Linear Algebra - Mathematics 544,   Sections 401 and 501


Spring 2006


University of South Carolina


      Instructor  
      Matthew Boylan  
  Office     LeConte 400G  
  Phone     777-8874  
  E-mail     boylan@math.sc.edu  
  Office hours     Wed. 11:00 - 12:00  
  Thurs. 2:00 - 3:00  
  and by appointment  

  • University of South Carolina Mathematics Department .

  • Course information :

  • Text : Introduction to Linear Algebra, by Johnson, Riess, and Arnold, 5th ed., Addison Wesley, 2002.

  • Meeting schedule :

          Section 401     Section 501  
      Lecture     MWF     12:20 - 1:10     LeConte 121     MWF     12:20 - 1:10     LeConte 121  

  • Exam schedule :

      Exam 1:     Wednesday     February 8     12:20 - 1:10     LeConte 121  
      Exam 2:     Wednesday     March 15     12:20 - 1:10     LeConte 121  
      Exam 3:     Wednesday     April 12     12:20 - 1:10     LeConte 121  
      Final Exam:     Saturday     April 29     2:00 - 5:00     LeConte 121  

  • Homework :

    Homework will be assigned each lecture but not collected. Instead, a weekly quiz will be given based on the homework.

  • Grading :

          Points/650     % of grade  
      Three hour exams:     100 pts. x 3     15% x 3  
      Final exam:     200 pts.     30%  
      Quizzes:     150 pts.     25%  
      Total:     650 pts.     100%  

  • Make-up policy :

    Missed quizzes and exams will not be made up.

  • Calculators :

    Calculators may be used to do homework, but not to do quizzes or exams.

  • Syllabus : (pdf)   (ps)

  • Other help resources : Private tutors , On-line materials for courses   (past 544 homepages),

    Math library   (linear algebra textbooks on reserve).


  • Lectures and Homework :

