6
Homotopy
We said at the beginning of this book that topology is about the study of
continuous functions and so the ultimate goal of topology should be to describe
all the continuous maps between any given pair of topological spaces. Of course,
with almo
Eigenvalue and Eigenvector Homework
Olena Bormashenko
November 14, 2011
For each of the matrices A below, do the following:
1. Find the characteristic polynomial of A, and use it to find all the eigenvalues of A.
2. State the algebraic multiplicity of eac
Order of Convergence
The Big-O notation is used to give an idea of the rate of convergence, but is often
insufficient to convey how fast fast convergence can be. For quickly converging
sequences, the order of convergence does a much better job. pn p of or
Homework 6
Ha Pham
November 12, 2008
Problem 1. Chapter 5 - ex 4: Suppose S, T L(V ) are such that ST = T S. Prove that
Ker(T I) is invariant under S for every F.
Proof. Suppose u Ker(T I) ie T u = u.
We want to show that Su Ker(T I) also ie (T I)Su = 0.
Numerical Analysis
Grinshpan
The Order of Convergence
Let cfw_an be a sequence of positive numbers converging to 0. We would like to measure
how fast the terms an converge.
The situation that we have in mind is that of the absolute error sequence an = |x
Math 601 Solutions to Homework 6
1. Find the eigenvalues for each of the following matrices. For each eigenvalue, find a basis of the corresponding eigenspace. Determine whether
the matrix is diagonalizable over the complex numbers.
4
6
4
(a) A1 = 2 3 4
Linear algebra II
Homework #1 solutions
1. Find the eigenvalues and the eigenvectors of the matrix
4 6
.
A=
2 5
Since tr A = 9 and det A = 20 12 = 8, the characteristic polynomial is
f () = 2 (tr A) + det A = 2 9 + 8 = ( 1)( 8).
The eigenvectors with eige
I
. -
Session 2265
Integration of the Greatest Integer Function
David Fung and Steve Ligh
Department of Mathematics
Southeastern Louisiana University
Hammond LA 70402
There have been much discussions in recent years about the teaching of calculus. Among t
Math 101
(Calculus I)
Fall, 2017
Giuliana Davidoff
Office Hours: To be announced. By appointment in the meantime.
Phone:
538-2506
Email:
(This is the best way to reach me.) gdavidof@mtholyoke.edu
Class Meetings: T Th 11:30 12:45 and Friday 3:15 4:05 in Ke
INFOSYS
Date of Test:- 11 April 2004 (Sunday)
Examination Center:- Tagore International School,
E- Block, East of Kailash,
New Delhi 110 065
Topic asked:- Analytical Reasoning And Logical Thinking (* No English test)
Type:- This test was direct recruitmen
Variables and Scope
Prof. Clarkson
Fall 2015
Todays music: "Let It Go" from Frozen
Review
Previously in 3110:
Aspects of a PL: syntax, semantics, idioms, libraries, tools
if expressions
Functions (recursive, anonymous)
Lab: higher-order functions, ope
Lists and Pattern Matching
Prof. Greg Morrisett, Dean of CIS
Fall 2015
Todays music: "Blank Space" by Taylor Swift
Review
Previously in 3110:
Functions: denition, application, anonymous,
higher-order
Variables: bindings, scope
Today:
Lists: OCaml's awe
CS 1110
Prelim 2 Review
Fall 2013
Exam Info
Prelim 2: 7:309:00PM, Thursday, Nov. 14th
Last name A G in Olin 155
Last name H K in Olin 165
Last name L R in Olin 255
Last name S Z in Upson B17
To help you study:
Study guides, review slide
CS 1110
Prelim 2 Review
Fall 2013
Exam Info
Prelim 1: 7:309:00PM, Thursday, October 17th
Last name A G in Olin 155
Last name H K in Olin 165
Last name L R in Olin 255
Last name S Z in Upson B17
To help you study:
Study guides, review sl
PREPARING FOR PRELIM 2
CS 1110: FALL 2013
This handout explains what you have to know for the second prelim. There will be a review session with
