Instructor: Filip Zivanovic, office hours (email me beforehand);
Course syllabus: If you have questions about the class, please check the syllabus. Your question will likely be answered there.
The most up-to-date course information and materials will be posted on this page.
In addition, Brightspace will be used to make announcements.
Course Description: Introduction to the theory of linear algebra with some applications; vectors, vector spaces, bases and dimension, applications to geometry, linear transformations and rank, eigenvalues and eigenvectors, determinants and inner products. May not be taken for credit in addition to AMS 210.
Textbook: Linear Algebra with Applications (5th edition) by Otto Bretscher.
Prerequisites: C or higher in AMS 151 or MAT 131 or 141 or coregistration in MAT 126 or level 7 on the mathematics placement examination.
Attendance: Strongly encouraged, but not mandatory.
Major Topics Covered: Systems of linear equations; Gaussian elimination and row echelon form; vectors and matrices; linear transformations; matrix multiplication and inverse matrices; the image and kernel of a linear transformation; subspaces; linear independence, bases, and dimension; coordinates; inner product spaces; projections; orthonormal bases and Gram–Schmidt orthogonalization; orthogonal transformations and matrices; determinants; eigenvalues and eigenvectors; and diagonalization.
Quizzes and suggested problems: Most weeks include an in-class quiz. It will be held at the end of the class on the dates indicated in the tentative schedule below. Each quiz consists of one or two problems.
Syllabus:
Date Topics (textbook sections) Suggested problems Quiz
Tue Jan 26 Linear systems, matrices and vectors (1.1, 1.2) 1.1.9, 1.2.4, 1.2.5, 1.2.11
Thu Jan 28 Gauss–Jordan elimination, matrix operations (1.2, 1.3) 1.2.21, 1.3.4, 1.3.14, 1.3.20
Tue Feb 2 Linear transformations (2.1) 2.1.2, 2.1.3, 2.1.5, 2.1.20 1
Thu Feb 4 Linear transformations in geometry (2.2) 2.2.2, 2.2.4, 2.2.19, 2.2.20
Tue Feb 9 Matrix multiplication (2.3) 2.3.3, 2.3.4, 2.3.14, 2.3.20 2
Thu Feb 11 Inverses of linear transformations (2.4) 2.4.3, 2.4.6, 2.4.18, 2.4.32
Tue Feb 16 Image and kernel of linear transformations (3.1) 3.1.5, 3.1.14, 3.1.21, 3.1.24 3
Thu Feb 18 Subspaces and bases (3.2) 3.2.1, 3.2.5, 3.2.14, 3.2.27
Tue Feb 23 Dimension (3.3) 3.3.3, 3.3.11, 3.3.22, 3.3.27 4
Thu Feb 25 Coordinates (3.4) 3.4.5, 3.4.10, 3.4.15, 3.4.23(a)
Tue Mar 2 Orthogonal projections (5.1) 5.1.2, 5.1.5, 5.1.10, 5.1.15 5
Thu Mar 4 Midterm review (1.1–3.4)
Tue Mar 9 Midterm 1 (in class)
Thu Mar 11 Gram–Schmidt process (5.2) 5.2.5, 5.2.7, 5.2.29, 5.2.32
Mar 15–21 Spring recess — no classes
Tue Mar 23 Orthogonal transformations (5.3) 5.3.3, 5.3.7, 5.3.8, 5.3.15, 5.3.16
Thu Mar 25 Orthogonal projections revisited (5.1, 5.3) 5.3.40, 5.3.41, 5.3.42 6
Tue Mar 30 Vector spaces and inner product spaces (4.1, 5.5) 5.5.2, 5.5.5, 5.5.8, 5.5.17
Thu Apr 1 Determinants (6.1) 6.1.4, 6.1.9, 6.1.23, 6.1.28 7
Tue Apr 6 Further determinants (6.2) 6.2.3, 6.2.8, 6.2.17, 6.2.38
Thu Apr 8 Cramer’s rule (6.3) 6.3.1, 6.3.22, 6.3.25
Tue Apr 13 Midterm review (5.1–5.3, 5.5–6.2)
Thu Apr 15 Midterm 2 (in class)
Tue Apr 20 Diagonalization (7.1) 7.1.1, 7.1.4, 7.1.8, 7.1.15
Thu Apr 22 Eigenvalues (7.2) 7.2.3, 7.2.9, 7.2.11, 7.2.17 8
Tue Apr 27 Eigenvectors (7.3) 7.3.4, 7.3.10, 7.3.22, 7.3.24
Thu Apr 29 Applications of diagonalization (7.4) 7.4.2, 7.4.9 9
Tue May 4 Final review / buffer (1.1–7.4)
Thu May 6 Final review / buffer (1.1–7.4)
Tue May 11 Final exam: 2:15–5:00 pm, location TBA
Accessibility Support Center (SASC) Statement: If you have a physical, psychological, medical or learning disability that may impact your course work, please contact the Student Accessibility Support Center (SASC), ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.
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AI policies:
Unless the instructor states otherwise, the use of AI tools is not allowed to obtain solutions to homework problems, other assignments, or tests. All work you submit should be your own, without any AI assistance. Any exceptions from this policy will be clearly specified by the course instructor.
If the course policy allows AI tools to be used for a particular project, such use must be disclosed in detail. (For example, you should write “Graphics for this presentation were created using ChatGPT”.) The final content of your work is your responsibility. Any mistakes or errors are reflected in your grade, even if they were introduced by AI tools. In particular, if AI tools suggest some references or citations, it is your responsibility to verify the accuracy of these references or citations.