Linear Algebra with Abstract Vector Spaces

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Every Semester

This is an intensive course on linear algebra, taught at a sophisticated and abstract level.


Score of 5 in AP BC Calculus or A in MATH 1552 or equivalent or permission from Academic Office.

MATH 1553, MATH 1554, MATH 1564 and MATH 4305 are equivalent and only one can be taken for credit.

Course Text: 

Linear Algebra by Jim Hefferon, available for free online.

Topic Outline: 
Topic Text Sections Lectures
Solving Linear Systems and Gaussian Elimination One.I.1-3 3
Reduced Echelon Form One.III.1-2 2
Geometry of vectors One.II.1-2 1
Abstract vector spaces Two.I.1 1
Subspaces and spanning sets Two.I.2 2
Linear independence Two.II.1 1
Bases Two.III.1 2
Dimension Two.III.2 2
Vector spaces and linear systems Two.III.3 1
Isomorphisms Three.I.1-2 2
Linear transformations Three.II.1-2 3
Computing linear maps Three.III.1-2 2
Matrix operations Three.IV.1-3 2
Inverses Three.IV.4 1
Markov chains Three.Topic 1
Change of basis Three.V.1-2 2
Orthogonal projection Three.VI.1,3 1
Gram–Schmidt orthogonalization Three.VI.2 1
Line of best fit Three.Topic 1
Determinants Four.I.1-2 2
Laplace’s expansion Four.III.1 1
Complex vector spaces Five.I.1-2 1
Similarity Five.II.1 1
Diagonalizability Five.II.2 1
Eigenvalues and eigenvectors Five.II.3 2
Method of Powers and Page Rank Five.Topics 2
Jordan canonical form Notes 1