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Math 365, Computational Linear Algebra
Spring 2012
(1/18/2012-5/2/2012)
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Time and Venue: |
MoWe
8:30AM - 9:45AM, BEH 104 |
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Instructor: |
Dr. Pengtao Sun |
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Office Hours: |
MoWe 1:00PM - 2:00PM, or by
appointment@ SEB-2129 |
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Email: |
pengtao.sun@unlv.edu |
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URL: |
http://faculty.unlv.edu/sun |
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Phone: |
(702) 895-5175 |
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Reference
book: |
Matrix computations
(3rd. ed) By Gene Howard
Golub, Charles F. Van Loan |
Breakout Session
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Time and Venue: |
Fr 8AM - 9:15AM, WRI C305;
Fr 9:30AM - 10:45AM, BEH 221. |
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TA/Grader: |
Jiajia Wang |
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Email: |
wangj16@unlv.nevada.edu |
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CATALOG DESCRIPTION:
Computational Linear Algebra
contains matrices, linear systems of equations, linear programming,
least-squares approximations, determinants, eigenvalues and eigenvectors, matrix
inversion, elimination, iteration and other algorithms, precision and error
analysis, of computational cost of algorithms. Computer algorithms are
needed to be implemented for the practical methods.
The topical outline of course objectives is the
following:
| Chapter
1 |
Definitions and properties
of matrices |
| Chapter
2 |
Direct methods for linear
system |
| Chapter
3 |
Least square problems |
| Chapter
4 |
Simple iterative methods |
| Chapter
5 |
Methods for computing
eigenvalues |
PREREQUISITE:
Prerequisites MATH 182; CS 117 or CS 135.
LEARNING OUTCOMES:
By means of mathematical principles and
programming codes, the students are expected to do matrices calculations,
compute matrix determinant and inverse, and solve a linear algebraic system by
using some factorization methods (direct solver) as well as simple iterative
methods (iterative solver). In addition, the students will be able to fit the
data with smooth functions using least square method.
TEST AND GRADING POLICY:
There will be four (75-120 minutes) tests
given in this semester, the lowest one will be dropped. Each test is worth 25%,
covering the recently learned 1-2 chapters. The rest 25% points are assigned to
routine
homework.
Grades will be assigned on the basis of total
100 points,
distributed as follows:
|
Three tests |
25% each, total 75% |
|
Homework |
25% |
|
Total |
100 |
In addition, there will be 5 extra
points in maximum directly coming from the in-class performance sheet for
answering in-class questions, and are going to be used for upgrading your overall grade.
Final course letter grades will be assigned as follows:
|
A |
95-100 |
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A- |
90-94 |
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B+ |
86-89 |
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B |
80-85 |
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C+ |
76-79 |
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C |
70-75 |
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D |
60-69 |
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F |
0-59 |
NOTE: Your grade will be based EXCLUSIVELY on the
tests, homework and class performance record.
CLASS POLICIES:
BREAKOUT SESSION:
You are required to participate a
breakout session. The purpose of this breakout session is to answer all
students' questions, and a graduate assistant will be there to
organize the meeting and help the students with their homework questions.
HOMEWORK:
The homework problems that you should
work after each lecture are on the assignment list. You are required to do
the homework outside of class for each section after we have
completed the lesson. Homework are collected on a weekly basis. The
tests will be based on the assigned
homework questions.
ATTENDANCE:
You are required to attend class
regularly. If you miss a class for any reason, you are responsible for all
missed lectures, materials and announcements made in class.
MISSED EXAMS:
You will have one opportunity to make
up a test given on a day you were absent if you can provide sufficient
reason for this missed exam.
CALCULATORS:
A graphics calculator is useful as a study
and learning tool when used appropriately. However, calculus is a collection of
ideas which are not mastered through calculator skills only. Note that no
calculators are allowed on tests.
