COMPLEX ANALYSIS

The course aims to

Apply the concept and consequences of analyticity and the Cauchy-Riemann equations and of results on harmonic and entire functions including the fundamental theorem of algebra

Analyze sequences and series of analytic functions and types of convergence

Evaluate complex contour integrals directly and by the fundamental theorem, apply the Cauchy integral theorem in its various versions, and the Cauchy integral formula

Study the general properties of elliptic functions Weierstrass theory

PARTIAL DIFFERENTIAL EQUATIONS

The course aims to

·     Be familiar with the modeling assumptions and derivations that lead to PDEs

·      Recognize the major classification of PDEs and the qualitative differences between the classes of equations

·       Learn to solve heat and wave equations using various methods

Learn the use of integral transforms in solving partial differential equations

TOPOLOGY

The course aims to

·       Introduce the fundamental concepts of general topology

·       Study the properties of arbitrary topological spaces such as connectedness and compactness

Investigate the problems of topology involving the countability and separation axioms

TOPOLOGY

The course aims to

·       Introduce the fundamental concepts of general topology

·       Study the properties of arbitrary topological spaces such as connectedness and compactness

·       Investigate the problems of topology involving the countability and separation axioms

MATHEMATICAL STATISTICS

The course aims to

·       Study the advanced theory of statistical techniques

·       Construct the probability distribution of a random variable, based on real life situations

Learn the concepts of various stochastic processes and notion of statistics

MEASURE THEORY AND INTEGRATION

The course aims to

·       Introduce the basic Concept of Measure Theory.

·       Study  the properties of Riemann Integral.

·       Learn Measure Space, Signed Measure.

Gain Knowledge of Outer Measure.