A Primer of Algebraic D-Modules

A Primer of Algebraic D-Modules
Title A Primer of Algebraic D-Modules PDF eBook
Author S. C. Coutinho
Publisher Cambridge University Press
Pages 223
Release 1995-09-07
Genre Mathematics
ISBN 0521551196

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The theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications avoiding all unnecessary over-sophistication. It is aimed at beginning graduate students and the approach taken is algebraic, concentrating on the role of the Weyl algebra. Very few prerequisites are assumed, and the book is virtually self-contained. Exercises are included at the end of each chapter and the reader is given ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.

Algebraic D-modules

Algebraic D-modules
Title Algebraic D-modules PDF eBook
Author Armand Borel
Publisher
Pages 382
Release 1987
Genre Mathematics
ISBN

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Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent, holonomic, and regular holonomic D-modules, and of the Riemann-Hilbert correspondence. The theory of Algebraic D-modules has found remarkable applications outside of analysis proper, in particular to infinite dimensional representations of semisimple Lie groups, to representations of Weyl groups, and to algebraic geometry.

Commutative Algebra

Commutative Algebra
Title Commutative Algebra PDF eBook
Author David Eisenbud
Publisher Springer Science & Business Media
Pages 784
Release 2013-12-01
Genre Mathematics
ISBN 1461253500

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This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.

A Quantum Groups Primer

A Quantum Groups Primer
Title A Quantum Groups Primer PDF eBook
Author Shahn Majid
Publisher Cambridge University Press
Pages 183
Release 2002-04-04
Genre Mathematics
ISBN 0521010411

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Self-contained introduction to quantum groups as algebraic objects, suitable as a textbook for graduate courses.

Algebraic Geometry

Algebraic Geometry
Title Algebraic Geometry PDF eBook
Author Daniel Perrin
Publisher Springer Science & Business Media
Pages 267
Release 2007-12-16
Genre Mathematics
ISBN 1848000561

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Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.

A Primer in Mathematical Models in Biology

A Primer in Mathematical Models in Biology
Title A Primer in Mathematical Models in Biology PDF eBook
Author Lee A. Segel
Publisher SIAM
Pages 435
Release 2013-05-09
Genre Science
ISBN 1611972493

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A textbook on mathematical modelling techniques with powerful applications to biology, combining theoretical exposition with exercises and examples.

A Primer on Scientific Programming with Python

A Primer on Scientific Programming with Python
Title A Primer on Scientific Programming with Python PDF eBook
Author Hans Petter Langtangen
Publisher Springer
Pages 942
Release 2016-07-28
Genre Computers
ISBN 3662498871

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The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science. From the reviews: Langtangen ... does an excellent job of introducing programming as a set of skills in problem solving. He guides the reader into thinking properly about producing program logic and data structures for modeling real-world problems using objects and functions and embracing the object-oriented paradigm. ... Summing Up: Highly recommended. F. H. Wild III, Choice, Vol. 47 (8), April 2010 Those of us who have learned scientific programming in Python ‘on the streets’ could be a little jealous of students who have the opportunity to take a course out of Langtangen’s Primer.” John D. Cook, The Mathematical Association of America, September 2011 This book goes through Python in particular, and programming in general, via tasks that scientists will likely perform. It contains valuable information for students new to scientific computing and would be the perfect bridge between an introduction to programming and an advanced course on numerical methods or computational science. Alex Small, IEEE, CiSE Vol. 14 (2), March /April 2012 “This fourth edition is a wonderful, inclusive textbook that covers pretty much everything one needs to know to go from zero to fairly sophisticated scientific programming in Python...” Joan Horvath, Computing Reviews, March 2015