Applied Math Thesis

Submatriculants should have an adequate background to pass the Written Preliminary Examination upon admission to the program.

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A third and final attempt may be granted by the Department on a case-by-case basis.

The examinations, in advanced calculus, complex variables and linear algebra, may include some of the following material: Advanced Calculus: Real numbers.

The Masters of Arts program in AMCS is intended for students who wish to go into professional careers in Applied Mathematics, or wish to obtain sufficient background in Applied Mathematics to be a strong candidate for a doctoral program in Applied Mathematics, Mathematics, Statistics, Financial Mathematics etc.

While an undergraduate degree in Mathematics, or Applied Mathematics is not required, applicants to the program should have taken sufficiently many advanced undergraduate mathematics courses so that their interest in and aptitude for mathematics can be assessed.

The masters degree can also be earned by Penn Math Ph. To be admitted as a submatriculant a student must demonstrate a high level of mathematical aptitude and proficiency, usually by taking undergraduate mathematics courses at the level of MATH 312/512, 360-1, 370-1, 410, 425, 430, and receiving excellent grades.

Typically submatriculants are not permitted to use 500-level Mathematics courses, other than MATH 546-7, 570-1, 580-586, toward their list of required courses, and must take a preponderance of Mathematics courses.Master’s students who choose the Written Comprehensive Examinations option must pass with an overall grade of B.The three-part Written Comprehensive Examination is administered by the department twice a year in early September and early January.Beyond Calculus, two semesters of Mathematical Analysis, a semester of Linear Algebra, a semseter of Probability, and a semester of Complex Analysis are strongly recommended.The masters degree is typically earned in 3 to 4 semesters, depending upon the student's background.There is also a requirement to pass the Written Preliminary Exam and to submit and defend a Masters thesis, take two additional courses in lieu of the Masters thesis, with the approval of the Graduate Group Chair. Undergraduates at Penn can request permission to submatriculate into the AMCS Masters degree program.To receive the Masters degree a student must have at least a 3.0 cumulative grade point average in courses counted toward the degree. AMCS does not allow double counting of courses: you must take 8 courses, not counted toward any other degree, and write a Masters thesis, or take two additional courses on an advanced topic, which are also not being counted toward another degree.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, linear transformation, inner product, systems of linear equations, matrices, determinants, ranks, eigenvalues, diagonalization of matrices, quadratics forms, symmetric and orthogonal transformations.Students in the masters program take at least eight graduate courses from the list of approved courses numbered 500 and above, including at least one each in applied algebra, applied analysis, probability and statistics, and numerical methods.With permission of the Graduate Group Chair, certain courses with a 400-number may be counted toward the course requirement for the Masters degree.


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