Upon completion of the course the student will be proficient with the language and the main results of linear algebra, which is arguably *the*
most important course in all undergraduate mathematics. The secondary course objective is to facilitate the transition of the students from the computationally
oriented introductory mathematical courses to the upper level undergraduate math courses,
which require significantly more abstract thinking and ability to prove mathematical statements.
An introductory linear algebra course, which is a prerequisite for this course, is devoted mainly to the
computational aspects of solving systems of linear equations. As an abstract mathematical discipline, linear algebra
studies linear operators acting on vector spaces. One of our goals in this course is to see how abstract concepts help clarify and understand deeper computational procedures.
A significant attention will be paid to the logical structure and technique of various proofs, and all (well, almost) facts in this course will be proved.

__Classes:__MWF 9:00am-9:50am, NDSU Walster Hall Rm 217__Office hours:__MWF 12:00pm-12:50pm or by appointment (Minard 408E22)-
__Syllabus:__(pdf) __Textbook:__Sergei Treil,*Linear Algebra Done Wrong*(pdf)

- Linear Algebra Done Right by Sheldon Axler
- Linear Algebra by Serge Lang
- Linear Algebra by Kenneth M Hoffman and Ray Kunze
- Linear Algebra by Gilbet Strang (video course through MIT Opencourseware)
- Algebra by Michael Artin

- Systems of linear equations. Operations on matrices.
- Determinants.
- Vector spaces.
- Linear transformations. Intro to spectral theory.
- Inner product spaces.
- Structure of operators in inner product spaces.

- 01. How to solve a linear system
- 02. Matrices
- 03. Row echelon form
- 04. Determinants. Properties and computation
- 05. Determinant. Formal definition
- 06. What does it mean to prove a theorem?
- 07. Vector spaces. Basis. Dimention
- 08. Rank of a matrix
- 09. Computing with bases
- 10. Linear transformations
- 11. The field of complex numbers
- 12. Eigenvalues and eigenvectors of a linear operator. Diagonalization
- 13. Inner product spaces
- 14. Structure of operators in inner product spaces
- 15. Singular value decomposition

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