Math 2030 -- Linear Algebra I 
Course Description

Format: 5 Lecture hours per week for 6 weeks.

Text: Lee W. Johnson, R. Dean Riess, & Jimmy T. Arnold, "Introduction to Linear Algebra," (4th ed.) Addison-Wesley, New York, 1997. Chapters 1-3.

References:

• Kenneth Hoffman, Ray Kunze, "Linear Algebra," (2nd ed.) Prentice-Hall, New Jersey, 1971.
• Paul R. Halmos, "Finite-Dimensional Vector Spaces," Springer Undergraduate Texts in Mathematics, New York, 1974.
• Paul R. Halmos, "Linear Algebra Problem Book," MAA Dolciani Mathematical Expositions #16, 1995.

Syllabus:

• Matrices and Linear Equations
• Echelon Form and Gauss-Jordan Elimination
• Applications
• Matrix Operations
• Linear Independence and Nonsingular Matrices
• Data Fitting, Numerical Integration/Differentiation
• Matrix Inverses and Their Properties
• The Vector Space Rⁿ
• Subspaces, Bases
• Dimension, Orthogonal Bases
• Linear Transformations from Rⁿ to R^m
• Least-Squares Solutions to Inconsistent Systems, Applications
• The Eigenvalue Problem
• Determinants
• The Characteristic Polynomial
• Eigenvectors and Eigenspaces
• Complex Eigenvalues and Eigenvectors
• Similarity Transformations and Diagonalization
• Difference Equations, Markov Chains
• Systems of Differential Equations