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Course Criteria
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1.00 Credits
This courses intends to deepen and develop current elementary teachers' content and pedagogical content knowledge for teaching mathematics. The specific mathematical concepts addressed are PSSA Standard 2.1 Numbers, Number Systems and Number Relationships; 2.3 Measurement and Estimation; 2.5 Mathematical Problem Solving and Communication; 2.6 Statistics and Data Analysis; and 2.9 Geometry. The vehicle through which we will understand these topics is observing children's thinking and how they make sense of mathematics. These observations will be made through reading cases, observing videocases, and reflecting on your own classroom experiences. This graduate course is currently only open to teachers participating in the MATHPRO grant.
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1.00 Credits
Topological spaces, connectedness, compactness, continuity, separation, and countability axioms. Metric, product, function, and uniform spaces.
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1.00 Credits
Historical and axiomatic foundations of geometry. Euclidean and non-Euclidean geometries.
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1.00 Credits
Mathematics for physicists will be studied in this course. The motivation is drawn from physics, but it is designed to be of interest to students of both disciplines. Prerequisite: permission of the instructor.
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1.00 Credits
Adjacency, connectedness, trees, directed graphs, circuits, network flow, and extensive applications.
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1.00 Credits
Floating point arithmetic, development of computational algorithms and error estimates for root approximation, interpolation and approximation by polynomials, numerical differentiation and integration, cubic splines, least-squares, linear systems, lab component. Prerequisite: permission of the instructor.
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0.00 Credits
Required laboratory for MATH 643 Numerical Analysis.
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1.00 Credits
Systems of linear equations, determinants, vector spaces, canonical forms for linear transformations and matrices, bilinear forms, inner product spaces, applications to such other areas as geometry, differential equations, linear programming. Prerequisite: permission of the instructor.
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1.00 Credits
Advanced topics in group theory including solvable groups, field theory, Galois theory.
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1.00 Credits
Techniques drawn from partial differential equations, transform methods, Fourier and complex analysis, and variational calculus.
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