MATH 133, Winter, 2003, Vectors, Matrices and Geometry

Instructors and Sections.
  • Web page : www.math.mcgill.ca/labute/courses/133.html
  • Text: Linear Algebra, by David Poole.
  • Contents: Geometric vectors, dot product, lines and planes (Sections 1.1, 1.2, 1.3, Cross Products). Systems of linear equations, spanning sets and linear independence (Sections 2.1, 2.2, 2.3). Matrices, matrix algebra, subspaces, basis, dimension, rank, linear transformations (Sections 3.1, 3.2, 3.3, 3.4, 3.5). Eigenvalues and eigenvectors, determinants, similarity and diagonalization (Sections 4.1, 4.2, 4.3, 4.4). Orthogonality, orthogonal complements and orthogonal projections, the Gram-Schmidt process. (Sections 5.1, 5.2, 5.3).
  • Midterm: The midterm is on Wednesday, Feb 19. The midterm will be held in class and the exam will last 50 min. The midterm is worth 10% of your grade.
  • WeBWorK assignments: These assignments will be available on the Web and will be answered on the Web. Your WebWorK assignments are at http://msr01.math.mcgill.ca/webwork/m133w03. The initial login/password is your 9 digit student number. Please CHANGE your password the first time you log in. If you experience technical problems with WeBWorK please contact the administrator at wwadmin@math.mcgill.ca. There are ten assignments and nine best will count for the grade. Missed assignments cannot be redone. The WeBWorK assignments are worth 20% of your grade. The additional information about WeBWorK assignments is available at http://www.math.mcgill.ca/~jaksic/webwork.html.
  • Written assignments: There will be 10 written assignments posted in the table at the bottom of the page (in .ps, .pdf and .dvi format). The assignments will be collected and returned in the class. After the due date the solutions will be posted in the table below. Missed assignments cannot be redone--instead, nine best out of ten will count for the grade. The written assignments are worth 5% of your grade.
  • WebCT: Your scores on assignments, midterm, final, and your final mark will be posted on WebCT.
  • Grading: Maximum of the following: Assignments 25%, Midterm 10%, Final 65% OR Assignments 25%, Final 75% OR Final 100%.
  • Missed midterm cannot be redone: If you miss the midterm for any reason, the weights for your mark will be the maximum of the following: Assignments 25%, Final 75% OR Final 100%.
  • Supplemental: There will be a supplemental exam, counting 100% of the supplemental grade. No additional work will be accepted for D, F, or J.
  • Help Desk: http://www.math.mcgill.ca/students/helpdesk.php You are strongly encouraged to make use of this resource.
  • Old Exams: Old exams and assignments can be found at http://www.math.mcgill.ca/189-133a
  • Additional Notes

    Detailed Syllabus
     
    Week Material Written Assignment Comments Learn More!
    Jan. 6-17 Overview of the course.
    Vectors. Sections 1.1, 1.2, 1.3. Exploration: The Cross Product.      		 Assignment 1:  ps or  pdf

    Due: Friday, Jan 24, in class.

    Solutions: ps or pdf

    		*

    History of vectors.

    More about vectors I, II, III, IV.

    Jan. 20-24 Systems of linear equations. Sections 2.1, 2.2. None *

    More about linear equations.

    Jan. 27-31 Spanning sets and linear independence. Section 2.3. Assignment 2:  ps or  pdf

    Due: Friday, Feb 7, in class.

    Solutions: ps or pdf

    		*

    Real vector spaces.

    Feb. 3-7 Matrix operations. Matrix algebra. The inverse of a matrix. Sections 3.1, 3.2, 3.3. Assignment 3:  ps or  pdf

    Due: Fri, Feb 14, in class.

    Solutions: ps or pdf

    		 *

    More about matrix algebra.

    Feb. 10-14 The inverse of a matrix (continuation). Subspaces, basis, dimension, and rank. Section 3.3, 3.4. Assignment 4:  ps or  pdf

    Due: Fri, Feb 21. in class.

    Solutions: ps or pdf

    		 *

    Real vector spaces.

    Feb. 17-21 Subspaces, basis, dimension, and rank (continuation). Section 3.4. Midterm (Wed. Feb 19, in class).   Assignment 5:  ps or  pdf

    Due: Friday, March 7, in class.

    Solutions: ps or pdf

    		* *
    Feb. 24-28 Break  None * *
    March 3-7. Linear transformations.   Assignment 6:  ps or  pdf

    Due: Friday, March 14, in class.

    Solutions: ps or pdf

    		*

    More about linear transformations.

    March 10-14 Introduction to eigenvalues and eigenvectors. Determinants. Sections 4.1, 4.2. Assignment 7:  ps or  pdf

    Due: Friday, March 21, in class.

    Solutions: ps or pdf

    		*

    History of matrices and determinants.

    More about determinants I, II.

    March 17-21 Eigenvalues and eigenvectors. Similarity and diagonalization. 4.3, 4.4. Assignment 8:  ps or  pdf

    Due: Friday, March 28, in class.

    Solutions: ps or pdf

    		*

    More about eigenvalues and eigenvectors.

    March 24-28 Similarity and diagonalization (continuation). Orthogonality. 4.4, 5.1. Assignment 9:  ps or  pdf

    Due: Friday, April 4, in class.

    Solutions: ps or pdf

    		* *
    March 31-April 4 Orthogonal complements and orthogonal projections. The Gram-Schmidt process. Sections 5.2, 5.3. Assignment 10:  ps or  pdf

    Due: Wednesday, April 9, in class.

    Solutions: ps or pdf

    		* *
    April 7-11 Review. None * *