ACADEMIC INTEGRITY:
Academic integrity is the pursuit of scholarly
activity in an open, honest and responsible manner. Academic integrity is a
basic guiding principle for all academic activity at
University of Nevada, Las Vegas, and all members of the University community are expected to act in
accordance with this principle. Consistent with this expectation, the
University's Code of Conduct states that all students should act with personal
integrity, respect other students' dignity, rights and property, and help create
and maintain an environment in which all can succeed through the fruits of their
efforts.
Academic integrity includes a commitment not to engage in or
tolerate acts of falsification, misrepresentation or deception. Such acts of
dishonesty violate the fundamental ethical principles of the University
community and compromise the worth of work completed by others.
Based on the University's
Student
Academic Misconduct Policy, a range of academic sanctions may be
taken against a student who engages in academic dishonesty.
LECTURE SCHEDULE
(Tentatively):
WEEK
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DAY/DATE
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SECTION(S) COVERED
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1
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Wednesday Jan 18 |
CLASS BEGINS / Introduction
Chapter 1:
Definition and Properties of Matrices
§1.1 Linear algebraic
system, matrices and vectors |
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2 |
Monday Jan 23 |
§1.2 Operation rules
of matrices, vectors and scalars |
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Wednesday
Jan 25 |
§1.2 Operation rules
of matrices, vectors and scalars |
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3
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Monday
Jan 30 |
§1.3 Properties of
matrix and transpose matrix |
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Wednesday
Feb 1 |
§1.4 Inverse matrix |
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4
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Monday
Feb 6 |
§1.5 Determinant of
matrix |
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Wednesday
Feb 8 |
§1.5 Determinant of
matrix |
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Friday
Feb 10 |
TEST #1 |
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5
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Monday
Feb 13 |
Chapter 2: Direct
Methods for Solving Linear Algebraic System
§2.1 Gaussian
elimination method |
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Wednesday
Feb 15 |
§2.1 Gaussian
elimination method |
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6
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Monday
Feb 20 |
Washington’s Birthday
Recess |
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Wednesday
Feb 22 |
§2.1 Gaussian
elimination method |
|
7 |
Monday
Feb 27 |
§2.2 LU
decomposition method |
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Wednesday
Feb 29 |
§2.2 LU
decomposition method, |
|
8 |
Monday
Mar 5 |
§2.3 Cholesky
decomposition method |
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Wednesday
Mar 7 |
§2.3 Cholesky
decomposition method
§2.4 QR factorization
Method |
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Friday
Mar 9 |
TEST #2 |
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9 |
Monday
Mar 12 |
Chapter 3: Least
Squares Problems and QR Factorization Method
§3.1 Introduction to
curve fitting |
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Wednesday
Mar 14 |
§3.2 Least Squares
problems |
|
10 |
Monday
Mar 19 |
§3.3 Normal
equation |
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Wednesday
Mar 21 |
§3.4 Householder
matrix |
|
11 |
Monday
Mar 26 |
§3.5 Householder
reflection method |
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Wednesday
Mar 28 |
§3.5 Householder
reflection method |
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12
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Monday
Apr 2 |
Spring Break |
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Wednesday
Apr 4 |
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13
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Monday
Apr 9 |
§3.6 Application of
Least Square problem - curve fitting |
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Wednesday
Apr 11 |
Chapter 4: Simple
Iterative Methods
§4.1 Definition of
iteration scheme and matrix
§4.2 Jacobi method |
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Friday
Apr 13 |
TEST #3 |
|
14 |
Monday
Apr 16 |
§4.3 Programming
iterative methods |
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Wednesday
Apr 18 |
§4.4 Gauss-Seidel
method |
|
15 |
Monday
Apr 23 |
§4.5 Successive
overrelaxation method |
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Wednesday
Apr 25 |
Chapter 5: Methods for
Computing Eigenvalues
§5.1 Definitions of
eigenvalue problems |
|
16 |
Monday
Apr 30 |
§5.2 Power method |
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Wednesday
May 2 |
REVIEW
LAST DAY OF
CLASSES |
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17 |
Wednesday
May 9 |
8:00am – 10:00am
TEST #4 |
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