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Math 365, Computational Linear Algebra

Spring 2012

(1/18/2012-5/2/2012)

 

Time and Venue: MoWe 8:30AM - 9:45AM, BEH 104
Instructor: Dr. Pengtao Sun
Office Hours:

MoWe 1:00PM - 2:00PM, or by appointment@ SEB-2129

Email: pengtao.sun@unlv.edu
URL: http://faculty.unlv.edu/sun
Phone: (702) 895-5175
Reference book:

Matrix computations (3rd. ed) By Gene Howard Golub, Charles F. Van Loan

 

Breakout Session

Time and Venue:

Fr 8AM - 9:15AM, WRI C305;

Fr 9:30AM - 10:45AM, BEH 221.

 
TA/Grader: Jiajia Wang  
Email: wangj16@unlv.nevada.edu  

 


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
A- 90-94
B+ 86-89
B 80-85
C+ 76-79
C 70-75
D 60-69
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
DAY/DATE
SECTION(S) COVERED

1

Wednesday
Jan 18

CLASS BEGINS / Introduction

Chapter 1: Definition and Properties of Matrices

§1.1 Linear algebraic system, matrices and vectors

2

Monday
Jan 23
§1.2 Operation rules of matrices, vectors and scalars


Wednesday
Jan 25
§1.2 Operation rules of matrices, vectors and scalars

3

Monday
Jan 30
§1.3 Properties of matrix and transpose matrix


Wednesday
Feb 1
§1.4 Inverse matrix

4

Monday
Feb 6
§1.5 Determinant of matrix


Wednesday
Feb 8
§1.5 Determinant of matrix 
  Friday
Feb 10
TEST #1

5

Monday
Feb 13

Chapter 2: Direct Methods for Solving Linear Algebraic  System

§2.1 Gaussian elimination method


Wednesday
Feb 15
§2.1 Gaussian elimination method 

6

Monday
Feb 20
Washington’s Birthday Recess

 
Wednesday
Feb 22
§2.1 Gaussian elimination method

7

Monday
Feb 27
§2.2 LU decomposition method 

 
Wednesday
Feb 29
§2.2 LU decomposition method,

8

Monday
Mar 5
§2.3 Cholesky decomposition method

 
Wednesday
Mar 7

§2.3 Cholesky decomposition method

§2.4 QR factorization Method

  Friday
Mar 9
TEST #2

9

Monday
Mar 12

Chapter 3: Least Squares Problems and QR Factorization Method

§3.1 Introduction to curve fitting


 
Wednesday
Mar 14
§3.2 Least Squares problems

10

Monday
Mar 19
§3.3 Normal equation

 
Wednesday
Mar 21
§3.4 Householder matrix

11

Monday
Mar 26
§3.5 Householder reflection method 

 
Wednesday
Mar 28
§3.5 Householder reflection method

12

Monday
Apr 2
 

Spring Break


 
Wednesday
Apr 4

13

Monday
Apr 9
§3.6 Application of Least Square problem - curve fitting

 
Wednesday
Apr 11

Chapter 4: Simple Iterative Methods

§4.1 Definition of iteration scheme and matrix

§4.2 Jacobi method

  Friday
Apr 13
TEST #3

14

Monday
Apr 16
§4.3 Programming iterative methods
  Wednesday
Apr 18
§4.4 Gauss-Seidel method

15

Monday
Apr 23
§4.5 Successive overrelaxation method

 
Wednesday
Apr 25

Chapter 5: Methods for Computing Eigenvalues

§5.1 Definitions of eigenvalue problems

16

Monday
Apr 30
§5.2 Power method
  Wednesday
May 2

REVIEW

LAST DAY OF CLASSES

17

Wednesday
May 9

8:00am – 10:00am

TEST #4

Last updated: 04/16/2012

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