Introduction to Algebraic Geometry 1st Edition by Justin R Smith (PDF)

Description

This book is intended for self-study or as a textbook for graduate students or advanced undergraduates. It presupposes some basic knowledge of point-set topology and a solid foundation in linear algebra. Otherwise, it develops all of the commutative algebra, sheaf-theory and cohomology needed to understand the material. It also presents applications to robotics and other fields.

User’s Reviews

Editorial Reviews: Review This book provides a profound introduction to some of the basicprinciples of both classical and modern algebraic geometry forgraduate students or advanced undergraduates. Assuming only someprevious knowledge of linear algebra and general topology, it alsopresents all the concepts, methods and results from commutativealgebra, sheaf theory and cohomology as far as necessary to developthe foundations of algebraic geometry. These allied mathematicalframeworks are treated separately in four appendices after the maintext, thus making the textbook essentially self-contained, andtherefore particularly suited for self-study by beginners or as anaccompanying course book, respectively. Reviewer: Werner Kleinert (Berlin) Zentralblatt MATH: Zbl 1332.14001

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I’ve just received Justin Smith’s hefty volume and upon first reading am greatly impressed. I’ve skimmed thru several chapters and sections and found the text clear, the proofs detailed, and the many worked out examples bring the material to life. (For example, his discussion of the Sylvester matrix and Residual is a model of clarity and likewise for his treatment of projective space. If schemes have eluded you, try out his exposition.) This book seems positioned above Cox, Little, O’Shea and is to me clearer than Hartshorn or Eisenbud,albeit slightly less detailed technically.Not only do you get a nice intro to algebraic geometry, you also get a complete review of algebra, sheaves, vector bundles, and cohomology (which take up 1/2 the entire book!) as well as solutions/hints to hundreds of problems.If one has to quibble, and I don’t, one could lament that the author focuses on (usually complete) fields of characteristic 0, omitting largely char p. And, as one other review has pointed out, there are a number of typos — but I often find them fun to try to find.Finally, I can highly recommend this book on price alone — It is a wonderful addition to the literature on the field and a real help for self-study..

⭐This is one of the best mathematics textbooks ever written.Justin R. Smith’s book is inductive (like good textbooks on physics), extremely digestible, and is immediately useful.It is written for associative neural-net minds like ours, and hence is the opposite of any book by Bourbaki (who writes for sequential computers, and certainly not for humans).In tribute to this desirable oppositeness, Justin R. Smith has earned the prestigious title Ikabruob.The book is also extremely affordable.

⭐The contents are excellent and well presented. The book is paperback and there was a bend in a corner of the cover. The packing could have been done better. I have become more appreciative of thinner texts.

⭐A very pedagogical book on algebraic geometry. However one needs a strong background in graduate level real and complex analysis. The author motivates each topic with examples that are easy to understand.

⭐My only complaint about this book is that it contains a large number of typos, I’m constantly writing in the book to fix errors. Other than that, I like it. It’s well organized and easy to read.

⭐Very useful and clear textbook. Extremely readable. Author provides motivation and examples. I want to thank the author and ask him to write more!

⭐Very well written. Easy to read.

⭐Algebraic Geometry – woohoo!

⭐£16 for an algebraic geometry book? Couldn’t sniff it at. But I was surprised and a little sceptical when I realized it wasn’t a cheap Dover reprint, but an original self-published work. However, it is hard to imagine a more self-contained introduction. Almost half of the book is appendix, explaining the necessary commutative algebra, category theory, sheaf theory, and cohomology to understand the main body of the text. The main text begins with a glimpse of the classical theory, intended to motivate the more modern approach that comes later. Next comes the theory of affine varieties and local properties, and the exposition is for the most part clear and well-written. Although unusual to see in a textbook, this section also contains code examples showing how to do polynomial calculations in Gröbner bases in several mathematical packages. I have not read further than the local properties section.I am an undergraduate doing a coursework project in algebraic geometry, and this book has proved absolutely invaluable. The proofs of some of the theorems are the clearest I have been able to find anywhere. In terms of downsides, well, all textbooks contain some small errors and, being self-published, there are quite a few in here. But so far, there have been none that I wasn’t able to pretty quickly correct with a pencil and carry on reading. Also, sometimes the exercises feel like a bit of an afterthought. Some sections only have a small number, some don’t have any, and in the sections I’ve read so far have tended to be a bit on the easy side.Nonetheless, I still give this book 5 stars, because it’s enormous, clearly written, and at a great price.

⭐This is an easily digested Introduction to Algebraic Geometry, for there is ample room in a 628 page text to lay the groundwork. Many examples and worked solution are also included.Physically the book is large, in height width and thickness.Nearly half the book ( 282 pages ) are Appendices, which are great texts in their own righteven though they lack solutions to their set Example ( problems ).The last Appendix E contains Solutions to selected Problems in the main forward Text.Cross-referencing within the Text is exemplary, and directs you to the required page and Paragraph.Highly recommended as an Introduction to a difficult subject.

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