Math 118C Homework 3 Solutions
Charles Martin
April 21, 2009
9.19 Show that the system of equations
3x + y z + u2 = 0
x y + 2z + u = 0
2x + 2y 3z + 2u = 0
can be solved in terms of x, in terms of y , in terms of z , but not in terms of u.
For k = 1, 2, 3
PROJECTIVE GEOMETRY
b3 course 2003
Nigel Hitchin
hitchin@maths.ox.ac.uk
1
1
Introduction
This is a course on projective geometry. Probably your idea of geometry in the past
has been based on triangles in the plane, Pythagoras Theorem, or something more
an
Homework #01, due 1/20/10 = 9.1.2, 9.1.4, 9.1.6, 9.1.8, 9.2.3
Additional problems for study: 9.1.1, 9.1.3, 9.1.5, 9.1.13, 9.2.1,
9.2.2, 9.2.4, 9.2.5, 9.2.6, 9.3.2, 9.3.3
9.1.1 (This problem was not assigned except for study, but its useful
for the next pr
Solutions to Homework 9
46. (Dummit-Foote 10.3 #2) Suppose Rn Rm . Let I be a maximal ideal of R, then Rn /IRn
Rm /IRm . By the exercise 12 of section 2, this implies that (R/I )n
(R/I )m , and as these are
vector spaces over the eld R/I , we have n = m.
1
Draft: Life insurance mathematics in discrete time
Tom Fischer
Darmstadt University of Technology, Germany
Lecture at the METU Ankara, Turkey
April 12-16, 2004
2
A recent version of the lecture notes can be downloaded under
www.mathematik.tu-darmstadt.d
BU Department of Mathematics
Math 344 First Midterm Examination
Solution Key
Date: April 8, 2009
Time: 17:00-18:00
Full Name:
Student Number:
Signature:
Q1
Q2
Q3
Q4
pts pts pts pts
Total
100 pts
1) (5pts each) An urn contains m balls numbered 1, 2, . . .