Ebook Download | Algebraic Geometry: A First Course | Last year we used this title as a main reference for the first two quarters of a year-long introductory sequence on algebraic geometry, at the beginning graduate student level (2nd year). Our professor --who was himself a former student of Harris, and a specialist in the Mori program-- backed up the presentation with personal lecture notes, moving mostly in parallel to the book's topics. In the third quarter of the sequence, we moved up to cover the theory of sheaves and schemes from Robin Hartshorne's advanced treatise. Prior to this point, my only exposure to the subject was from the corresponding chapter in Dummit and Foote's algebra, and also from a recent introductory text, "An Invitation to Algebraic Geometry" by Karen Smith et al. At this stage of my studies I was mainly testing the waters; my ineterest on the one hand was driven by a curiosity for the subject itself, which has a reputation for being difficult and hard to grasp, and on the other hand, from its pivotal role in the formulation of new physical theories of mirror symmetry and string theory (for more in this direction, see the 1999 AMS title by A. Cox and S. Katz).
Back to the present text, as the editorial notes correctly point out, this Harris book emphasizes the classical algebraic geometry from the 19th & early 20th centuries prior to the introduction of highly abstract machinery, due to the work of A. Groethendieck in the 50's and 60's. Therefore it's quite natural to base the treatment mostly on the examples and concrete constructions, which were the guiding principles of the abstract development in the first place. This approach also makes the subject accessible for the newcomers who may not have an advanced background in commutative algebra or category theory, and who may not be intending to specialize in the area but merely wish to gain a general understanding of the ideas involved. I found my experience with the subject very fulfilling, and enjoyed many aspects of the presentation. I only suspect many of you could have a similar rewarding experience embarking upon this journey! For the application-oriented readers, I should recommend the Springer-Verlag title "Ideals, Varieties and Algorithms" by Cox et al. which has separate chapters on the Groebner bases, invariant theory, and the robotics.
Back to the present text, as the editorial notes correctly point out, this Harris book emphasizes the classical algebraic geometry from the 19th & early 20th centuries prior to the introduction of highly abstract machinery, due to the work of A. Groethendieck in the 50's and 60's. Therefore it's quite natural to base the treatment mostly on the examples and concrete constructions, which were the guiding principles of the abstract development in the first place. This approach also makes the subject accessible for the newcomers who may not have an advanced background in commutative algebra or category theory, and who may not be intending to specialize in the area but merely wish to gain a general understanding of the ideas involved. I found my experience with the subject very fulfilling, and enjoyed many aspects of the presentation. I only suspect many of you could have a similar rewarding experience embarking upon this journey! For the application-oriented readers, I should recommend the Springer-Verlag title "Ideals, Varieties and Algorithms" by Cox et al. which has separate chapters on the Groebner bases, invariant theory, and the robotics.
Tidak ada komentar:
Posting Komentar