Textbook: There is no textbook. I will post all lecture notes on this webpage. For supplementary reading I recommend Gilbert Strang's Introduction to Linear Algebra (any edition).
Lecture: 10:05-11:30 MTuWThF on Zoom
Office Hours: 11:30-12:30 MTuWTh on Zoom
Here is the course syllabus.
Here is an article by Alan Tucker (1993) on The Growing Importance of Linear Algebra in Undergraduate Mathematics. Quote: This author is personally a bit frustrated that calculus gets all of the first year
and half of the second year of the lower-divison core mathematics sequence.
Hopefully early in the next century, there will be a 'redistricting' of the lower-
division mathematics sequence and linear algebra will get equal time with calculus.
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Date |
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Homework 1
Solutions
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Fri, May 22
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Points vs. Vectors
Vector Arithmetic, Pythagorean Theorem
Lots of Examples
Vector Space Concept, Introduction to Linear Equations
HW1 Discussion, Lines and Hyperplanes
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Quiz1
Example
Solutions
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Tues, May 26
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20 minutes at the beginning of class
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Homework 2
Solutions
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Fri, May 29
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Two or Three Lines in 2D, Two Planes in 3D
The Idea of Elimination, Two or Three Planes in 3D
Independence and Dimension, 2 Equations in 4 Unknowns
HW2 Discussion, Determinant of a 2X2 Matrix
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Quiz2
Solutions
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Mon, Jun 1
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20 minutes at the beginning of class
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Homework 3
Solutions
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Fri, June 5
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Some Technical Definitions, Gaussian Elimination
Gaussian Elimination on a Computer, Interpreting the RREF
Review of RREF, Definition of Ax=b
Fundamental Theorem of Linear Algebra
HW3 Discussion, FTLA Discussion
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Quiz3
Solutions
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Mon, Jun 8
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20 minutes at the beginning of class
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Homework 4
Solutions
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Fri, June 12
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Matrices = Linear Functions
Matrix Multiplication = Composition of Linear Functions
Matrices in Calculus, Matrix Arithmetic
Invertibility of Functions and Matrices
HW4 Discussion, Orthogonal Matrices
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Quiz4
Solutions
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Mon, Jun 8
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20 minutes at the beginning of class
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Homework 5
Solutions
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Mon, June 22
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Least Squares Approximation
Projection Onto a Subspace
Review of Projection, Introduction to Diagonalization
Computation of Eigenvalues and Eigenvectors
Linear Systems of Recurrence and Differential Equations
HW5 Discussion, Non-Orthogonal Projections
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Quiz5
Solutions
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Tues, June 23
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20 minutes at the beginning of class
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Discussion and Review
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Why do we call it Diagonalization?
Complex Numbers, Spectral Theorem, Singular Value Decomposition ...
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Final Project
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Fri, June 26
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Write a summary of what you learned in the course.
Minimum 2 pages, Maximum 10 pages
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