Exam 1
October 5, 2010
Joel M. Cohen
Name:
Math 432
11:00-12:15
1. (35 points) Let R2 be the plane with the standard topology and X the plane
with the dictionary ordering topology.
(a) Prove that the latter topology is strictly bigger than the standard to
Exam 1
October 5, 2010
Joel M. Cohen
Name:
Math 432
11:00-12:15
1. (35 points) Let R2 be the plane with the standard topology and X the plane
with the dictionary ordering topology.
(a) Prove that the latter topology is strictly bigger than the standard to
Exam 1
October 12, 2006
Joel M. Cohen
Name:
Math 432
3:30-4:45 p.m.
1. (35 points) Let R be the real numbers with the standard topology and X the
real numbers with the nite complement topology. Since the latter has many fewer
open sets, given a function f
Exam 2
December 7, 2006
Joel M. Cohen
Name:
Math 432
3:30-4:45 p.m.
1. (20 points) Let R be given the nite complement topology (the closed sets are
R and nite sets). Prove that every subset is compact.
2. (20 points) Show that no two of R1 , R2 and R3 are
Exam 2
December 7, 2006
Joel M. Cohen
Name:
Math 432
3:30-4:45 p.m.
1. (20 points) Let R be given the nite complement topology (the closed sets are
R and nite sets). Prove that every subset is compact.
2. (20 points) Show that no two of R1 , R2 and R3 are
Exam 1
October 12, 2006
Joel M. Cohen
Name:
Math 432
3:30-4:45 p.m.
1. (35 points) Let R be the real numbers with the standard topology and X the
real numbers with the nite complement topology. Since the latter has many fewer
open sets, given a function f
Exam 1
October 5, 2010
Joel M. Cohen
Name:
Math 432
11:00-12:15
1. (35 points) Let R2 be the plane with the standard topology and X the plane
with the dictionary ordering topology.
(a) Prove that the latter topology is strictly bigger than the standard to
Math 432 - Numerical Linear Algebra - Fall 2011
Homework 4
Assigned: Wednesday, September 21, 2011
Due: Wednesday, September 28, 2011
1. (Special Matrices)
Consider the problem Ax = b where A is a tridiagonal matrix. What is the
operation count for the fo
Math 432 - Numerical Linear Algebra - Fall 2011
Homework 3
Assigned: Friday, September 16, 2011
Due: Wednesday, September 21, 2011
1. (Finite Precision Arithmetic)
Use three-digit rounding arithmetic to compute the following sums (sum in the
given order):
Math 432 - Numerical Linear Algebra - Fall 2011
Homework 1
Assigned: Tuesday, August 30, 2011
Due: Wednesday, September 7, 2011
Include a cover page and a problem sheet.
Always clearly label all plots (title, x-label, y -label, and legend).
Use the sub
Exam 1
October 12, 2006
Joel M. Cohen
Name:
Math 432
3:30-4:45 p.m.
1. (35 points) Let R be the real numbers with the standard topology and X the
real numbers with the nite complement topology. Since the latter has many fewer
open sets, given a function f
Exam 2
December 7, 2006
Joel M. Cohen
Name:
Math 432
3:30-4:45 p.m.
1. (20 points) Let R be given the nite complement topology (the closed sets are
R and nite sets). Prove that every subset is compact.
2. (20 points) Show that no two of R1 , R2 and R3 are
First Exam Solutions
Math 432. Differential Equations
Spring 2011
The questions:
1. Determine whether the function y = 2e x + 3e2x is a solution to the differential equation
.
y = 2e x + 3e2x
dy/dx = 2e x + 6e2x
d 2y/dx2 = 2e x + 12e2x
dy/dx + 2y = 2e x +
Math 432 - Numerical Linear Algebra - Fall 2011
Homework 5
Assigned: Wednesday, September 28, 2011
Due: Wednesday, October 5, 2011
1. (Special Matrices)
Consider the matrix
b 1 0
1 4 1 .
0
15
(a) For what values of b will this matrix be positive denite?
(
Math 432 - Numerical Linear Algebra - Fall 2011
Homework 2
Assigned: Wednesday, September 7, 2011
Due: Wednesday, September 14, 2011
Include a cover page and a problem sheet.
Always clearly label all plots (title, x-label, y -label, and legend).
Use th