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# ðŸ“™ Undergraduate algebraic geometry by Miles Reid â€” epub download

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**Undergraduate Algebraic Geometry free epub by Miles Reid**

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This book is intended to provide us with a short (135 pages), down to earth and fluently motivated introduction to algebraic geometry. And it does a great job. While the author does not clearly state his intentions in advance, I think it would be safe to assume that this is meant to accompany a more standard text on the subject (Hartshorne, Harris, Shafarevich, etc), and that the author's main goal was to give the quickest possible route to the heart of the subject, making sure the reader stays interested throughout rather than that he is presented with the firmest logical structure. I would like to stress that despite of what I wrote so far, this book does present rigorous proofs and clear definitions.
The style is friendly, straightforward and unpretentious. Everything is well motivated, and one occasionally gets to hear the author's personal perspective or view about a certain topic. I will quote two examples. When discussing the Zariski topology, the author writes "The Zariski topology may cause trouble to some students; since it is only being used as a language, and has almost no content, the difficulty is likely to be psychological rather than technical". This was very calming for me to read, as I have been previously struggling with the "deep meaning" of the Zariski topology, and no book has had the honesty to tell me that I shouldn't worry that much about it. As a second example of the author's style, after a Q.E.D. in page 53 the author explains that "The proof of (b) is a typical algebraist's proof: it's logically very neat, but almost completely hides the content: the real point is that ..."
Chapter 1 begins with the concrete example of conics, intended to motivate the later definitions of the projective plane. Next elliptic curves and their group law is discussed. The chapter ends with a brief survey of the genus of curves.
Chapter 2 is more technical; its purpose is to build the algebraic foundations needed for Hilbert's Nullstellensatz. Among topics covered are Noetherian rings, Hilbert's Basis Theorem, algebraic sets, the Zariski topology, prime ideals and a nice motivation for the Nullstellensatz. Next coordinate rings, morphisms, varieties and other standard topics are introduced.
Chapter 3, titled "Applications", uses the previous material to discuss some nice geometric topics. I especially enjoyed the section on the 27 lines on a cubic surface.
I would highly recommend this book to anyone not very familiar with algebraic geometry; for instance, it could be a good reading to decide if you want to take a more serious study (e.g. a university course) of the subject. If I were to suggest only one text for someone who just wants to know what algebraic geometry is all about, it would definitely be this one.

## About book:

## About file:

Security code:

- Series:
**London Mathematical Society student texts 12** - Author:
**Miles Reid** - Year:
**1988** - Publisher:
**Cambridge University Press** - Language:
**English** - ISBN:
**0521356628,9780521356626,0521355591**

- File size:
**7 722 365** - Format:
**djvu**

Security code:

Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise pol...

Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. With the minimum of prerequisites, Dr. Reid introduces the reader to the basic concepts of algebraic geometry, including: plane...

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 ...

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 and assumes only the standard background of undergra...

This is a genuine introduction to algebraic geometry. The author makes no assumption that readers know more than can be expected of a good undergraduate. He introduces fundamental concepts in a way that enables students to move on to a more advanced book ...

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...

Once thought to be high-brow estoeric mathematics, algebraic geometry is now finding applications in a myriad of different areas, such as cryptography, coding algorithms, and computer graphics. This book gives an overview of some of the techniques involve...

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 and assumes only the standard background of undergra...

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic meth...

"John Gardner was famous for his generosity to young writers, and (this book) is his . . . gift to them. The Art of Fiction will fascinate anyone interested in how fiction gets put together. For the young writer, it will become a necessary handbook, a ste...

This new book by eminent scholar Michael Davidson gathers his essays concerning formally innovative poetry from modernists such as Mina Loy, George Oppen, and Wallace Stevens to current practitioners such as Cristina Rivera-Garza, Heriberto Yepez, Lisa Ro...

The literature of science fiction packs up the facts and discoveries of science and runs off to futures filled with both wonders and warnings. Kids love to take the journeys it offers for the thrill of the ride, but they can learn as they travel, too. Thi...