MTH 215 Introduction to Linear Algebra-Fall 2003


Info Sheet&Contract

INSTRUCTOR: Dr. Carl Libis

OFFICE: 212 Tyler Hall

TELEPHONE: (401) 874-9067

E-MAIL: clibis@math.uri.edu

COURSE SCHEDULE: Section 02 MWF 3:00-3:50 PM Wales Hall 226

OFFICE HOURS: MWF 12:00-12:50 PM, R 1:30-2:20 PM, or by appointment

TEXT: Linear Algebra, 3rd edition, by Fraleigh and Beauregard, Addison-Wesley Publ., 1995

Accomodations: Students who require accommodations and who have documentation from Disability Services (874-2098) should make arrangements with me as soon as possible.

Here are some useful links for linear algebra:
          Linear Algebra Toolkit
          S. Smith's Math 310 Home page
          Math Archives - Linear & Matrix Algebra
          STAT/MATH Center - Linear Algebra with Maple
          Open Directory Project - Linear Algebra
          Notes on Linear Algebra
          F. Wattenberg's Example of Linear regression and linear transformations - scroll down to the 3rd example
          Practice Linear Transformations
          Demo Version of operations on matrices

Topics: vectors, matrices, linear systems, linear transformations, determinants, eigenvalues, eigenvectors, and orthogonality.

Homework & class work: Suggested homework problems are gien for all sections that we cover in class. Do as many of these as possible and keep the solutions (include the question as well) in a loose leaf notebook. You must be self disciplined to do all of the suggested homework problems and to make sure each one is done correctly. Remember you learn math by doing it. Doing all of the homework is essential. It helps you to practice doing all of the problems so that you can do them quickly enough when the time comes to take a test. Bring this notebook to my office hours to show me your work and ask questions. I will ask students to put up the solutions to homework problems on the board in class. This will count as class work. Also, during class you will sometimes work in groups and hand in your work. This will also count as class work.

Class attendance: Class attendance is expected and strongly encouraged.

Exams and evaluation: There will be short quizzes in class. The questions will be similar to homework problems from material covered in the previous week. There will be three in-class exams. A comprehensive final exam will be given during the final exam period. The course grades will be based on class work, Maple assignements, quizzes, exams, and the final exam.

Class work ................................................50 points
Maple assignments .....................................50 points
Quizzes ....................................................100 points
Three in-class exams  ...............................300 points
Final exam ................................................200 points
Total .......................................................700 points

Calculator: You will find your graphing calculator to be helpful, but not essential for this course. You will need at least a scientific calculator.  Mathematical software packages are very helpful when performing computations in linear algebra, and they can provide a useful tool when learning it as well. We will use the Maple software package for this course. Learn more about Maple. You may have purchased the disk LINTEK with your book. This gives you a way to practice computations and have your work corrected. Exercises using LINTEK are given at the end of the homework sections in our text. You may do as many of these as you like. They are good practice.

To submit electronically:  Go to the home page of the math dept. http://www.math.uri.edu
Select:  Access Electronic Submission of Maple Hmk.  From there, use your postoffice e-mail address as your identification and your Social Security number as your password.  If you fail to do the electronic submission then hand it in on paper by the due date.  Just include the exercises, to avoid printing unnecessary pages.

Maple Assignments: Listed below are the Maple assignments for this section of MTH 215. Begin working on the projects well in advance, as you may find that you have questions.  Please come to my office hours with your questions.


EXTRA CREDIT:  In Determinant Tic-Tac-Toe, Player 1 enters a 1 in an empty 3 x 3 matrix. Player 0 counters with a 0 in a vacant position and play continues in turn until the 3 x 3 matrix is completed with five 1's and four 0's. Player 0 wins if the determinant is 0 and player 1 wins otherwise. Assuming both players pursue optimal strategies, who will win and how?
 
 

MTH 215 Schedule and Syllabus-Fall 2003


Date Section Lecture Topics Pages Suggested Exercises
09/03 1.1 Vectors in Euclidean Spaces 2-19 1,5,9,13,15,17,21,23,25,33,35,39
09/05   Vectors in Euclidean Spaces    
09/08 1.2 The Norm and the Dot Product 20-35 1,3,5,7,9,11,13,25,27,33,36,40
09/10   The Norm and the Dot Product    
09/12 1.3 Matrices and Their Algebra 35-51 1-15 (odd),19,20,21,45
09/15   Matrices and Their Algebra    proofs:  27, 31, 32
09/17 1.4 Solving Systems of Linear Equations 51-73 1-15(odd),21,23,25,29,41-45,47,49,56
09/19   Solving Systems of Linear Equations    
09/22 1.5 Inverses of Square Matrices 73-87 1-13 (odd),16,18,19,21,23
09/24   Inverses of Square Matrices   proofs: 24, 35
09/26 1.6 Homogeneous Systems, Subspaces, and Bases 88-102 1,3,9,17,19,23,25,29,30,31,38,42,43,44
09/29   Homogeneous Systems, Subspaces, and Bases   proofs: 12, 14, 45
10/01 2.1 Independence and Dimension 125-136 7,9,11,12,15,19,21,22,25,27,28
10/03   Review 1.1-1.6    
10/06   EXAM 1    
10/08   Independence and Dimension    
10/10 2.2 The Rank of a Matrix 136-141 1,3,4,5,8,11,12
10/13   COLUMBUS DAY    
10/15 2.3 Linear Transformations of Euclidean Spaces 142-154 1,2,3,5,7,9,10,11,13,14,21,23,25
10/17   Linear Transformations of Euclidean Spaces    
10/20 2.4 Linear Transformations of  the Plane 154-166 1,2,3,6,7,8,10,11,12,13,14,15
10/22   Linear Transformations of  the Plane    
10/24 4.1  Areas, Volumes, and Cross Products 238-250 1,3,5-7,10-15,19,20,21,25,26,30,31,33,34,37,38
10/27   Review 2.1-2.4, 4.1    
10/29   EXAM 2    
10/31 4.2 The Determinant of a Square Matrix 250-263 1,5,7,10,11,13,15-21,22-25,27,29-31
11/03   The Determinant of a Square Matrix     
11/05 4.3 Computation of Determinants and Cramer's Rule 263-273 1,3,5,7,9,15,17,19,21,22,25,27,29,33,35
11/07   Computation of Determinants and Cramer's Rule    
11/10 5.1 Eigenvalues and Eigenvectors 286-305 1,3,5,7,9,13,15
11/12   TUESDAY CLASSES MEET    
11/14   Eigenvalues and Eigenvectors    
11/17 5.2 Diagonalization 305-317 1,3,5,7,9,11,13
11/19   Diagonalization    
11/21 6.1 Projections 326-337 1,3,5,7,9,11,13,15,17,19,21
11/24   Projections    
11/26 6.2 The Gram-Schmidt Process 338-349 1,3,5,7,9,11,13,17,19
12/01   The Gram-Schmidt Process    
12/03   Review 4.2, 4.3, 5.1, 5.2, 6.1, 6.2    
12/05   EXAM 3    
12/08   Review    
12/10   READING DAY    
12/12   FINAL EXAM at 3:00 PM - 6:00 PM