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# ðŸ“™ Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra by David A. Cox, John Little, Donal Oâ€™Shea â€” free epub

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Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated?The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.The algorithms to answer questions such as those posed above are an important part of algebraic geometry. Although the algorithmic roots of algebraic geometry are old, it is only in the last forty years that computational methods have regained their earlier prominence. New algorithms, coupled with the power of fast computers, have led to both theoretical advances and interesting applications, for example in robotics and in geometric theorem proving.

## About book:

## About file:

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- Series:
**Undergraduate texts in mathematics** - Author:
**David A. Cox, John Little, Donal Oâ€™Shea** - Year:
**2007** - Publisher:
**Springer** - Language:
**English** - ISBN:
**9780387356518,0387356509,9780387356501,0387356517**

- File size:
**3 822 184** - Format:
**pdf**

Security code:

There are many introductions to algebraic geometry focusing on similar topics to this one (varieties affine and projective). However this one is especially friendly to newcomers and is the only such book that I think is accessible to an average undergradu...

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