A self-contained introduction to algebraic geometry.
Algebraic geometry is, roughly speaking, the study of geometric
objects that can be defined "algebraically", i.e., by means
of polynomials. (A one-dimensional object is a "curve"; a
two-dimensional one is a "surface", etc.)
Thus, the curves y = cos x and y=ex from first-year
calculus are not algebraic, but the curves y=x2, y = x3,
4x2 + 9y2 = 36 , etc. are algebraic. Since "curves" are the
simplest interesting geometric objects,
perhaps the natural way to get
an exposure to algebraic geometry is to begin
with a study of algebraic curves, the topic of this course.
Algebraic geometry has both differential geometry and algebraic
number theory as mathematical neighbours.
Apart from its own intrinsic beauty, algebraic geometry
has found applications both within mathematics (algebraic curves figure
fundamentally in the famous recent proof by Wiles of Fermat's Last
Theorem) and outside it (modern theoretical physics, coding theory).
Both the text and the grading scheme will be announced later.
Students interested in 4150X should speak with the instructor
before the course begins (in part, to determine whether they have
adequate preparation for it). It is recommended that students
have already taken MATH 3020 6.0 before taking this course, in
addition to the official prerequisites below.
Prerequisite:AS/SC/MATH 2022 3.0 or AS/SC/AK/MATH 2222 3.0; 6
credits from 3000-level MATH courses without second digit 5; or
permission of the course coordinator.
Coordinator: Y. Gao