detailed examples to help you study. To prepare for the prelim, you can (1) practice writing functions and
cla
LAST NAME_first name_ Cornell Net id_
CS1110
Prelim 2
14 April 2011
This 90-minute exam has 5 questions (numbered 0.4) worth a total of 100 points. Scan the whole test
before starting. Budget your time wisely. Use the back of these pages if you need more
LAST NAME_first name_ Cornell Net id_
CS1110
Prelim 2
8 November 2011
This 90-minute exam has 6 questions (numbered 0.5) worth a total of 100 points. Scan the whole test
before starting. Budget your time wisely. Use the back of these pages if you need mor
Cornell net id _
Name _
Section day _
Section time _
CS 1110 Prelim 2
Grading and posting of grades done Thursday night
18 March 2010
This 90-minute exam has 6 questions (numbered 0.5) worth a total of 100 points. Spend a few minutes
looking at all the qu
LAST NAME_first name_ Cornell Net id_
CS1110
Prelim 1
9 Nov 2010
This 90-minute exam has 5 questions (numbered 0.4) worth a total of 100 points. Scan the whole test
before starting. Budget your time wisely. Use the back of these pages if you need more spa
LAST NAME_first name_Cornell Net id_
CS1110 Prelim 2 10 Nov 2009
This 90-minute exam has 5 questions (numbered 0.4) worth a total of 100 points. Scan the whole test before starting. Budget your time wisely. Use the back of these pages if you need more spa
CS 1110
Prelim 1 Review
Fall 2013
Exam Info
Prelim 1: 7:309:00PM, Thursday, October 17th
Last name A G in Olin 155
Last name H K in Olin 165
Last name L R in Olin 255
Last name S Z in Upson B17
To help you study:
Study guides, review sl
CS 1110
Prelim 1 Review
Fall 2013
Exam Info
Prelim 1: 7:309:00PM, Thursday, October 17th
Last name A G in Olin 155
Last name H K in Olin 165
Last name L R in Olin 255
Last name S Z in Upson B17
To help you study:
Study guides, review sl
PREPARING FOR PRELIM 1
CS 1110: FALL 2012
This handout explains what you have to know for the rst prelim. There will be a review session with
detailed examples to help you study. To prepare for the prelim, you can (1) practice writing functions in
Python,
LAST NAME_first name_ Cornell Net id_
CS1110 Prelim 1 8 March 2011
This 90-minute exam has 5 questions (numbered 0.4) worth a total of 100 points. Scan the whole test
before starting. Budget your time wisely. Use the back of the pages if you need more spa
LAST NAME_first name_ Cornell Net id_
CS1110 Prelim 1 6 October 2011
This 90-minute exam has 5 questions (numbered 0.4) worth a total of 100 points. Scan the whole test
before starting. Budget your time wisely. Use the back of the pages if you need more s
LAST NAME_first name_ Cornell Net id_
CS1110 Prelim 1 7 Oct 2010
This 90-minute exam has 5 questions (numbered 0.4) worth a total of 100 points. Scan the whole test
before starting. Budget your time wisely. Use the back of these pages if you need more spa
LAST NAME_first name_ Cornell Net id_
CS1110 Prelim 1 8 Oct 2009
This 90-minute exam has 5 questions (numbered 0.4) worth a total of 100 points. Scan the whole test before starting. Budget your time wisely. Use the back of these pages if you need more spa
NAME _ Cornell Net id _
1 /6
CS100J Prelim 1 25 September 2006
This 90-minute exam has 6 questions (numbered 0.5) worth a total of 100 points. Scan the whole test before starting. Budget your time wisely. Use the back of these pages if you need more space
NAME _ Cornell Net id _
1 /6
CS100J Prelim 1 22 February 2007
This 90-minute exam has 6 questions (numbered 0.5) worth a total of 100 points. Scan the whole test before starting. Budget your time wisely. Use the back of these pages if you need more space.