Linear Algebra

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Linear Algebra

General Information:

Linear algebra is the branch of mathematics concerning vector spaces, often finite or countably infinite dimensional, as well as linear mappings between such spaces. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.

Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear ones.

Reading List:

1-Hoffman, Kunz, Linear algebra 2nd Edition, Prentice Hall.

2-Seldon, Axler, Linear algebra done right, Springer.

3-Paul R. Halmos, Finite dimensional vector spaces.

Class Hours:

Saturday,(14-16)(16-18)

Monday,(8-10)

Course Content: Here is a glimpse of the syllabus you will learn.

1-Linear Equations

2-Vector Spaces

3-Linear Transformation

4-Determinants

5-Elementary Canonical Forms

Grading

The grading breakdown for this reading course is divided as follows:

40% Midterm exam

20% Weekly assignments

40% Final exam

Homework

Each week, I will assign a set of homework exercises, which will be due the next
meeting. Most of them will be assigned from the textbook.

Course Notes:

After each lecture, I will put the handouts and other useful materials related to current lecture.

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