Caroline Grant Melles's Books

Adventures in Graph Theory

By: W. David Joyner,Caroline Grant Melles

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Adventures in Graph Theory

By: W. David Joyner,Caroline Grant Melles

This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation. This book can also serve as a reference for anyone interested in exploring how they can apply graph theory to other parts of mathematics.

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Page Count

344

Publisher

Birkhäuser

Published Date

ISBN 10

3319683837

ISBN 13

9783319683836

Singularities in Algebraic and Analytic Geometry

By: Caroline Grant Melles,Ruth Ingrid Michler

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Singularities in Algebraic and Analytic Geometry

By: Caroline Grant Melles,Ruth Ingrid Michler

This volume contains the proceedings of an AMS special session held at the 1999 Joint Mathematics Meetings in San Antonio. The participants were an international group of researchers studying singularities from algebraic and analytic viewpoints. The contributed papers contain original results as well as some expository and historical material. This volume is dedicated to Oscar Zariski, on the one hundredth anniversary of his birth. Topics include the role of valuation theory in algebraic geometry with recent applications to the structure of morphisms; algorithmic approaches to resolution of equisingular surface singularities and locally toric varieties; weak subintegral closures of ideals and Rees valuations; constructions of universal weakly subintegral extensions of rings; direct-sum decompositions of finitely generated modules; construction and examples of resolution graphs of surface singularities; Jacobians of meromorphic curves; investigation of spectral numbers of curve singularities using Puiseux pairs; Gröbner basis calculations of Hochschild homology for hypersurfaces with isolated singularities; and the theory of characteristic classes of singular spaces - a brief history with conjectures and open problems.

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Page Count

202

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821820052

ISBN 13

9780821820056

Adventures in Graph Theory

By: W. David Joyner,Caroline Grant Melles

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Adventures in Graph Theory

By: W. David Joyner,Caroline Grant Melles

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Page Count

344

Publisher

Birkhäuser

Published Date

ISBN 10

3319683837

ISBN 13

9783319683836

Singularities in Algebraic and Analytic Geometry

By: Caroline Grant Melles,Ruth Ingrid Michler

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Singularities in Algebraic and Analytic Geometry

By: Caroline Grant Melles,Ruth Ingrid Michler

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Page Count

202

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821820052

ISBN 13

9780821820056

Topics in Algebraic and Noncommutative Geometry

Proceedings in Memory of Ruth Michler, July 20-22, 2001, Luminy, France [and] October 25-28, 2001, Annapolis, Maryland

By: Ruth Ingrid Michler,Caroline Grant Melles

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Topics in Algebraic and Noncommutative Geometry

Proceedings in Memory of Ruth Michler, July 20-22, 2001, Luminy, France [and] October 25-28, 2001, Annapolis, Maryland

By: Ruth Ingrid Michler,Caroline Grant Melles

This book presents the proceedings of two conferences, Resolution des singularites et geometrie non commutative and the Annapolis algebraic geometry conference. Research articles in the volume cover various topics of algebraic geometry, including the theory of Jacobians, singularities, applications to cryptography, and more. The book is suitable for graduate students and research mathematicians interested in algebraic geometry.

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Page Count

256

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821856596

ISBN 13

9780821856598

Book's by Caroline Grant Melles

Adventures in Graph Theory

Adventures in Graph Theory

Singularities in Algebraic and Analytic Geometry

Singularities in Algebraic and Analytic Geometry

Adventures in Graph Theory

Adventures in Graph Theory

Singularities in Algebraic and Analytic Geometry

Singularities in Algebraic and Analytic Geometry

Topics in Algebraic and Noncommutative Geometry

Topics in Algebraic and Noncommutative Geometry

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