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Kilmer S: An Introduction to Point-Set
Topology

An Introduction to Point-Set Topology

A Hybrid Texas Style Approach

Generalized Matrix Inversion: A Machine Learning Approach

Differential algebra explores properties of solutions of systems of (ordinary or partial, linear or non-linear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration and symmetry analysis of differential equations. These proceedings consist of tutorial and survey papers presented at the Second International Workshop on Differential Algebra and Related Topics at Rutgers University, Newark in April 2007. As a sequel to the proceedings of the First International Workshop, this volume covers more related subjects, and provides a modern and introductory treatment to many facets of differential algebra, including surveys of known results, open problems, and new, emerging, directions of research. It is therefore an excellent companion and reference text for graduate students and researchers.

Differential Algebra and Related Topics II

Introductory Ring Theory

Annals of Mathematics Studies

A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fieldsThis book introduces a comprehensive theory of adelic line bundles on quasi-projective varieties over finitely generated fields, developed in both geometric and arithmetic contexts. In the geometric setting, adelic line bundles are defined as limits of line bundles on projective compactifications under the boundary topology. In the arithmetic setting, they are defined as limits of Hermitian line bundles on projective arithmetic compactifications, also under the boundary topology. After establishing these foundational definitions, the book uses the theory to explore key concepts such as intersection theory, effective sections, volumes, and positivity of adelic line bundles. It also applies these results to study height functions of algebraic points and prove an equidistribution theorem on quasi-projective varieties. This theory has broad applications in the study of numerical, dynamical, and Diophantine properties of moduli spaces, quasi-projective varieties, and varieties over finitely generated fields.

Adelic Line Bundles on Quasi-projective Varieties

Hypocrisy++: On Philosophy Of Probability And Sociology Of Ideologies

Ausgewählte Fragestellungen und wichtige Konzepte

Algebra und Zahlentheorie

Elementary Linear Algebra, International Adaptation

Non-commutative Ring Theory

This book is a monograph about hybrid networks of singular and non-singular, 1-dimensional flows and equilibriums in self and product polynomial systems. The higher-order singular 1-dimensional flows and singular equilibriums are for the appearing bifurcations of lower-order singular and non-singular 1-dimesnional flows and equilibriums. The infinite-equilibriums are the switching bifurcations for two associated networks of singular and non-singular, 1-dimensional flows and equilibriums. The corresponding mathematical conditions are presented, and the theory for nonlinear dynamics of self and product polynomial systems is presented through a theorem. The mathematical proof is completed through the local analysis and the first integral manifolds. The illustrations of singular 1-diemsnional flows and equilibriums are completed, and the sampled networks of non-singular 1-dimensional flows and equilibriums are presented.

Two-Dimensional Self and Product Polynomial Systems

AK Peters/CRC Recreational Mathematics Series

A Greatly-Expanded, Much-Abridged Edition of The Symmetries of Things

The Magic Theorem

This book deals with the problem of bounding numerical invariants of nonsingular projective algebraic varieties from a unified point of view. Starting with a new insightful proof of the Castelnuovo theorem, the author proceeds with giving (sharp) bounds for basic numerical invariants (such as Betti, Hodge, and Chern numbers) of algebraic varieties of arbitrary dimension and classifying the varieties on the boundary. Many important results are proved in several different ways underlining different aspects of the topic. However, studying numerical invariants is just a pretext for the exploration of the rich and versatile interplay between geometry and topology of projective algebraic varieties which forms the core of the book. A special role in this study is played by the dual varieties and their degrees classically called classes. While making an extensive use of Lefschetz theory (which is now also available for varieties over an algebraically closed field of positive characteristic), the author also develops a new variant of Morse theory which yields statements (including bounds) on the level of CW-complexes and provides bounds for the homology of real algebraic varieties. In this way one also gets stronger forms of some classical results on the topology of projective varieties, such as weak and hard Lefschetz theorems, Hopf type formula etc. A detailed outline of the exciting centennial history of this topic and a list of intriguing open problems contribute to the value of the book. The exposition is accessible to students with only basic knowledge of algebraic geometry and topology.

Bounding Numerical Invariants Of Algebraic Varieties

These lecture notes offer a general overview of a two-dimensional topological field theory called the Poisson Sigma Model. It is based on a series of talks given by the author at the University of California, Berkeley and the University of Massachusetts, Amherst in the fall of 2018 and the spring of 2019. This book contains an introduction to symplectic, Poisson and graded geometry, the path space construction for Lie algebroids via the reduced phase space of the Poisson Sigma Model, and the Cattaneo-Felder interpretation of Kontsevich's star product via Feynman diagrams. It also describes in detail particular cases of the Poisson Sigma Model, including constant, linear (2-dimensional BF-theory) and quadratic Poisson structures. The target audience of this book is graduate students and researchers with an interest in the mathematical aspects of classical and quantum field theory. No prior exposure to physics or Poisson geometry is required.

Introduction To The Poisson Sigma Model, An

An Introduction to Point-Set Topology

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