Math 662
Homework 1
Spring 2014
Drew Armstrong
Problem 0 (Drawing Pictures). Sketch the curves y 2 = f (x) in R2 for the following
polynomials f (x) R[x]: f (x) = x3 and f (x) = (x + 1)(x2 + ) for < 0
Math 662
Homework 3
Spring 2014
Drew Armstrong
Problem 0. (Drawing Pictures) What does the curve y 2 = x2 (x+1) look like at innity?
We dene n-dimensional real projective space RP n as the set of line
Math 662
Homework 2
Spring 2014
Drew Armstrong
Problem 0. (Drawing Pictures) The equation y 2 = x3 x denes a curve in the
complex plane C2 . What does it look like? Unfortunately we can only see real
Math 662
Final Exam
Spring 2014
Drew Armstrong
1. (Galois Connections) Let R be any ring. Given any set of points S K n we dene
a set of polynomials I(S) := cfw_f R[x1 , . . . , xn ] : f () = 0 for al
Math 662
Homework 4
Spring 2014
Drew Armstrong
Problem 0. (Drawing Pictures) We have drawn algebraic curves in R2 , C2 and RP 2 . Now
we will try to draw an algebraic curve in CP 2 . Let , , C be dist
Math 662
Homework 4
Spring 2014
Drew Armstrong
Problem 0. (Drawing Pictures) We have drawn algebraic curves in R2 , C2 and RP 2 . Now
we will try to draw an algebraic curve in CP 2 . Let , , C be dist
Math 662
Homework 2
Spring 2014
Drew Armstrong
Problem 0. (Drawing Pictures) The equation y 2 = x3 x denes a curve in the
complex plane C2 . What does it look like? Unfortunately we can only see real
Math 662
Homework 3
Spring 2014
Drew Armstrong
Problem 0. (Drawing Pictures) What does the curve y 2 = x2 (x+1) look like at innity?
We dene n-dimensional real projective space RP n as the set of line
Math 662
Homework 1
Spring 2014
Drew Armstrong
Problem 0 (Drawing Pictures). Sketch the curves y 2 = f (x) in R2 for the following
polynomials f (x) R[x]: f (x) = x3 and f (x) = (x + 1)(x2 + ) for < 0