Passing the written comprehensive examinations is part of one of the alternatives for fulfilling the requirements for the master of science degree in mathematics. Passing with the grade of A is a prerequisite to the oral preliminary examination for the Ph.D. degree in mathematics. In the fall term, the Department offers a series of workshops, taught by an advanced graduate assistant, to help students prepare for the written examinations. Complex Variables Complex numbers, analytical functions, Cauchy-Riemann equations, Cauchy's integral and applications, power series, maximum principle, Liouville's theorem, elementary functions and their conformal maps, bilinear transformation, classification of singularities, residue theorem and contour integration, Laurent series, Rouche's theorem, number of zeros and poles. Linear Algebra Vector spaces, linear dependence, basis, dimension, inner product, linear transformation, systems of linear equations, matrices, determinants, ranks, eigenvalues, diagonalization of matrices, quadratics forms, symmetric and orthogonal transformations.
Cooperative preparation is encouraged, as it is for all examinations.
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