MATH 1564 - Linear Algebra with Abstract Vector Spaces
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MATH 1564 covers linear algebra and abstract vector spaces. It is a core math course worth 4 credit hours. It is offered each fall semester.
Topic List
- Systems of equations
- Geometry of vectors
- Abstract vector spaces
- Spanning, independence, and bases
- Isomorphism and the Fundamental Theorem of Vector Spaces
- Linear transformations, and the matrix of a transformation
- Matrix operations
- Matrix and transformation inverses
- Markov chains
- Change of basis
- Orthogonal projection, Gram-Schmidt, line of best fit
- Determinants
- Complex vector spaces
- Similarity, diagonalizability, eigenvalue and eigenvector
- Page ranking
- Jordan canonical form
Prerequisite Knowledge
Calculus with a high score.
Calculus is used very little in this course. The calculus prerequisite only shows that you are able to learn mathematics at this level.
Equivalent Courses
MATH 1553 and MATH 1554, each of which covers linear algebra but with less emphasis on abstraction.
This course is preferable to the others for mathematicians and similar theorists.
Resources
- A textbook often used for this course is Linear Algebra by Hefferon.