    Lectures Homework
      Dates     Sections     Topics     Problems     Quiz date  
      Jan     9     M         Introduction and administration          
      11     W     1.1     Introduction to matrices and systems of linear equations     (1.1) 12, 13, 14, 33, 35, 38     Wed., 1/18  
      13     F     1.2     Echelon form and Gauss-Jordan elimination     (1.2) 15, 16, 20, 25, 28, 31, 36, 37, 44     Mon., 1/23  
      18     W     1.3     Consistent systems of linear equations     (1.3) 3, 5, 6, 8, 10, 12, 14, 16, 18, 19, 22, 24     Mon., 1/23  
      20     F     1.5     Matrix operations     (1.5) 1d, 5, 9c, 11a, 17, 27, 31, 41, 43, 45, 53, 54, 55, 58, 59     Mon., 1/30  
      23     M     1.5, 1.6     Algebraic properties of matrix operations     (1.6) 1, 3, 11, 13, 15, 17, 21, 26, 27, 30, 41, 43, 46, 47, 49     Mon., 1/30  
      25     W     1.6             Mon., 1/30  
      27     F     1.7     Linear independence and nonsingular matrices     (1.7) 5, 9, 23, 31, 33, 47, 50, 51, 52, 53, 55, 57     Mon., 2/6  
      30     M     1.7, 1.9     Matrix inverses and their properties     (1.9) 1, 6, 11, 13, 19, 27, 31, 39, 45, 48     Mon., 2/6  
      Feb     1     W     1.9         (1.9) 51, 58, 61, 68, 70, 72, 74     Mon., 2/6  
      3     F     3.2     Vector space properties of R^n     (3.2) 1, 3, 7, 9, 11, 15, 18, 19, 21, 23, 29, 30, 31, 32      
      6     M     3.3     Examples of subspaces     (3.3) 1, 5, 11, 13, 17, 25, 27, 31, 35, 43, 49, 50, 51, 53     Mon., 2/20  
      8     W         Exam I     Covers: Sections and Homework 1.1 - 1.3, 1.5 - 1.7, 1.9, 3.2; class notes: 1/11 - 2/3; quizzes: 1 - 4      
      10     F     3.3             Mon., 2/20  
      13     M     3.4     Bases for subspaces     (3.4) 3, 7, 9, 13, 19, 23, 27, 29, 30, 31, 33, 36, 38, 39     Mon., 2/20  
      15     W     3.4, 3.5             Mon., 2/20  
      17     F     3.5     Dimension     (3.5) 3, 7, 11, 13, 17, 23, 26, 27, 32, 33, 35, 36, 38, 39, 42     Mon., 2/27  
      20     M     3.6     Orthogonal bases for subspaces     (3.6) 3, 7, 9, 17, 19, 23, 24, 25, 28     Mon., 2/27  
      22     W     3.6, 3.7     Linear transformations     (3.7) 5, 9, 11, 15, 19, 23 ,25, 29, 35, 36, 39, 40, 44     Mon., 2/27  
      24     F                 Mon., 3/13  
      27     M     4.1     The eigenvalue problem for 2 x 2 matrices     (4.1) 1, 5, 9, 17, 18, 19     Mon., 3/13  
      Mar     1     W     4.2     Determinants and the eigenvalue problem     (4.2) 9, 13, 19, 21, 23, 25, 26, 27, 28, 29, 30, 31a, 33     Mon., 3/13  
      3     F                 Mon., 3/13  
      13     M     4.3     Elementary operations and determinants     (4.3) 5, 9, 13, 17, 23, 25, 27, 28     Mon., 3/27  
      15     W         Exam II     Covers: Sections and Homework, 3.3-3.7, 4.1, 4.2; class notes: 2/6-3/3; quizzes: 5 - 7      
      17     F     4.4     Eigenvalues and the characteristic polynomial     (4.4) 3, 9, 15, 20, 24, 25, 27, 30     Mon., 3/27  
      20     M                 Mon., 3/27  
      22     W     4.5     Eigenspaces and Eigenvectors     (4.5) 1, 5, 13, 17, 18, 21, 22, 23     Mon., 3/27  
      24     F     4.7     Similarity transformations and diagonalization    (4.7) 5, 7, 15, 17, 25, 26, 27 b, c 31, 43     Mon., 4/3  
      27     M     4.7             Mon., 4/3  
      29     W     5.2     Vector spaces     (5.2) 5, 7, 9, 10, 13, 15, 18, 19, 25, 27, 29, 31, 33     Mon., 4/3  
      31     F     5.3     Subspaces     (5.3) 1, 3, 5, 7, 9, 11, 17, 19, 21, 23, 24, 26, 27, 31 b, d     Mon., 4/10  
      Apr     3     M     5.3             Mon., 4/10  
      5     W     5.4     Linear independence, bases, and coordinates     (5.4) 3, 5, 9, 10, 12, 13, 17, 19, 23, 24, 26, 27, 29, 31     Mon., 4/10  
      7     F     5.4, 5.5     Dimension     (5.5) 1, 3, 5, 7, 13, 15, 16, 17      
      10     M     5.7     Linear transformations     (5.7) 1, 3, 7, 9, 10, 11, 13, 19, 20, 22, 26, 27      
      12     W         Exam III     Covers: Sections and homework, 4.3, 4.4, 4.5, 4.7, 5.2 - 5.5; class notes: 3/13 - 4/10; quizzes: 8 - 10      
      14     F     5.7              
      17     M     5.8     Operations with linear transformations     (5.8) 1, 3, 5, 9, 11, 18, 20, 21, 23, 24, 25, 26, 28      
      19     W     5.9     Matrix representations for linear transformations     (5.9) 1, 2, 5, 7, 9, 13, 15, 19, 21, 23      
      21     F     5.10     Change of basis and diagonalization     (5.10) 1, 3, 5, 7, 9 11, 13, 16, 18      
      24     M     5.10              
      29     Sat.         Final Exam, 2 - 5     Cumulative