1506 - Lecture Notes in Mathematics
Differential Algebraic Groups of Finite Dimension
Häftad, Engelska, 1992
270 kr
Skickas inom 10-15 vardagar
Differential algebraic groups were introduced by P. Cassidy and E. Kolchin and are, roughly speaking, groups defined by algebraic differential equations in the same way as algebraic groups are groups defined by algebraic equations. The aim of the book is two-fold: 1) to provide an algebraic geometer's introduction to differential algebraic groups, and 2) to provide a structure and classification theory for the finite dimensional ones. The main idea of the approach is to relate this topic to the study of: a) deformations of (not necessarily linear) algebraic groups and b) deformations of their automorphisms. The reader is assumed to possess some standard knowledge of algebraic geometry but no familiarity with Kolchin's work is necessary. The book is both a research monograph and an introduction to a new topic and thus will be of interest to a wide audience from researchers to graduate students.