2005, XII, 293 p. 52 illus., Softcover
ISBN: 0-8176-4381-8
About this textbook
This work treats an introduction to commutative ring theory and
algebraic plane curves, requiring of the student only a basic
knowledge of algebra, with all of the algebraic facts collected
into several appendices that can be easily referred to, as needed.
Kunz's proven conception of teaching topics in commutative
algebra together with their applications to algebraic geometry
makes this book significantly different from others on plane
algebraic curves. The exposition focuses on the purely algebraic
aspects of plane curve theory, leaving the topological and
analytical viewpoints in the background, with only casual
references to these subjects and suggestions for further reading.
Table of contents
Preface
* Conventions and Notation
* Part I: Plane Algebraic Curves
* Affine Algebraic Curves
* Projective Algebraic Curves
* The Coordinate Ring of an Algebraic Curve and the Intersections
of Two Curves
* Rational Functions on Algebraic Curves
* Intersection Multiplicity and Intersection Cycle of Two Curves
* Regular and Singular Points of Algebraic Curves. Tangents
* More on Intersection Theory. Applications
* Rational Maps. Parametric Representations of Curves
* Polars and Hessians of Algebraic Curves
* Elliptic Curves
* Residue Calculus
* Applications of Residue Theory to Curves
* The Riemann?Roch Theorem
* The Genus of an Algebraic Curve and of its Function Field
* The Canonical Divisor Class
* The Branches of a Curve Singularity
* Conductor and Value Semigroup of a Curve Singularity
* Part II: Algebraic Foundations
* Algebraic Foundations
* Graded Algebras and Modules
* Filtered Algebras
* Rings of Quotients. Localization
* The Chinese Remainder Theorem
* Noetherian Local Rings and Discrete Valuation Rings
* Integral Ring Extensions
* Tensor Products of Algebras
* Traces
* Ideal Quotients
* Complete Rings. Completion
* Tools for a Proof of the Riemann?Roch Theorem
* References
* Index
* List of Symbols
2006, VIII, 545 p. 96 illus., Hardcover
ISBN: 3-540-23235-4
About this book
This book contains several contributions on the most outstanding
events in the development of twentieth century mathematics,
representing a wide variety of specialities in which Russian and
Soviet mathematicians played a considerable role. The articles
are written in an informal style, from mathematical philosophy to
the description of the development of ideas, personal memories
and give a unique account of personal meetings with famous
representatives of twentieth century mathematics who exerted
great influence in its development.
This book will be of great interest to mathematicians, who will
enjoy seeing their own specialities described with some
historical perspective. Historians will read it with the same
motive, and perhaps also to select topics for future
investigation.
Table of contents
D.V.Anosov: Dynamical Systems in the 1960s: The Hyperbolic
Revolution.- V.I.Arnold: From Hilbert's Superposition Problem to
Dynamical Systems.- A.A.Bolibruch: Inverse Monodromy Problems of
the Analytic Theory of Differential Equations.- L.D.Faddeev: What
Modern Mathematical Physics is Supposed to be.- R.V.Gamkrelidze:
Discovery of the Maximum Principle.- Yu.S.Il'yashenko: The
Qualitative Theory of Diferential Equations in the Plane.- P.S.Krasnoshchekov:
Computerization... Let's be Careful.- V.A.Marchenko: The
Generalized Shift, Transformation Operators, and Inverse Problems.-
V.P.Maslov: Mathematics and the Trajectories of Typhoons.- Yu.V.Matiyasevich:
Hilbert's Tenth Problem: Diophantine Equations in the Twentieth
Century.- V.D.Milman: Observations on the Movement of People and
Ideas in Twentieth-Century Mathematics.- E.F.Mishchenko: About
Aleksandrov, Pontryagin and Their Scientific Schools.- Yu.V.Nesterenko:
Hilbert's Seventh Problem.- S.M.Nikol'skii: The Great Kolmogorov.-
A.N.Parshin: Numbers as Functions: The Development of an Idea in
the Moscow School of Algebraic Geometry.- A.A.Razborov: The P=NP-Problem:
A View from the 1990s.- L.P.Shil'nikov: Homoclinic Trajectories:
From PoincarAc to the Present.- A.N.Shiryaev: From "Disorder"
to Nonlinear Filtering and Martingale Theory.- Ya.G.Sinai: How
Mathematicians and Physicists Found Each Other in the Theory of
Dynamical Systems and in Statistical Mechanics.- V.M.Tikhomirov:
Approximation Theory in the Twentieth Century.- A.M.Vershik: The
Life and Fate of Functional Analysis in the Twentieth Century.- A.G.Vitushkin:
Half a Century as one day.- V.S.Vladimirov: Nikolai Nikolaevich
Bogolyubov - Mathematician by the Grace of God.- V.I.Yudovich:
Global Solvability Versus Collapse in the Dynamics of an
Incompressible Fluid.- Name Index
2005, Approx. 335 p. 21 illus., Softcover
ISBN: 1-85233-922-5
About this textbook
This volume provides a complete introduction to metric space
theory for undergraduates. It covers the topology of metric
spaces, continuity, connectedness, compactness and product
spaces, and includes results such as the Tietze-Urysohn extension
theorem, Picard's theorem on ordinary differential equations, and
the set of discontinuities of the pointwise limit of a sequence
of continuous functions. Key features include:
a full chapter on product metric spaces, including a proof of
Tychonoff’s Theorem
a wealth of examples and counter-examples from real analysis,
sequence spaces and spaces of continuous functions
numerous exercises ? with solutions to most of them ? to test
understanding.
The only prerequisite is a familiarity with the basics of real
analysis: the authors take care to ensure that no prior knowledge
of measure theory, Banach spaces or Hilbert spaces is assumed.
The material is developed at a leisurely pace and applications of
the theory are discussed throughout, making this book ideal as a
classroom text for third- and fourth-year undergraduates or as a
self-study resource for graduate students and researchers.
Table of contents
Preface.- Preliminaries.- Basic Concepts.- Topology of a Metric
Space.- Continuity.- Connected Spaces.- Compact Spaces.- Product
Spaces.- References.- Index.
Description
This book is a survey of current topics in the mathematical
theory of knots. For a mathematician, a knot is a closed loop in
3-dimensional space: imagine knotting an extension cord and then
closing it up by inserting its plug into its outlet. Knot theory
is of central importance in pure and applied mathematics, as it
stands at a crossroads of topology, combinatorics, algebra,
mathematical physics and biochemistry.
Audience
Professional mathematicians, Physicists and lay people with a
flair for mathematics
Contents
Hyperbolic Knots - Colin Adams
Braids: A Survey - Joan S. Birman and Tara E. Brendle
Legendrian and Transversal Knots - John B. Etnyre
Knot Spinning - Greg Friedman
The Enumeration and Classification of Knots and Links - Jim Hoste
Knot Diagrammatics - Louis H. Kauffman
A Survey of Classical Knot Concordance - Charles Livingston
Knot Theory of Complex Plane Curves - Lee Rudolph
Thin Position in the Theory of Classical Knots - Martin
Scharlemann
Computation of Hyperbolic Structures in Knot Theory - Jeff Weeks
Hardbound, ISBN: 0-444-51452-X, 502 pages, publication date: 2005