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Axiomatic, analytic, transformational, and algebraic approaches to geometry will be used. The relationship between Euclidean geometry, the geometry of complex numbers, and trigonometry might be emphasised. Topics embrace internal product spaces, norms, self adjoint and regular operators, orthogonal and unitary operators, orthogonal projections and the spectral theorem, bilinear and quadratic types, generalized eigenvectors, and Jordan canonical form. Properties of two- and three-dimensional shapes, rigid motion transformations, similarity, spatial reasoning, and the process and methods of measurement. Class activities provoke investigations of underlying mathematical construction within the exploration of shape and area. Emphasis is on the reason of the mathematical thought course of.
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