An Invitation To Algebraic Geometry
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The aim of this book is to describe the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.
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I highly recommend the book "An Invitation to Algebraic Geometry" by Karen E. Smith et. al., as an introduction. It'll give you a taste of the field, without delving too deeply into technicalities.
on “How I Learned to Love Algebraic Geometry” ↗If you do have some math background, "An Invitation to Algebraic Geometry" by Karen Smith et al is a lovely, slim volume that gets to important ideas right away. "Ideals, Varieties, and Algorithms" is an "invitation to computational geometry" by Cox, Little, and O'Shea. I…
on “How I Learned to Love Algebraic Geometry” ↗You need to go more slowly and do lots of examples. Maybe start with * Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen and William Traves, An Invitation to Algebraic Geometry, Springer, Berlin, 2004. and then this: * Igor R. Shafarevich, Basic Algebraic Geometry, two volumes, third edition, Springer, 2013.
on “A Homological Proof of P != NP: Computational Topology via Categorical Framework” ↗