In this term I am teaching the following courses in Tabriz university:
Algebra II (Galois Theory),
Linear Algebra,
Calculus II,
Calculus I.
Linear Algebra
Systems of linear equations, Matrices and elementary row operations, vector spaces, bases and dimensions, Linear transformations, Matrix representations, Linear functionals and dual spaces, Characteristic values and vectors, Minimal polynomial, The theorem of Cayley and Hamilton, Diagonalization and triangularization, Inner product spaces, orthogonalization, Adjoint of a Transformation, Self-adjoint and unitary operators.
Algebra II
The theorems of isomorphism, Series of subgroups, Soluble and nilpotent groups, Rings and ideals, Fields and field extensions, Degree of an extension, Ruler and compass problems, K-automorphisms and Galois group, Normal and separable extensions, Galois correspondence, Solving of equations by radicals, Finite fields.
Calculus I
System of real numbers, Absolute value, Complex numbers, Real functions, Limit and continuty, Diffrentation and it's applications, Integration, Sequences and series.
Calculus II
Equlidean space, Inner and exterior products, Norm and it's properties, Matrix and linear transformations, Equation of plan in n-space, Curves in n-space, Changing parametr, Tangent vectors, Frenel system, Scalar field, Derivation of a scalar field, Partial diffrentials, Directional derivations, Gradient and tangent plan, Exterme points, Lagrange multiplier method, Chain role, Vector fields, Derivation of a vector field, Jacobi matrix, Curl and divergence, Chain role for vector fields, Potential functions, Line integrals, Characterization of potentials, Integration in plan, Green's theorem, Surface integrals, Area of a surface, Integration in 3-dim space, Changing variable, Orientable surfaces, Stocks's theorem, Divergence theorem.
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