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Linear Algebra (Honors)

291

Systems of Linear Equations, Matrices, Vector Spaces, Linear Transformations, Applications.

Text: 

Elementary Linear Algebra, Larson, 8th edition, Brooks/Cole.

Prerequisite: 

MATH 122 or MATH 142, or MATH 126 or MATH 146 with a grade of C- or higher, and invitation from the Department of Mathematics. Not open to students with credit in Math 290 and Math 590.

Credit Hours: 
2

Chapters

1. Systems of linear equations; Gaussian elimination; matrices, matrix operations, properties, and inverses; and applications (including polynomial curve fittings, approximating integrals, network analysis, electrical circuits, chemical equations, input-output models) Sections 1.1-1.9.

2. Determinants, cofactor expansion, properties, Cramer's rule Sections 2.1-2.3.

3. Vectors in R2, R3, Rn, norm, dot-product, distance in Rn, orthogonality Sections 3.1-3.3.

4. Real vector spaces, subspaces, simple examples including spaces of functions and polynomials, spanning, linear independence, basis, dimension, change of basis, rank and nullity of a matrix, and properties of matrix transformations, applications. Sections 4.1-4.10.

5. **Eigenvalues and Eigenvectors, diagonalization, applications (e.g., Fibonacci type sequences). Sections 5.1-5.2.

8. Linear transformations, matrix representation, compositions, isomorphisms, inverses, similarity, dilations, reflections rotations, etc. Sections 8.1-8.5.

Additional topics*

Orthogonal Bases: Gram-Schmidt Process. LU-Factorization, Fast Fourier Transform

*These and other topics at the instructor's discretion may be covered if time permits. ** Usually about one-third of the students are also enrolled in 220/221 and will need eigenvalues/eigenvectors.


This course will differ from the standard Math 290 in that it will go more deeply into both the theoretical and applied material. Depending on the instructor's preferences, there may be a computer lab component as well.


(Porter 2016 )

Frequency: 
Every Fall Semester
Every Spring Semester

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